Temporal relationship between dancer’s body movements and music beats in classical ballet

Abstract

Musicality is one of the most essential aspects of dance performance: Dancers control their bodies to the music, and audiences appreciate dances beautifully harmonized with music. The present study explores the physical reality of the dance musicality from the perspective of synchronization between music beats and body movements. Specifically, we investigated the temporal relationship between dancer’s body movements and metronome beats when a dancer performed four basic classical ballet movements (i.e., changement, passé, jeté, and tendu) to the metronome. We measured body movements of 10 ballet dancers using an optical motion capture system and force plates, and analyzed what movement reference points of dancer’s body motion (e.g., movement endpoints and ground reaction force peaks) occurred on or close to the beat and offbeat. Specific reference points coincided with the beat timing common to most dancers, but the different reference points were synchronized with the beat depending on the movements. These reference points were consistent with those reported in previous studies of the temporal relationship between music and body movements. Therefore, the present result suggests that humans have a set of common movement features that can serve as reference points for music-motion synchronization, and dancers select appropriate ones according to the target movements.

Introduction

Musicality is the capacity that makes it possible to perceive, appreciate and produce music^1,2; this ability is not limited to music itself but also music-related human activities including dance performance. Dance is the coordination of our movement to music and with others³ and forms a rhythmic component of human musicality⁴. The link between music and dance is so tight that their coordination can be readily perceived by observers. In the field of dance, thus, the term “musicality” often means the ability to organize the body movement in accordance with the music: Audiences are captivated by the dance performances that are beautifully harmonized with the music, and musicality is often used as a criterion for judging in dance competitions.

Therefore, the essence of dance musicality lies in the coordination between the music and the dancer’s movements. Under this premise, there seem to be at least two aspects of musicality. One is the expression of artistic content, specifically how the dancer’s body movements reflect the content of music: Gentle, flowing movements pair well with sweet music, while sharp, striking movements align with intense music. Another aspect is temporal synchronization, that is, how well the dancer’s body movements synchronize with the musical beats. The present article focuses on the latter issue.

In public dance performances such as classical ballet (as opposed to group or social dances), performers and audiences are usually separate, with the former exclusively dancing and the latter merely observing the performance (though some audiences may find themselves swaying along with the dancers). Therefore, the issue of music-dance synchronization can be discussed from both the performers’ and audiences’ viewpoints: Dancers strive to synchronize their movements with the music, while audiences perceive the synchrony through the dancers’ visual motion and the musical sound. Below, we focus on the perspective of a dancer performing a solo dance.

The ability to synchronize body movements to music is not limited to trained dancers but is common to all humans. Many studies have reported that rhythmic sound stimuli entrain periodic body movements^{5, 6, 7, 8, 9, 10, 11–12}. The feeling of the urge to move in response to music, known as “groove,”⁵ is considered the entrainment of our motor system to the rhythmic structure of music. Even newborns can detect a musical beat¹³. Infants hearing music produce spontaneous rhythmic movements during their first year^{14, 15–16}although the ability to entrain these movements reliably to a beat takes several years to develop^{16, 17, 18, 19, 20–21}. The finding that the capacity to organize body movements to music is not innate but develops over time suggests that dance musicality depends on individuals and, consequently, influences the aesthetic appeal of dancers’ performances.

Body movements in a dance performance consist of various primitive actions, such as vertical leg movements and rotational arm movements. When dancing to music, a dancer consciously performs such actions to ensure that their timing, or the timing of the perceptual events accompanying them, matches the musical beats. Therefore, the synchrony between music and dance is presumably based on the dancer’s subjective judgment of the temporal relationship between action-related perception and music-beat perception. The present study aims to examine this relationship by means of movement analysis.

Here, it is crucial to recognize that externally observable body state (i.e., kinematic/biomechanical variables) and conscious body perception (i.e., perceptual measure) are dissociable. Humans often have an inaccurate awareness of their body posture and movements^22,23 and this discrepancy highlights the need for caution when interpreting motion analysis data. Nevertheless, our sensory system continuously collects information about the kinematic states of our body outside of conscious awareness, and this unconsciously processed sensory data plays a crucial role in guiding motor control. Moreover, certain kinematic features, such as movement endpoints, appear to be perceptually salient, and these salient features likely serve as reference points for perceiving the timing. Therefore, reference points extracted through movement analysis are likely to correlate with the perceptual cues for movement timing.

So far, many studies have been conducted to reveal the body movement of ballet dancers. However, most such studies focused on the biomechanical properties of dancers: They focused mainly on the physical and biomechanical mechanisms of dancers’ movements^{24, 25, 26, 27, 28–29} the difference between experts and novices^{30, 31, 32, 33–34} and the physical stresses which are potential causes of dancers’ injury^{35, 36–37}. Some other studies focused on the relationship between perceptual measures and biomechanical variables^34,38,39. However, to our knowledge, few studies examined the temporal relationship between the dancers’ movements and music. Our previous study⁴⁰ analyzed this relationship for a physical exercise to music and revealed that the local peaks of vertical ground reaction force (GRF) and movement feature points (e.g., endpoints of arm and leg movements) occurred on or close to musical beats. This suggests the importance of somatosensory information conveying GRF peaks and movement endpoints for synchronizing body movements with music. However, it is uncertain whether the same principle applies to both self-contained physical exercise and classical ballet for public performance.

In classical ballet performances, the director primarily determines the dancers’ movements. For paired and group dance, such as pas de deux and corps de ballet, dancers must also synchronize their movements with other dancer(s). Despite these external factors, each dancer has a sense of naturally synchronizing their movements with the music beats and offbeats. In other words, dancers have their own standard timing when moving to music, and they likely make fine adjustments following the director’s instruction using their standard timing as a reference. Therefore, in the present study, we first identify potential movement features that could serve as reference points and then examine the temporal relationship between such feature points and music beats. We ask whether the reference points aligned with music beats are consistent with the feature points previously identified as synchronized with auditory stimuli in other human movements. Such consistency implies that humans may share a set of common features that can serve as reference points for synchronizing body movement with music beats.

In the present study, we picked up four standard movements of classical ballet dance as experimental subjects: Two (changement and passé) are vertical leg/body movements and the others (jeté and tendu) are left-right leg movements. We utilized a metronome to produce periodic beats, thereby eliminating the influence of artistic content in music and focusing on the effect of beat timing. Participants were asked to perform these movements in sync with the metronome sounds, and we analyzed the temporal relationship between movement feature points and metronome beats for each movement.

Methods

Participants

Ten female dancers aged 20 to 30 participated in the experiment. Among them, two dancers (ID: #3 and #4) were professional dancers, aged 29 to 30, actively performing with Japanese professional ballet companies. The remaining participants were undergraduate and graduate students and graduates from the Performance Arts Course of Ochanomizu University, all amateur dancers with 14–21 years of experience. The experiment was approved by the Institutional Review Board for Biological and Medical Research of Ochanomizu University (#2023-5, 7/10/2023 and #2023-16, 1/15/2024). It was in accordance with the ethical standards in the Declaration of Helsinki. We obtained written informed consent from all participants. The data analysis study conducted at the University of Electro-Communications was also approved by the Institutional Review Board for Human Subjects Research (H23048, 6/19/2024) of the University of Electro-Communications.

Apparatus

We measured the dancers’ body movement using an optical motion capture system (Vicon Nexus; Vicon Motion Systems Ltd., Oxford, UK, with 8 cameras) at a frame rate of 250 Hz. Retroreflective markers were attached to 35 body sites using a plug-in full-body gait model. Ground reaction force (GRF) was measured using a force plate (Kistler Instruments, Hampshire, UK) at a sampling rate of 1 kHz via external analog inputs to the Vicon system. The force plate was covered with a linoleum sheet to create conditions like those in a dance studio. The metronome sound was generated using free audio editing software (Audacity, ver.3.1.0) on a Windows 10 PC. It was then played through a monoaural speaker of a compact sound player (TY-ANX1, Toshiba, Japan) and recorded via an analog input of the Vicon system at a sampling rate of 1 kHz. Vicon Nexus software (version 1.8.5; Vicon Motion Systems, Oxford, UK) was used to collect and process data from the motion capture system, as well as the analog force and sound signals.

Task and procedure

The participant’s task was to perform the specified ballet movements in sync with the metronome’s rhythm. The target movements were changement, passé, jeté (outward), and tendu (outward). Clad in leotards and pointe shoes, the participants executed these movements in an open space without the support of a ballet barre. The metronome’s tempo was set to 60 beat per minute (bpm) for passé, jeté, and tendu, and 80 bpm for changement. Participants were instructed to dance fluidly and intuitively to the metronome’s beat without explicit guidance on the timing of their movements. Participants repeated the movements at least 16 times for changement and 24 times for the other movements.

For readers unfamiliar with classical ballet, we briefly describe these movements (see Fig. 1 for illustrations).

Fig. 1 [Images not available. See PDF.]

Explanatory illustration of four target movements. Each panel illustrates the sequence of dancer’s body movements of a target movement within a single cycle. Participants performed these movements to the metronome. Symbols (capital letters) indicate the movement feature points whose timing we examined in relation to the metronome beats. The meaning of the symbols is summarized in Table 1.

Table 1. Movement reference points for four target movements.

Symbol	Objective criterion	Physical event
Changement
GC	GRF onset	Feet contact the ground
GP1	GRF’s first peak	Feet kick the ground to support the body
BB	C7’s bottom point	Body is at the bottom
GP2	GRF’s second peak	Feet kick the ground to jump up
GL	GRF offset	Feet leave the ground
BT	C7’s top point	Body is at the top
Passé
BB	C7’s bottom point	Body is at the bottom
VBU	C7’s peak upward velocity	Body moves up the fastest
BR	Offset of C7’s upward velocity	Body has ridden on tiptoe
VFU	Ankle’s peak upward velocity	Working toot goes up fastest
FT	Ankle’s highest point	Working foot is at the top
VFD	Ankle’s peak downward velocity	Working foot goes down fastest
BF	Onset of C7’s downward velocity	Body starts to come down from the tiptoe
VBD	C7’s peak downward velocity	Body moves down the fastest
Jeté
FLS	Onset of ankle’s velocity	Working foot starts to move rightward (outwards)
VR	Ankle’s peak rightward velocity	Working foot moves rightward (outwards) fastest
FR	Ankle’s rightmost point	Working foot reaches the rightmost position
VL	Ankle’s peak leftward velocity	Working foot moves leftward (inwards) fastest
FLE	Offset of ankle’s velocity	Working foot returns to the starting position
Tendu
FRS	Onset of toe’s velocity	Working foot starts to move leftward (inwards)
VL	Toe’s peak leftward velocity	Working foot moves leftward fastest
FL	Toe’s leftmost point	Working foot is in the leftmost position
VR	Toe’s peak rightward velocity	Working foot moves rightward fastest
FRE	Offset of toe’s velocity	Working foot returned to the rightmost position

1. Changement: The dancer starts in the fifth position (with the feet parallel, the heel of the front foot touching the big toe of the back foot, and the heel of the back foot touching the little toe of the front foot), then slightly bends her knees and jumps straight up. She switches the positions of her feet while in the air and lands back in the fifth position with the front and back feet reversed.

2. Passé: The dancer slides one foot (the working foot) up from the fifth position, passing it in front of the knee of the other leg (the supporting leg). At the same time, she stands on the tiptoe of the supporting leg. She then slides the working foot down along the supporting leg and returns to the fifth position with the working leg behind the supporting leg. She repeats this movement, alternating the working foot.

3. Jeté: The dancer starts in the first position (toes turned out and heels together), then extends her right leg straight out to the side and lifts it into the air. She brings the right leg back inward, returning to the initial position. The dancer can synchronize either her outward or inward movement to the beat. In our experiment, we specifically instructed her to align her outward movement with the beat.

4. Tendu: The dancer starts in the first position and gradually extends the right leg out to the side while keeping the toe in contact with the floor. She then returns to the initial position by moving the right leg back, maintaining extension throughout the movement. As with jeté, the dancer were asked to align her outward movement with the beat.

Data analysis

Marker position data were pre-processed using Vicon Nexus software, with further analysis conducted in MATLAB (Mathworks, USA). Positional data are expressed in xyz coordinates, where the x-axis represents the front-back direction (positive towards the back), the y-axis represents the left-right direction (positive towards the right), and the z-axis represents the up-down direction (positive upwards).

Motion data were filtered with a 4th-order zero-phase low-pass filter (cutoff frequency: 50 Hz), and velocity were calculated using numerical derivatives. GRF data were filtered with a 4th-order zero-phase low-pass filter (cutoff frequency: 400 Hz). We analyzed the vertical component of GRF to identify key temporal events. Specifically, we extracted three critical time points: GRF offset (i.e., the moment when the feet left the floor), GRF onset (i.e., the moment when the feet landed on the floor), and GRF peak (i.e., the time at which the vertical GRF reached its local maximum). For sound signal analysis, we identified beat timings by detecting local maxima in the rectified sound signal.

We discarded the first several cycles of motion data and used the subsequent 10 cycles of data for further analysis because the body movements were unstable at the beginning of a trial. We defined several “movement reference points” (i.e., distinctive kinematic events that can be used to align body movements with the metronome beats) for each movement. We analyzed the temporal relationship between these reference points and the beats and offbeats for every cycle. We employed a custom-designed MATLAB program to identify these points in the movement trajectory. However, to ensure accuracy, we manually reviewed the results and applied manual corrections when the algorithm failed to detect points correctly.

Table 1 summarizes the reference points used in the following analysis (also indicated in Fig. 1). The rationale for their selection is explained below.

1. Changement: This movement is primarily vertical jumping, and thus, her vertical motion and the dynamic (kinetic) interaction between her feet and the floor are presumably crucial for giving sensory cues for synchronization. Therefore, we concentrated our analysis on the behaviors of vertical body motion and vertical GRF. We selected the height of the neck (C7: the seventh cervical vertebra) as a representative variable of body movement, as this anatomical landmark provides a reliable indicator of overall vertical displacement of the body’s center of mass during the movement. Specifically, we extracted the top and bottom points of C7 (BT and BB), which could be identified as the local maximum and minimum of the C7 marker’s z coordinate. Regarding the vertical GRF, we selected its onset (corresponding to the floor contact: GC), offset (corresponding to the floor leaving: GL), and two local peaks (GP1 and GP2) which corresponded to the impact forces of landing and takeoff (see Fig. 2 for a sample profile of GRF).

2. Passé: We focused on the vertical movement of legs and feet, as the alternating leg lifts are the characteristic of this movement. Specifically, we selected the highest and lowest points (i.e., top and bottom) of the working foot’s ankle (FT and FB), along with the points of its maximal upward and downward velocities (VFU and VFD). We also examined the vertical position of C7 as the dancer elevates her entire body by rising onto the tiptoe of the supporting foot, synchronizing this action with the movement of the working foot. We identified the lowest point of C7 (BB), the end of the upward movement (corresponding to the full rising onto the tiptoe: BR), and the start of the downward movement (corresponding to the initiation of the fall from the tiptoe: BF). We note that BB (the lowest point of C7) and FB (the lowest point of the working foot) nearly coincided, as will be shown later (Fig. 3). Therefore, we will exclusively refer to BB, omitting separate references to FB.

3. Jeté: This movement primarily involves lateral leg movements, and we selected the marker position on the right ankle as the representative variable of foot movement. Specifically, we chose the point at which the ankle starts its rightward movement (FLS), the point at which the ankle returns to the starting position (FLE), and the point at which the ankle reaches the rightmost position (FR). In addition, we extracted the points of maximal outward (rightward) and inward (leftward) velocities of the right ankle (VR and VL, respectively).

4. Tendu: Although both jeté and tendu involve lateral leg movements, the foot remains at its rightmost position for a while in tendu, whereas in jeté, the foot briefly touches the rightmost position. Thus, we chose different reference points between these movements. Specifically, we extracted the point at which the toe starts to move inward from the rightmost position (FRS), the point at which the toe returned to the rightmost position (FRE), and its leftmost point (FL). We also extracted the points of maximal outward (rightward) and inward (leftward) velocities of the right ankle (VR and VL, respectively). Note that the toe’s marker position was chosen as a representative variable rather than the ankle’s marker because it provided reference points most stably and reliably.

Fig. 2 [Images not available. See PDF.]

Temporal behaviors of C7 height and vertical GRF for changement. The top and bottom panels show C7’s vertical position and vertical GRF over a movement cycle for two representative participants, respectively. The horizontal axis represents the time relative to the metronome beat. Data from 10 cycles of motion are overlaid in these plots. The colored dots indicate the movement feature (or reference) points. Temporal profiles of C7 and GRF were maintained over cycles, meaning that the movements of the two participants were both in sync with the metronome, but their timings were apparently different from each other. GP1 was aligned closely with the beat for Participant #3, whilst GL occurred just before the beat and GP1 was aligned closely with the offbeat for Participant #9.

Fig. 3 [Images not available. See PDF.]

Temporal distributions of movement reference points for changement. The temporal distributions of six movement reference points are shown for individual participants. The horizontal axis represents the time relative to the metronome beat. Small colored dots indicate the points in individual cycles, and large colored circles indicate their medians. Participants are sorted in order of the relative timing of BT. GC and GP1 are located close to the metronome timing for 7 out of 9 participants, meaning that most dancers landed on the floor in sync with the metronome beats.

Results

Changement

We successfully obtained data from 9 out of 10 participants. Data from Participant #4 were corrupted and thus unusable. Figure 2 depicts the movement trajectory of C7 and vertical GRF for two representative participants (#3 and #9). The horizontal axis represents time, with the origin indicating the metronome beat timing and its width corresponding to a full movement cycle. Therefore, the boundaries of the horizontal axis correspond to the offbeat, marking the halfway point in the movement cycle. Data from 10 cycles of actions are superimposed in this plot, with six movement reference points marked by colored dots.

Two points should be noted. First, C7’s vertical trajectories formed symmetric smooth curves resembling sinusoidal waves: C7’s height maintained a smooth change, with minimal disruption from floor landings and jump-offs. This suggests that only the extreme points serve as movement reference points for vertical body movements. Furthermore, despite minor inter-cycle variations, the C7 and GRF profiles exhibited remarkable consistency across all cycles, demonstrating that the dancers’ motion was synchronized with the metronome beats.

Second, however, the timing of the body motion differed significantly between the two participants. Specifically, GP1 is aligned closely with the beat for Participant #3, meaning that this participant gave peak GRF at landing (just after the floor contact) in sync with the beat. As for Participant #9, in contrast, GL occurred just about 100 ms before the beat, and GP1 was aligned with the offbeat, suggesting that this participant may give peak GRF at the offbeat rather than the beat.

Figure 3 summarizes the temporal distributions of the movement reference points for individual participants, where small dots represent the reference point timings in individual cycles and large filled circles indicate their medians. Participants are sorted according to the relative timing of BT. The timing of GC is located about −100–0 ms before the beat for seven participants, as seen in Participant #3. In addition, the peak GRF after landing (GP1) occurred around or just after the beat. These facts clearly show that most dancers landed close to the metronome beats. The view that floor landing is a critical reference point for these dancers is supported by the fact that the inter-participant temporal variability (i.e., range of median timing) was smallest for GC and GP1 (~ 100 ms): the median timing ranges of the other reference points (BT, BB, GPS and FL) were wider (150–200 ms).

The movement timings of the remaining participants (#2 and #9) differed significantly from this pattern. As pointed out above, GP1 was close to the boundary of the horizontal axis, meaning that she landed on the floor in sync with the offbeat; that is, her movement was in anti-phase relative to the majority of participants. This suggests that the offbeat functioned as a rhythmic marker for her, similar to how the beat serves as a reference point for the majority. As for Participant #2, in contrast, GP2 occurred ~ 50 ms before the beat, suggesting that she kicked the floor in sync with the beat to jump up. Here, we should note that the timings of the C7’s top and bottom points (BT and BB) were distant from both the beat and offbeat, indicating that the extremes (or turning points) of vertical body movement did not align with the rhythmic markers. Therefore, the timing of changement appears to be driven by somatosensory (and possibly auditory) cues related to the dancers’ interaction with the floor (e.g., landing and kicking) rather than the vertical body movement.

We see considerable inter-trial variations in the precise timing of motor reference points, common to all participants: Their ranges were about 50–100 ms, which was wider than the temporal variation observed in finger tapping (for example, Repp⁴¹ showed that the standard deviation of tap-tone asynchrony in key tapping was ~ 10 ms for musicians and ~ 15 ms for college students). We will analyze more detailed characteristics of temporal variations of the movement reference points, below.

In sum, most dancers landed on the floor in sync with the metronome beat in changement, suggesting that perceptual cues associated with floor contact are strongly linked to the beat timing. This alignment indicates that the tactile sensation and sound caused by landing likely serve as key perceptual markers for synchronizing movement with the rhythm.

Passé

We successfully obtained data from all participants. Figure 4 (a) shows the temporal behaviors of C7 height and foot height for one participant (#9), where the foot height is given by the z-coordinate of the ankle of the working leg. Eight movement reference points are indicated by dots of different colors. Two points should be noted. First, the foot height varied continuously and smoothly throughout the cycle while the C7 height remained elevated (that is, the dancer stood on her tiptoe) for more than half of a cycle. The C7 position only transiently lowered in accordance with the downward movement of the working leg. Specifically, the bottom of C7 movement (BB) coincided with the bottom of foot movement (FB). In addition, BF and VFD were close to each other, and BR and VFU were also close to each other, indicating that the vertical body and leg movements were well coordinated and synchronized. Second, VBD and BB (= FB) almost agreed with the metronome beat, and FT was close to the offbeat timing. This suggests that, for this participant, the up-and-down movement of the working leg was in sync with the beat. We do not show the behavior of vertical GRF here, but we did not see any consistent feature in GRF profiles in passé.

Fig. 4 [Images not available. See PDF.]

Movement trajectories and temporal distribution of movement reference points for passé. (a) The temporal changes in C7 (top panel) and foot heights (bottom panel) in passé are depicted for one participant. Eight reference points are indicated by dots with different colors. The foot height varied continuously over the cycle while the C7 height was kept at the highest position for a time and transiently went down in sync with the foot movement. The timing of BB almost agreed with the beat, and that of FT was close to the offbeat. (b) The temporal distributions of the movement reference points are plotted for individual participants, as in Fig. 3. VBD and BB were close to the metronome beat for eight participants, while for the remaining participants, they were close to the offbeat. This suggests a strong association between the timing of endpoints of leg/foot movements with the beat and offbeat in passé.

Figure 4 (b) summarizes the temporal distributions of the movement reference points for individual participants, as in Fig. 3. For most participants, the timings of VBD and BB were closely aligned with the metronome beat, and FT was close to the offbeat though their precise timings varied considerably between the participants. The remaining participants likely moved in anti-phase to the majority of participants. The fact that one of the two professional dancers (#4) belonged to the major group whilst the other (#3) belonged to the minor group implies that either timing strategy can be valid and potentially standard within the professional dance context. Therefore, VBD and FT are the common key feature points in passé.

In sum, most dancers moved down the body and working foot to the floor around the metronome beat in passé, suggesting that floor landing is associated with the beat, as in changement. Furthermore, the foot’s highest point is associated with the offbeat, meaning that the endpoints of upward and downward leg/foot movements were both aligned with the rhythmic structure. The remaining dancers moved in anti-phase with the majority, supporting the importance of the floor landing and endpoints of leg/foot movement.

Jeté

We successfully obtained data from all participants. Figure 5 (a) illustrates the temporal behaviors of the lateral foot position (top panel) and its velocity (bottom panel) for a participant (#7). The foot position is represented by the y-coordinate of the working (i.e., right) foot’s ankle. The horizontal foot motion exhibited asymmetry in the left-right direction: The foot remained at its leftmost position for about 200 ms, and then it traced a bell-shaped trajectory as it moved back and forth in a rightward direction. In other words, while the foot paused at the left endpoint, it did not stop at the right endpoint. This pattern suggests a movement strategy where the participant anchored their foot motion on the left side before executing a fluid motion towards and away from the right side. Second, VR was closely aligned with the metronome timing, meaning that the dancers’ leg/foot moved rightwards fastest at the beat. Furthermore, VL occurred just before the offbeat. This timing pattern demonstrates that the participant’s fastest leg/foot movements were anchored to both the primary beat and the offbeat.

Fig. 5 [Images not available. See PDF.]

Movement trajectories and reference points in jeté. (a) The lateral position and velocity of the right ankle are shown for one participant. Five reference points are indicated by dots with different colors. VR almost coincided with the beat timing, and VL was slightly before the offbeat timing for this participant. (b) The temporal distributions of the reference points are plotted for individual participants. The tendency that VR and VL aligned closely with the beat and offbeat timing is consistently observed for all participants. This suggests that the peak velocity points of foot movement are associated with the beat and offbeat in jeté.

Figure 5 (b) summarizes individual participants’ temporal distributions of the movement reference points. Temporal characteristics observed in the representative participant (#7) were consistent across all participants, albeit with some individual variability. Specifically, VR occurred near the beat timing whilst VL was aligned closely with the offbeat timing. On the other hand, the timing of movement initiation and endpoints (i.e., FLS, FR, and FLE) occurred away from both beat and offbeat timing.

In sum, all dancers moved the working foot fastest rightward at the metronome beat, and the movement initiation and endpoint did not coincide with the beat timing in jeté.

Tendu

We successfully obtained data from all participants. Figure 6 (a) shows the temporal behaviors of the lateral foot position (top panel) and velocity (bottom panel) of a participant (#3), where the foot position is given by the y-coordinate of the right toe. The foot movement pattern observed in tendu contrasts with that in jeté (see Fig. 5 (a)): In tendu, the foot remained at its rightmost position for about 300 ms, and moved back and forth in a leftward (inward), drawing a bell-shaped trajectory. Second, FRE occurred around the metronome timing, meaning that the dancers’ leg returned to the rightmost position around the beat. In addition, VL occurred at the offbeat.

Fig. 6 [Images not available. See PDF.]

Movement trajectories and reference points in tendu. (a) The lateral position and velocity of the right toe are shown for one participant. Five motor reference points are indicated by colored dots. The foot remained at the rightmost point for about 300 ms (from FRE to FRS) and moved to the leftward, drawing a bell-shaped trajectory. FRE and VL almost coincided with the beat and offbeat timing, respectively. (b) The temporal distributions of the movement reference points are plotted for individual participants. The tendency that FRE and VL almost aligned with the beat and offbeat timing for seven participants, while the others (#2, #7, and #10) showed different patterns of result.

Figure 6 (b) summarizes the temporal distributions of the reference points. FRE was closely aligned with the metronome beat for all participants, indicating that the endpoint of rightward movement is anchored to the beat. However, it should be noted that three Participants (#2, #7, and #10; all amateur dancers) did not hold the foot at the rightmost position: The interval between FRE and FRS was notably brief, lasting only 50–150 ms, significantly shorter than that of the majority of participants. For these participants, moreover, VL was away from the offbeat timing, suggesting that they employed a fundamentally different strategy for performing tendu to the metronome.

In sum, the endpoint of rightward foot movement aligned with the metronome beat in tendu, though some dancers exhibited a different temporal relationship.

Temporal variation of movement reference point

If a specific reference point is tightly linked to the metronome beat, it is expected that such a reference point shows less temporal variability than other reference points. In other words, the temporal variability of a reference point can indicate how consistently a dancer aligns a specific reference point with the beat.

To test this conjecture, we calculated the interquartile ranges (IQR) of the timing of movement reference points as a measure of temporal variability. Note that we also calculated the mean absolute deviation (MAD) as another measure of variability and obtained a similar result. Figure 7 summarizes the IQRs of all reference points for four movements. Each plot indicates IQRs for individual participants, with solid lines representing the “majority participants” (i.e., those who showed common tendency) and broken lines representing the “minority participants” (i.e., those who did not show common tendency). Red thick plots show the inter-participant medians of the majority groups. Symbols in red and blue indicate the reference points that aligned closely with the beat and offbeat timings, respectively.

Fig. 7 [Images not available. See PDF.]

Temporal variabilities of movement reference points. IQRs of the timing of movement reference points are plotted for four target movements. Each line indicates IQRs of different reference points for one participant, where solid and broken lines represent the results for the participants who shared the common tendency (i.e., majority group) and the other participants, respectively. Red thick curves show the inter-participant medians of the majority group. Symbols in red and blue colors indicated the reference points close to the primary beat and offbeat, respectively. The median IQRs had smaller values at the reference points that occurred near the beat or offbeat for passé, jeté and tendu, while for changement, they remained nearly uniform across all reference points.

For changement, the median IQR forms an almost flat curve though individual data show quite different profiles: It seems difficult to draw any definitive conclusions from this data. For passé, the median IQR shows remarkable drops at FT and VBD. This indicates that the timings of the reference points around the primary beat (VBD) and offbeat (FT) were the most stable, supporting our conjecture. As for jeté, the median IQR showed slight drops at VR and VL, which occurred near the primary beat and offbeat, respectively. This again supports our conjecture. For tendu, finally, the median IQR was smallest at FRE, which aligned with the primary beat, though no drop can be found at VL. We conducted statistical tests to evaluate the effect of reference points on IQR for the majority group. Kruskal-Wallis tests (i.e., non-parametric ANOVA) indicated that the reference points had no statistically significant effect for all movements (F(5, 36) = 4.27, p = 0.5114 for changement, F(7, 56) = 10.15, p = 0.1800 for passé, F(4, 45) = 2.08, p = 0.7203 for jeté, and F(4, 45) = 1.58 p = 0.8122 for tendu). The lack of a significant effect can be attributed to substantial individual differences which can be found in Fig. 7, but a larger dataset would likely reveal significant effects, particularly for passé, juté and tendu, given the apparent trends observed in the figure. However, detecting a significant effect for changement may be challenging due to the inherent difficulty in executing jumping movements consistently which leads to greater variability in timing of each reference point.

Therefore, we found a tendency that the reference points with minimal IQRs generally agreed with those in sync with the beat or offbeat, although this effect was not statistically significant. This result is at least consistent with our conjecture that classical ballet dancers aim to synchronize a specific reference point to the metronome beat or offbeat. Future studies should replicate this tendency with a larger participant pool to validate the result.

Discussion

The present study investigated the temporal relationship between the ballet dancers’ body movements and the metronome beats when dancers performed four basic movements of classical ballet to the metronome, with the aim of exploring the foundations underlying the dancers’ musicality in classical ballet. We defined several movement reference points for each movement and analyzed the time difference between these reference points and the metronome beats. For each movement, specific movement reference points aligned with the beat or offbeat and this relationship was shared by most participants. We also showed that the temporal variability of the reference point was the smallest for those that occurred at the beat or offbeat. On the other hand, some participants (including one professional dancer) showed relationships different from that of most participants, typically in anti-phase with those of the majority of participants. This implies that the offbeat may function as a rhythmic marker akin to the beat for dancers.

Sensory events related to motor actions are provided by somatosensory information and other sensory signals accompanying the actions, including visual, auditory, and vestibular information⁷. For example, when a dancer stretches out her leg, the endpoint of the leg movement is detected primarily based on somatosensory information and visual information of the leg. On the other hand, floor landing can be informed based on cutaneous information from the soles of the feet, proprioceptive information from the leg muscles, vestibular information triggered by rapid deceleration at landing, and auditory information generated by the collision between shoes and ground. Each of these multiple sensory events can serve as a cue to synchronize the body movements with music. In addition, prediction or anticipation of these events could be additional means to judge the timing of body motion. Actually, the observation that the offbeat serves as a rhythmic marker similar to the beat indeed supports the role of anticipation because the offbeat is not explicitly defined by the external stimuli (i.e., metronome sound). Our fundamental questions here are what sensory cues dancers rely on when dancing to music, and why these particular cues are chosen as crucial cues. Below, we review the present results from these points of view.

In changement, we found that most dancers landed on the floor just before the metronome beat, suggesting that sensory information accompanying floor landing is essential. Our previous study showed that the timing of peak vertical GRF aligned with the music beat when participants performed a physical exercise to music⁴⁰ and the present result also showed that the peak vertical GRF (GP1) occurred close to the metronome beat (Figs. 2 and 3). These findings together suggest the importance of the tactile stimulus to the soles at landing. In addition, the sound at landing presumably provides another strong cue because it is brought in the same auditory modality as the metronome sound. On the other hand, C7’s top and bottom points were far from the beat and offbeat timing, meaning that these endpoints have little significance in changement. This may be partly because the top and bottom points of body height cannot be readily detected as a distinct somatosensory event (Especially at the top position, the dancer’s body is in the air, and no tactile stimuli are provided).

In passé, the working foot touched the floor and the body reached the lowest position (BB) around the metronome beat, and the timing of the highest foot position was close to the offbeat for most dancers. In contrast, the peaks of vertical GRF did not coincide with the beat (data not shown), meaning that the tactile stimulus to the soles is unlikely to be used as a reference marker in this movement. Rather, in contrast to changement, the endpoints of upward and downward foot movements are crucial for synchronizing the body movement with the metronome beat in this movement.

For jeté, the peak velocity point of the working foot movement (VR) occurred at the metronome beat, and both movement initiation and endpoints did not align with the beat, commonly for all participants. This implies that the fastest motion point is crucial for comparing with the beats. One concern with considering this reference point as essential is that the point of fastest motion does not appear to provide distinct sensory events. Maybe, some other sensory cues or expectations may tell the fastest motion point rather than the foot velocity itself. For example, the dancer receives a horizontal GRF when she moves her leg in the lateral direction. Actually, the horizontal GRF showed slight peaks about 100 ms before the metronome beat, although these peaks were not sharp (data not shown). Therefore, we should not forget the possibility that the tactile cues from kicking the floor sideways may serve as a reference for synchronizing the leg motion with the beat.

Finally, in tendu, the endpoint of the rightward movement of the working foot coincided with the metronome beat. The movement endpoint often serves as the reference point, as in passé, and presumably, this principle also works in tendu.

Therefore, the movement reference points synchronized with the music beats and offbeats varied across different movements (specifically, the floor landing for changement, the endpoint of leg movement for passé and tendu, and the maximal velocity point for jeté). This implies that no single, universal rhythmic maker may exist for all movements in classical ballet: Multiple reference points can serve as effective cues for music-movement synchronization. However, these reference points could be summarized into the somatosensory information related to the interaction with the floor (i.e., vertical and horizontal GRF) and the movement endpoint or turning point (i.e., top, bottom or side point of the leg); both of which have been found in other human movements to music in the previous study⁴⁰. Considering the close relationship between sensory events and perceptual cues, moreover, this suggests that dancers pay attention to an appropriate reference cue from possible perceptual markers, depending on the rhythmic structure of the movement they are performing.

This issue is also related to the segmentation of body movement in dancing. As mentioned in Introduction, dance body movements consist of simple actions (i.e., segments) and dancers pay attention to specific perceptual events associated with these segments. The present result showed that movement endpoint (including floor contact in jumping action), rather than movement initiation, is the primary perceptual cue. Some previous studies also showed that visual information around the endpoints of cyclic movement were important for visuomotor coordination^{42, 43–44}. Thus, the timing of the end of the segment is likely key to achieving music-dance synchronization.

Dance performance is a form of communication between dancers and audiences where the dancer’s body serves as its medium⁴⁵ and thus, the characteristics of dance performance should be investigated from both the dancer’s and the audience’s perspectives. In the present study, we explored dance musicality from the dancer’s viewpoint and the result suggests that it is founded by human general sensory cues related to beat-dance synchronization. In the next step, we should examine the musicality from the audience’s viewpoint.

This topic is essentially the problem of synchrony perception between visual and auditory stimuli because the dancer’s body motion is provided by the visual channel while the music sound is provided by the auditory channel. Visuo-audio synchronization perception has been extensively investigated^{46, 47, 48, 49–50}. Although most conventional studies dealt with simple discrete actions whose visual and auditory timings were precisely determined, recent studies have treated more realistic problems including music performance^{51, 52, 53, 54, 55, 56, 57, 58, 59–60}. The question of how dancers’ motions appear to be in sync with the music is a specific case of this problem though we should note that it is not simple sensory issues but also related to motor issues. We should further investigate this problem using realistic dance performances as experimental subjects. Such challenges would enhance our understanding of the perceptual mechanism underlying musicality in dance performances.

Finally, the present article focuses on the synchrony between the dancer’s motion and musical beats. On the other hand, dancers often introduce temporal deviation between their motion and expected timing as a means of artistic expression: Excellent dancers skillfully manage such deviations to add artistic and emotional impressions to their dance. However, such effectiveness of temporal deviations even highlights the importance of the expected timing: If the audience cannot feel the expected timing, the artistic deviation would not serve as a means of artistic expression. Therefore, the temporal relationship between the body movements and the beats found in the present study is the fundamental basis of musicality in dance performance.

Acknowledgements

The authors would like to acknowledge the contributions of our colleagues at Ochanomizu University for their assistance with data collection. This work was supported by JSPS KAKENHI Grant Number JP22K19748.

Author contributions

T.W. analyzed the experimental data, visualized the results, and prepared the original draft. Y.T. conducted the experiment in Ochanomizu University and obtained the experimental data. M. K.-M. designed the study, acquired the funds, and critically commented on the draft. Y.S. designed the study, acquired the funds with M.K.-M., validated the data analysis, and revised the manuscript. All authors reviewed the manuscript.

Data availability

The datasets generated and/or analyzed during the current study are available in the dryad repository: https://doi.org/10.5061/dryad.dncjsxm8v.

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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