Cellists’ sound quality is shaped by their primary postural behavior

Abstract

During the last 20 years, the role of musicians’ body movements has emerged as a central question in instrument practice: Why do musicians make so many postural movements, for instance, with their torsos and heads, while playing musical instruments? The musical significance of such ancillary gestures is still an enigma and therefore remains a major pedagogical challenge, since one does not know if these movements should be considered essential embodied skills that improve musical expressivity. Although previous studies established clear connections between musicians’ body movements and musical structures (particularly for clarinet, piano or violin performances), no evidence of direct relationships between body movements and the quality of the produced timbre has ever been found. In this study, focusing on the area of bowed-string instruments, we address the problem by showing that cellists use a set of primary postural directions to develop fluid kinematic bow features (velocity, acceleration) that prevent the production of poor quality (i.e., harsh, shrill, whistling) sounds. By comparing the body-related angles between normal and posturally constrained playing situations, our results reveal that the chest rotation and vertical inclination made by cellists act as coordinative support for the kinematics of the bowing gesture. These findings support the experimental works of Alexander, especially those that showed the role of head movements with respect to the upper torso (the so-called primary control) in ensuring the smooth transmission of fine motor control in musicians all the way to the produced sound. More generally, our research highlights the importance of focusing on this fundamental postural sense to improve the quality of human activities across different domains (music, dance, sports, rehabilitation, working positions, etc.).

Full text

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
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Cellists’ sound quality is shaped
by their primary postural behavior
Jocelyn Rozé*, Mitsuko Aramaki, Richard Kronland-Martinet & Sølvi Ystad
During the last 20 years, the role of musicians’ body movements has emerged as a central question
in instrument practice: Why do musicians make so many postural movements, for instance, with
their torsos and heads, while playing musical instruments? The musical signicance of such ancillary
gestures is still an enigma and therefore remains a major pedagogical challenge, since one does
not know if these movements should be considered essential embodied skills that improve musical
expressivity. Although previous studies established clear connections between musicians’ body
movements and musical structures (particularly for clarinet, piano or violin performances), no
evidence of direct relationships between body movements and the quality of the produced timbre
has ever been found. In this study, focusing on the area of bowed-string instruments, we address the
problem by showing that cellists use a set of primary postural directions to develop uid kinematic
bow features (velocity, acceleration) that prevent the production of poor quality (i.e., harsh, shrill,
whistling) sounds. By comparing the body-related angles between normal and posturally constrained
playing situations, our results reveal that the chest rotation and vertical inclination made by cellists
act as coordinative support for the kinematics of the bowing gesture. These ndings support the
experimental works of Alexander, especially those that showed the role of head movements with
respect to the upper torso (the so-called primary control) in ensuring the smooth transmission of ne
motor control in musicians all the way to the produced sound. More generally, our research highlights
the importance of focusing on this fundamental postural sense to improve the quality of human
activities across dierent domains (music, dance, sports, rehabilitation, working positions, etc.).
Playing a musical instrument is an activity that involves complex auditory-motor interactions. Whether creating
a short sound or developing a whole phrase, musicians must continuously establish a clear relationship between
the actions aorded by their instrument and the auditory feedback resulting from their actions1–3. Research in
neuroscience has demonstrated that such an active process intricately interweaves the auditory and motor regions
of the brain as a neural substrate of cognitive representation4,5. In the case of the cello, for example, longitudi-
nal studies conducted with non-musician participants and an MRI-compatible (Magnetic Resonance Imaging)
instrument revealed that “brain plasticity” emerged as an integrative function of the neural network in auditory-
motor information processing6. Both musical actions and percepts would thus depend on a single underlying
mental representation governing both auditory encoding and motor control along the same goal-directed action.
From these perspectives of embodied music cognition, we should consider the musical expressivity produced
by instrumentalists as a link between sonic and corporeal movements and analyze their musical intentionality
through the prism of a repertoire of learned gestural primitives7,8. Research in human biomechanics has high-
lighted that such a repertoire is composed of synergies, i.e., muscular cooperation patterns aiming to attain a
given action9. A strong consequence of the synergetic mechanisms is that each voluntary action, such as moving
a bow on a string, should be accompanied by anticipatory postural adjustments called APAs10–12. Anticipation
is crucial in musical practice because of the coupling between coordination and postural balance, which implies
that the fulllment of a single goal-directed action may be encoded beforehand as a selective activation of the
musicians’ joint degrees of freedom (DOFs)13–15. In dance practice, conversely, the mirror neuron system may
decode the perceived expressiveness into ne movement structures through the same kind of grounded synergetic
processes16–18. In the domain of rehabilitation, rhythmic auditory stimuli were ecient in reducing movement
disorders and improving walking abilities in Parkinson’s disease and stroke patients19–23.
Due to the weight of teaching habits, ignorance or misunderstandings, the role of embodiment among musi-
cians has been largely underestimated, despite evidence of its importance for the development of prociency
OPEN

*email: roze@prism.cnrs.fr
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in many domains24. is underestimation is a recurrent problem in higher music education institutions that
traditionally encourage the rapid acquisition of technical skills without suciently considering the develop-
ment of musicians’ postural relations with their instruments25. Such pedagogical methods have always been
the subject of heated debates and remain controversial today because of the high rates of dropouts due to psy-
chological frustrations and musculoskeletal disorders among musicians26. Many students actually need to stop
this end-gaining process and adopt alternative methods drawn from experimental psychology27,28, particularly
the Alexander technique, which states that a well-directed primary postural control, i.e., a dynamic orientation
of the head, neck, and upper back, has many benets for coordination and musical expressivity29. Although
very ecient in practice, this assumption has never been scientically examined due to the diculty of making
accurate measurements of a musician’s primary postural control and of assessing its acoustical inuence in an
undisturbed way. In the area of bowed-string instruments, pioneer musical research analyzed sound features
with bowing machines by focusing on physical control variables such as bow force and bow velocity but without
considering the musician’s body30–33. Other studies assessed the instrumentalists’ auditory-motor mappings by
means of motion and sound synthesis techniques with an electric violin34–36. More recently, psycholinguistic
studies explored violinists’ cognitive processes by correlating perceptual adjectives of violin sounds (round, harsh,
light, mellow, dark, etc.) to physical features of the acoustic signal and haptic feedback of the instrument37–39.
Over the past two decades, we thus observed an increasing interest among the scientic community in better
understanding the signicance of musicians’ corporeal movements related to their expressive sound features. e
results revealed the importance of such “ancillary” gestures in supporting or accompanying the instrumentalists’
“eective gestures” that are directly responsible for sound production40–46. In particular, investigations of clarinet-
ists’ movements have shown that their sense of musical phrasing may be aected during ancillary impairment,
i.e., when asked to move as little as possible while keeping their natural expressive intention or when the bell
of their instrument was immobilized47. Such disembodied experimental conditions enable us to infer stable and
reproducible patterns between musicians’ nonobvious movements and their audible components.
In this study, we examined the key inuence of musicians’ primary postural directions on their sound quality.
is study is based on an experimental protocol48 that enabled us to compare the auditory-motor interactions of
highly skilled cellists between two postural conditions: a natural condition and a posturally constrained condition
in which the chest and the head were blocked by a safety race harness and a neck collar, respectively (cf “Meth-
ods” section). In the context of postural immobilization, the cellists’ timbre quality was consistently degraded
on some key notes of the more demanding passages (cf Fig.1). We supposed that this loss of expressiveness may
correspond to specic deciencies in the motor coordination of the right arm and impact the uency, i.e., the level
of precision, of the kinematic variations of the bow velocity. is assumption was inferred from the specialized
literature on cellists’ physiology: the term bow “speed” can be used to describe the degree of motor coordination
between the cellist’s body segments49; bow/string adherence, which shapes the timbre of the sound, would be
more related to bow displacement than to bow pressure because no sound can be produced by only pressing the
bow on a string without any movement50. We also built our experimental design on the assumptions provided by
motor theories of perception51–53, that predict complementary relationships between nonverbal “gesticulations”
in the case of speech and ancillary gestures in the case of music54,55. A psycholinguistic protocol actually revealed
that inhibitions of nonverbal gestures caused speech to become much more laborious and tense, altering both
intonation and expressiveness of the message56. is kind of connection was hypothesized in the music area
through the existence of sonic-gestural objects, i.e., mental constructs in which auditory and motion elements
co-occur both in the minds of the performer and the listener57. Such motor imagery of the musical experience
would contain dyadic properties likely to activate linkages between the structure of the written score and esthetic
Figure1. e musical passage and note investigated for this study. Spectrograms correspond to examples of the
acoustic signal of an E4 note (the rst one of this score sequence) played by the same cellist with good timbre
quality (round) in the normal situation [N] and poor timbre quality (harsh) in the posturally-constrained
situation [SCH] (Static Chest and Head).
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concepts of the perceived sound58,59. According to this model, features that characterize the produced sounds
may reveal the morphology of moving sonic shapes related to the kinematic displacements of the cellists.
Here, we chose to analyze cello sounds, commonly judged as poor or “harsh” in classical music, in terms of
incorrect moving sonic forms60. In practice, this means that the acoustic signal variations analyzed within a harsh
cello note may be expected to correlate with unsuitable bow velocity patterns, potentially induced from erroneous
chest or head directions. Such sonic movements can be highlighted by crossing advanced methodological aspects
of functional anatomy and acoustic processing (cf “Methods” section). Actually, movement scientists consider
movement coordination the result of an organized motor activity, which can be divided into several elementary
actions, also called functional units61. Similarly, psychoacousticians represent instrumental timbre within a per-
ceptual space of several dimensions that are oen related to temporal and spectral sound facets62,63. As cellists
continuously modulate their gestures while playing, we may thus suppose that they use specic functional motion
units to shape particular features of their sound production. is assumption guided us to design a statistical
framework and to perform functional comparisons of the cellists’ kinematic and acoustic features between the
normal and constrained conditions (cf Fig.2b). e conception of this approach was inspired by research in the
medical and biological engineering elds that provides ecient methods for comparing human motion patterns
over time and for quantitatively emphasizing pathological deviations from a reference control group64–67. e
results of those studies demonstrate that functional data analysis (FDA)68 and especially functional principal
component analysis (FPCA)69,70 have better discriminatory power than the classical PCA multivariate approach71.
FPCA is an emerging modern technique that extracts the principal modes (PCs) of a set of continuous waveforms
and quanties their dierences across subjects as temporal deviations from the mean curve72. e technique has
proven valuable for modeling simple motor behaviors73–75 or biomechanics of complex sport movements76,77,
and in analyzing coarticulation patterns of musicians78–81 or spontaneous movement responses to music54,82.
In this study, we carried out functional PCA to determine the dominant components of the cellists’ audio-
motor functional units and to assess their degradation on both the motion and the acoustic sides. e cellists’
bow velocity variations were dened as the main goal-directed actions, and the functional units set up to reach
this goal were dened as the linear combinations of joint-related angular time series (cf Table1). e acoustic
Figure2. (a) Kinematic model of the cellists’ trunk and right arm bowing presented at rest (frontal view). is
inertial system is composed of six key joints modeled as three single axes rotational joints in the Cardan/Euler
angle representation {roll (
ψn
), pitch (
θn
), yaw (
φn
)} where
n∈[1...6]
is the key joint number. (b) Statistical
framework illustrated for a given anatomic variable of the kinematic model. is framework is based on
functional principal component analyses (cf “Methods” section) and extracts two principal modes of variation
of the cellists’ behavior, which are referred to as major mode and minor mode in the text. e eects of each
mode are highlighted as functional deviations of the average time series between the normal (curves of blue
circles) and the constrained situation (curves of red crosses).
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variations were modeled by means of the descriptors highlighted in our previous work48 for characterizing the
perceived harsh phenomenon (cf Table2).
Table 1. Anatomic variables described as joint-related Euler angles {
ψ,θ,φ
} of the segmental kinematics. e
sign of each angle depends on its rotational direction that can be established from the resting kinematic model
(cf Fig.1a) by following the right-hand rule.
Euler angle Relation to segmental kinematics
Postural angles
root (1)

ψ1
Abdomen torsion To the le [
0◦
...
+90◦
]
To the right [
0◦
...
−90◦
]

θ1
Abdomen vertical inclination Forward [
0◦
...
−90◦
]
Backward [
0◦
...
+90◦
]

φ1
Abdomen lateral swing To the le [
0◦
...
−90◦
]
To the right [
0◦
...
+90◦
]
midtorso (2)

ψ2
Chest torsion To the le [
0◦
...
+90◦
]
To the right [
0◦
...
−90◦
]

θ2
Chest vertical inclination Forward [
0◦
...
−90◦
]
Backward [
0◦
...
+90◦
]

φ2
Chest lateral swing To the le [
0◦
...
−90◦
]
To the right [
0◦
...
+90◦
]
neck (3)

ψ3
Head torsion To the le [
0◦
...
+90◦
]
To the right [
0◦
...
−90◦
]

θ3
Head vertical inclination Forward [
0◦
...
−90◦
]
Backward [
0◦
...
+90◦
]

φ3
Head lateral swing To the le [
0◦
...
−90◦
]
To the right [
0◦
...
+90◦
]
ψ12 =ψ1+ψ2
Torso rotation To the le [
0◦
...
+90◦
]
To the right [
0◦
...
−90◦
]
Instrumental angles
rshoulder (4)

ψ4
Upper arm rotation External [
0◦
...
+90◦
]
Internal [
0◦
...
−90◦
]

θ4
Upper arm abduction Abduction [
0◦
...
+90◦
]
Adduction [
0◦
...
−90◦
]

φ4
Upper arm anteversion Antepulsion [
0◦
...
+90◦
]
Retropulsion [
0◦
...
−90◦
]
relbow (5)

ψ5
Forearm rotation Supination [
0◦
...
+90◦
]
Pronation [
0◦
...
−90◦
]

φ5
Forearm extension Full exion [
0◦
]
Full extension [
+180◦
]
rwrist (6)

ψ6
Hand rotation Supination [+]
Pronation [−]

θ6
Hand abduction Ulnar abduction [
0◦
...
+90◦
]
Radial abduction [
0◦
...
−90◦
]

φ6
Hand exion Palmar exion [
0◦
...
+90◦
]
Dorsal extension [
0◦
...
−90◦
]
ψ
56
=ψ
5
+ψ6
Forearm rotation Supination [
0◦
...
+90◦
]
Pronation [
0◦
...
−90◦
]
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Results
By applying the steps of our analysis framework, which are thoroughly described in “Methods” section, we could
infer two main functional auditory-motor linkages responsible for the perceived quality of cello sounds. In this
paper, these two principal modes of variation are referred to as the major mode and minor mode. Each func-
tional mode can be considered the coupling between an eigenposture65 and an eigensonicform88: an eigenposture
describes a specic aggregate of postural and instrumental joint motions, and an eigensonicform describes a
specic interaction of bow kinematics and acoustic features. FPCA analyses (cf Eq.3) revealed that the major
and minor eigenpostures captured approximately 95% of the total data variance, i.e., 70% for FPC1 and 25%
for FPC2. Similarly, the major and minor eigensonicforms captured approximately 75% of the total data vari-
ance aer smoothing, i.e., 60% for FPC1 and 15% for FPC2. Such percentages of the largest explained variance
were sucient to reveal the two most prominent timbre features and establish correlations with the kinematic
behavior variations. Here, we present this eigenfunction structure with two gures describing the major mode
(Fig.3) and the minor mode (Fig.4). For the sake of clarity, these gures only highlight the functional variables
that presented signicantly dierent behaviors between the normal and constrained situations.
Major mode of variations. As observed in Fig.3, the rst (or major) functional unit corresponds to global
amplitude variations at all the dierent stages of the sound-gesture chain. is was particularly salient at the
physical stage, which reects the “eective” sound-producing gesture (cf Fig.3c), where the bow velocity globally
decreased in the constrained condition (Bowvel:
t(7)=2.07
).
At the postural stage of the trunk motor chain (cf Fig.3a), which reects the ancillary gestures, this bowing
alteration eect appeared to be associated with marked amplitude reductions of the natural chest torsion (
ψ12
:
t(7)=8.37∗∗∗
) and head torsion (
ψ3
:
t(7)=−3.10∗
). e analyses of the normal condition in the graph actually
revealed surprising symmetrical evolutions towards zero for these two movements, with the chest torsion moving
from the le and the head torsion from the right, while these tendencies were lost in the constrained condition.
In accordance with Mantel49, we suggest that such a grounded tendency characterizes the need for a strong
helicoidal energy transfer along the spine during the bow pulling movements to ensure optimal bow velocity
amplitudes. e constrained condition also clearly aected the other degrees of freedom of the head, i.e., head
elevation (
θ3
:
t(7)=−3.42∗
) and head lateral swing (
φ3
:
t(7)=2.38∗
), for which the amplitude variations were
considerably smaller than their natural counterparts. Interestingly, these two analyses of the head under natural
conditions in the graph revealed that the bouncing trend during the bow pulling movement, up-and-down and
right-and-le was absorbed by the constraint.
At the instrumental stage (cf Fig.3b), which reects the interaction between eective and ancillary gestures,
the major eect of postural impairments resulted in consistent amplitude alterations of the shoulder articulation,
i.e., a loss of upper arm abduction (
θ4
:
t(7)=4.40∗∗
) and external rotation (
ψ4
:
t(7)=3.40∗
). is insucient
upper arm external rotation also appeared to be symmetrically coupled to a loss of forearm pronation (
ψ56
:
t(7)=−2.32
). us, in the constrained condition, the major mode reects a systematic locking position of the
whole right arm through unsuitably combined tendencies of upper arm internal rotations and forearm supina-
tions that aected the bow velocity.
e results of multivariate regression on the major FPC scores of these anatomical angles was signicant
(
R2=0.90∗∗
,
R2
adjusted
=0.77
∗∗
, cf regression graph of Fig.3e). It was therefore possible to infer a linear rela-
tionship predicting the global bow velocity amplitudes based on the set of anatomic angles selected by the rst
functional unit. More importantly, an additional stepwise regression extracted a combination of two angular
degrees of freedom that explained the global variations of the bow velocity:
is simple predictive relation highlights a major mechanism of the cellist’s coordination, in which the coupling
between the chest torsion (ancillary gesture) and the external rotation of the right arm (instrumental gesture)
guaranteed suitable bow velocity amplitudes. More details on this major coordination mode (or eigenposture)
could be obtained by computing correlations between the FPC scores. Interestingly, these results revealed that
chest torsion was the coordinative support for bow velocity amplitudes (
rBowvel
ψ12
=0.55
∗
). Further cross-correla-
tions of the major angle scores revealed a chain of three coupling systems, which characterizes the coordination
transfer within the major mode: (1) the system {
ψ12|ψ3|θ3
} showed the abovementioned symmetry of the chest/
head torsions (
rψ
3
ψ12
=−0.61
∗
); (2) the system {
ψ3|θ3|φ3|ψ4
} showed the importance of all the degrees of free-
dom of the head, especially of the head torsion, for activating the external rotation of the arm (
rψ
4
ψ3
=−0.71
∗∗
);
and (3) the system {
θ3|θ4
} showed that up-and-down head bouncing contributed to the amplitude of shoulder
(1)
Bowvel =0.75 ×ψ2−0.52 ×ψ4
Table 2. Acoustic descriptors used in the study and their correlation to the perceived harshness phenomenon.
Name Description Correlation to harshness
HSV Harmonic Spectral Variation83 Increase of harmonic asynchrony
ATS Attack Time Slope84 Slower attack slope of the temporal envelope
MFCCratio Ratio between MFCC coecients c2 and c185 Emergence of formantic area
SC Harmonic Spectral Centroid86 Increase of spectral centroid
TRIratio Ratio between tristimulus tr3 and tr1 + tr287 Spectral energy transfer towards high-frequency components
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abduction (
rθ
4
θ3
=−0.53
∗
). No signicant cross-correlations were obtained with the angle of prono-supination
(
ψ56
), which conrms that global bow velocity amplitudes were not controlled by the forearm but by the upper
arm at the shoulder level through the helicoidal work of the trunk.
From the acoustical point of view (cf Fig.3d), the major mode revealed that three of the ve sound signal
descriptors characterized the time-dependent perceptual dierences between round and harsh cello sounds in
terms of global amplitude variations. e graph analyses between normal and constrained situations revealed
energy decreases within the temporal envelope (Rms:
t(7)=3.04∗
), energy increases on the upper partials of the
spectral envelope (Triratio:
t(7)=−3.53∗∗
), and more harmonic asynchrony, especially during the birth phase
of the sound (Hsv:
t(7)=−2.08
). More details about this major acoustic mode (or eigensonicform) could be
obtained by computing correlations between the FPC scores. Surprisingly, these results revealed that the temporal
energy level was the main descriptor impacted by global changes in bow velocity (
rBowvel
Rms
=0.52
∗
). More trivially,
the cross-correlations of major acoustic scores revealed a strong collinearity between the amounts of harmonic
asynchronicity and high-frequency spectral energy (
rTriratio
Hsv
=0.75
∗∗∗
). No signicant cross-correlations were
Figure3. Major mode of the cellists’ functional variations. is mode explained 70% of the variance contained
in the kinematic data—(a) postural, (b) instrumental, (c) physical—and 60% of the variance contained in the
(d) acoustical data. At each stage of this functional unit, the eect of the major mode is visualized as functional
deviations of the average time series between the normal situation (curves of blue circles) and the constrained
situation (curves of red crosses). e attached boxplots present the distribution of FPC1 scores, i.e. the way
each individual curve contributed to the major mode, for each variable that signicantly discriminated the
postural conditions. Normal and constrained functional components were added or subtracted to or from the
mean curve, according to the mean sign of the FPC1 scores in each postural condition. e bottom right panel
(e) shows the graph obtained by linear regression of the major scores (FPC1) of the bow velocity with respect
to those of anatomic angles, which were signicantly dierent between the postural conditions (
R2=0.90∗∗
,
R2
adjusted
=0.77
∗∗
).
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obtained with the amount of temporal energy (Rms). ese results suggest that the major functional coordina-
tion unit essentially captured the temporal variations of the sound shape responsible for harshness perception,
independent of its purely spectral aspects.
Minor mode of variations. As observed in Fig.4, the second (or minor) functional unit corresponds to
local variations of data amplitudes at the dierent stages of the sound-gesture chain. At the physical stage, which
reects the “eective” sound-producing gesture (cf Fig.4c), the bow velocity decreased faster in the constrained
condition than in the normal postural condition (Bowvel:
t(7)=4.37∗∗
).
At the postural stage (cf Fig.4a), which reects the ancillary gestures, this bowing deceleration appeared to be
associated with a loss of natural bouncing between the chest torsion (
ψ12
:
t(7)=8.80∗∗∗
) and the head torsion
(
ψ3
:
t(7)=−2.35
). e analyses of the normal condition in the graph actually revealed surprising symmetrical
delays, chest torsion bouncing to the le and head torsion to the right, while these tendencies were lost in the
constrained condition. In accordance with Hoppenot25, we suggest that such a grounded tendency characterized
Figure4. Minor mode of the cellists’ functional variations. is mode explained 25% of the variance contained
in the kinematic data—(a) postural, (b) instrumental, (c) physical—and 15% of the variance contained in the
(d) acoustic data. At each stage of this functional unit, the eect of the minor mode is visualized as functional
deviations of the average time series between the normal situation (curves of blue circles) and the constrained
situation (curves of red crosses). e attached boxplots present the distribution of FPC2 scores, i.e. the way
each individual curve contributed to the minor mode, for each variable that signicantly discriminated the
postural conditions. Normal and constrained functional components were added or subtracted to or from the
mean curve, according to the mean sign of the FPC2 scores in each postural condition. e bottom right panel
(e) shows the graph obtained by linear regression of the minor scores (FPC2) of the bow velocity with respect
to those of anatomic angles, which were signicantly dierent between the postural conditions (
R2=0.91∗
,
R2
adjusted
=0.73
∗
).
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the need for a phase of active postural resistance to the bow pulling expansions to ensure optimal bow accel-
erations. is eect could also be observed in the lateral swings of the head (
φ3
:
t(7)=−2.36
) whose natural
right-and-le bouncing disappeared in the constrained condition. Another interesting minor eect concerned
the decrease in amplitude of the naturally vertical down-to-up inclinations of the chest (
θ2
:
t(7)=−3.09∗
) along
the bow-pulling movements.
At the instrumental stage (cf Fig.4b), which reects the interaction between eective and ancillary gestures,
the lack of an active resistance phase to the bow expansion was evidenced by the behavior of shoulder articula-
tion through the loss of upper arm abduction (
θ4
:
t(7)=3.39∗
) during the beginning of the movement. e
dierence in external rotation was also very interesting (
ψ4
:
t(7)=−2.83∗
) because it highlights the role of the
shoulder in providing natural support that ensured the projection of the whole right arm. Actually, the amount
of external rotation remained quite constant along a natural bow-pulling movement, whereas it drastically
decreased in the constrained condition. It could also be observed that this naturally sustained external rotation
guaranteed a reinforcement of the forearm pronation along the movement (
ψ56
:
t(7)=−2.05
), whereas in the
constrained condition, a forearm supination appeared as soon as the upper arm switched in internal rotation.
Importantly, the minor mode of variations also revealed a strong dierence in elbow exion/extension between
the two conditions (
φ5
:
t(7)=3.54∗∗
). In the normal condition, the elbow remained slightly bent during the
phase of active resistance before it considerably stretched out during the phase of bow expansion. By contrast,
in the constrained condition, the elbow increasingly exed and locked the whole arm movement. is elbow-
locking eect was also reected by two losses of mobility at the wrist level: the exion-to-extension progression
(
φ6
:
t(7)=3.48∗
) and the ulnar-to-radial inclination (
θ6
:
t(7)=2.38∗
).
As for the major mode, the results from multivariate regression on the minor FPC scores of these anatomic
angles were signicant (
R2=0.91∗
,
R2
adjusted =
0.73
∗
, cf regression graph of Fig.4e). It was therefore possible to
infer a linear relationship predicting the local bow velocity amplitudes, or bow accelerations, based on the set
of anatomic angles selected by the second functional unit. More importantly, an additional stepwise regression
extracted a combination of two angular degrees of freedom that explained the local variations of bow velocity:
is simple predictive relation highlights a minor mechanism of the cellist’s coordination, in which the coupling
between the vertical inclination of the chest (ancillary gesture) and the extension of the right wrist (instrumen-
tal gesture) ensured suitable bow accelerations. More details concerning this minor coordination mode (or
eigenposture) could be obtained by computing correlations between the FPC scores. Interestingly, the results
conrmed the importance of the vertical inclination of the chest (
rBowvel
θ2
=−0.58
∗
) and of the extension of
the wrist (
rBowvel
φ6
=0.73
∗∗
) during bow accelerations. e scores of elbow extension were also marginally cor-
related to those of the bow accelerations (
rBowvel
φ5
=
0.47
,
p=0.063
). Further cross-correlations of minor angle
scores revealed a chain of four coupling systems, which characterized the coordination transfer within the
minor mode: (1) system {
θ2|ψ12|ψ3|φ3
} showed the postural coupling among the chest torsion and vertical
inclination (
rψ
12
θ2
=−0.51
∗
), the bouncing symmetry of chest/head torsions (
rψ
3
ψ12
=−0.56
∗
), and the strong
dependence between head torsions and lateral swings (
rφ
3
ψ3
=0.90
∗∗∗
); (2) system {
ψ3|φ3|θ4|ψ4|ψ56
} showed the
importance of the degrees of freedom of the head, especially of the head torsion, to activate the external rotation
of the arm (
rψ
4
ψ3
=−0.71
∗∗
) and that of the coupling between this external rotation and the forearm pronation
(
rψ
56
ψ4
=0.52
∗
); (3) system {
ψ12|ψ3|φ3|θ6
} showed the indirect inuence of many postural angles, especially
the angles linked to head torsion and lateral swing on the wrist inclination (
rθ
6
ψ3
=−0.64
∗∗
and
rθ
6
φ3
=−0.66
∗∗
respectively); and (4) system {
φ5|φ6
} showed that the wrist extension was conditioned by the elbow extension
(
rφ
6
φ5
=0.71
∗∗
). ese results conrmed the importance of the double phase of postural resistance/expansion
along the movement for ensuring optimal bow pulling accelerations.
From the acoustical point of view (cf Fig.4d), the minor mode revealed that the same acoustic descriptors
as in the major mode with an additional fourth descriptor, the Mfccratio, were signicantly aected by the con-
strained condition. e analyses in the graph revealed an inability to maintain the acoustic signal energy during
the entire movement in the constrained condition. is eect was noticeable both in the temporal domain and in
spectral domains (Rms:
t(7)=2.08
, Triratio:
t(7)=−2.45∗
, respectively). In particular, the Mfccratio revealed
an excessive amount of high-frequency spectral energy at the beginning of the sound that corresponded to the
emergence of a formantic area (Mfccratio:
t(7)=−2.04
). More details concerning the minor acoustic mode (or
eigensonicform) could be obtained by computing correlations between the PC scores. Surprisingly, the results
revealed that the amount of high-frequency spectral energy was the main descriptor impacted by local changes in
bow velocity (
rBowvel
Triratio
=−0.58
∗
). More trivially, the cross-correlations of minor acoustic scores revealed a strong
collinearity between the amounts of spectral energy (
rHsc
Triratio =
0.88
∗∗∗
) and formantic energy (
rMfccratio
Triratio
=0.60
∗
).
No signicant cross-correlations were obtained with the amount of temporal energy (Rms). Complementary to
the major mode, these results suggested that the minor functional coordination unit had essentially captured the
variations in the spectral shape of the sound responsible for harshness perception (independent of its temporal
aspects).
Discussion
In summary, our functional analyses revealed that two primary postural directions are involved in the sound
quality produced by highly skilled cellists: rst, a major mechanism controlling bowing velocity (cf Eq.1) linked
to the evolution of the temporal shape of the sound and, second, a minor mechanism controlling bowing accel-
eration (cf Eq.2) linked to the evolution of the spectral content of the sound. ese results are consistent with
the physics of the instrument and the pioneering acoustic studies based on bowing machines. First, the bow
velocity should be correlated to the amount of transmitted vibrations to the surrounding air by the body of
(2)
Bowvel =0.41 ×θ2+0.64 ×φ6
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the cello and thus determine the energy level or intensity of the acoustic signal. Actually, harsh sounds cor-
respond to global decreases in bow velocity and weaker temporal proles of acoustic energy (cf major mode of
Fig.3c,d). Second, the bow acceleration should be correlated to the amount of high-frequency energy and thus
determine the quenching rates of upper partials in the spectrum89. Harsh sounds actually correspond to global
bow decelerations and higher quenching rates of spectral energy for upper partials (cf minor mode of Fig.4c,d).
Among the set of acoustic descriptors that characterize perceived harshness, harmonic asynchrony remains only
poorly explained by kinematic bowing analyses. is indicator of spectral uctuations might be inuenced more
strongly by the strict bow/string adherence nely tuned by the bow force parameter90. As a perspective, it may
thus be interesting to reiterate the same kind of functional analyses with dynamic features, i.e., the prediction
of variations in bow force from the muscular eorts estimated for each cellist’s body segment. Nevertheless, the
bow/string adherence quality involved in the perceived sound density depends on the bow velocity50, which was
insucient in this study when the right arm remained locked in a position of excessive supination and internal
rotation.
From our coordination study, such a tighter instrumental bowing gesture would be caused by inadequate
combinations of postural variables, particularly the loss of a symmetric combination between chest and head
torsion movements. e freedom of the head movement was particularly important to balance the chest tor-
sion with the external rotation of the right arm involved in both kinetic functionalities of the bowing (velocity
and acceleration). ese results are consistent with previous studies on cellists’ right arm behaviors, especially
the role of shoulder mobility during musical playing on the A string91,92. Furthermore, our ndings emerged
from large bow pulling gestures on one note, for which the impaired cellists could not compensate as simply as
elsewhere in the score. As the chest and head constraints aected the cellists’ sound quality on other notes to a
lesser extent, the execution of this particular note would stand for a limit in terms of postural adaptation, which
clearly depends on the score structure and not only on the ergonomics of the instrument. By generalizing to the
whole score, we suggest that this salient local eect of recurrent sound degradation highlights a more generic
deciency of cellists’ postural control, also called posturo-kinetic capacity12 in movement science. Even though
its variations may remain subtle, such a capacity would guarantee body stability during any goal-directed action,
such as bowing on one or several notes. Actually, the postural deviations of our highly skilled cellists were no
more than 5 degrees from the mean value in the major mode (cf Fig.3a), but this was enough to globally inu-
ence the quality of their auditory-motor interactions. is postural capacity is also highlighted through a double
phase of postural resistance/mobility to bow expansion in the minor mode (cf Fig.4a), which resulted in spectral
alterations in the sound when the musicians were posturally impaired. e constraints thus revealed the cel-
lists’ primary postural directions by disembodiment8, which supports the idea that the musicians’ structural and
expressive concepts are grounded in their sensorimotor networks.
e correlations established between the cellists’ movements and their sound quality features also provide
knowledge on their theoretical physiological principles49,93. Actually, our results suggest that the cellists’ bow-
ing actions would be more eective if organized in terms of “distal events”94,95, i.e., when their attention is not
centered on the movement itself but more on its potential inuence on the sound quality. Here, we suppose that
the postural impairment considerably disrupted the musicians’ natural sensations, i.e., the external focus of
attention needed to correctly perform an expressive musical task (professional cellists oen talk about “playing
without thinking”). As such, the context of this experiment may be considered a relevant “constrained action
hypothesis”96,97 for reinforcing the concept of supra-postural activity98,99: the quality and eciency of a task
would depend on this supra-postural control, i.e., the way individual body movements are subsumed into a
unied Gestalt for achieving the given goal. Interestingly, two of the seven cellists in our experiment stated that
they became more aware of their belly respiration insituations of postural impairment. In our opinion, these
remarks indicate that before being impaired, both respiratory and postural control were naturally piloted by an
external focus, i.e., by supra-postural commands of their attention. e constraint forced the cellists to adopt an
internal focus and to compensate by more conscious control of their movements. We hereby consider that these
scientic deductions give strong support to the concept of primary postural control, which was postulated as part
of the Alexander technique100, not only in the context of instrumentalists but also for any goal-directed actions
requiring a strong supra-postural activity. By encouraging performers to focus on the results of the actions rather
than on the actions themselves, the motor system could be trained in a more embodied and self-organized way
for natural and ecient performances.
ese ndings clearly suggest important applications for improving and optimizing practice habits among
musicians. is subject is a hot topic in research areas that assess the risk of musculoskeletal disorders among
musicians and search for strategies to promote health or reduce injury26,101,102. Feedback analyses of students
in higher music education institutions especially revealed the upper limb, upper trunk, and neck as the main
body parts aected by muscle pain syndromes102–104. e population of bowed-string players would also be more
aected by these postural disorders because of the asymmetric arm positions related to the trunk105,106. Such
results are clearly compliant with those of our study and reinforce the importance of integrating musicians’ pri-
mary postural control within individual rehabilitation programs. e magnitude of the cellists’ spinal curvatures
that we highlighted in relation to their sound quality may particularly help in developing strengthening-exibility
exercises targeting the trunk muscles of bowed-string players. As a whole, we think that the constrained condition
of our experiment altered the natural musicians’ action/perception cycle in a way that could be referred to as a
“phenomenological experience on non-sense”107. If cognition is our way of dealing with non-sense experiences,
then the tools established to reeducate the musicians’ proprioceptive feedback should authorize such an experi-
ence on nondoing or nonactivity consciousness, also known as inhibition in the Alexander technique29. We hereby
support the idea that the quality disruptions occurring in a musical discourse nd their origin in a faulty postural
awareness100, and may be solved by rening the musicians’ global perception of somatosensory processing.
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e ndings presented in this paper may also have a strong impact in other areas related to expert perfor-
mance, especially due to the statistical framework that we established. Sports biomechanics is one example of
a domain where body posture, dynamic somatic practice, and motor control need to remain inherently and
strongly connected to ensure the eciency of a given action66,76,77,108. For example, research on human-material
interfaces demonstrated that tennis players or runners need to nely tune the shock vibrations induced by the
racket or the ground surface109–111. In that context, functional data analyses may provide an opportunity to infer
continuous patterns of adaptation between the eector limb (hand or foot) and the entire body of these athletes.
By extension, such analyses could also highlight a functional interdependence between the sound produced in
reaction to the impact (with a racket/ground surface) and the biomechanical propagation of shock-induced
vibrations. Such examples suggest that our statistical framework may be suitable for analyzing the sound-gesture
relationships in a reverse way, i.e., assessing the role of auditory information on perceptual-motor processes. In
recent years, many studies have highlighted the benets of gestural sonication5,112–115, especially in the domains
of sports performance and motor rehabilitation116,117. For example, sonication eciently reduced the vari-
ability of golf swing gestures in novices118,119, or improved the pedal force eectiveness among cyclists120. e
benecial eects of sonication in reeducating patients with severe gait dysfunctions, such as Parkinson’s disease
patients, by rhythmic auditory cueing21–23,121, or neuromotor decits related to the uency of handwriting, such as
dysgraphia122–126, were also well recognized. In the same way, we suppose that such continuous auditory feedback
may help musicians and dancers improve or recover their body awareness, for example, through experiments of
sound tracing and motor mimicry, which are already known to stimulate covert mental images associated with
musical experience58,81,127,128.
Conclusion
In this paper, we assessed how postural impairments of highly skilled musicians aected their perceived sound
quality. rough functional analyses of cellists’ kinematic and acoustic interactions, it could be demonstrated
that feedforward deciencies of the primary postural command locally altered the quality of their musical
expression. Such ndings suggest that musical teaching should, to a much greater extent, consider the student?s
body as a global exible and proactive structure rather than focusing on specialized cognitive patterns that break
the sensorimotor processes into rigid units. is conclusion is consistent with embodied learning frameworks,
especially the Alexander technique, that correlate optimal body usage to proper directions of the spinal structure
and ne balance mechanisms between the head, neck, and trunk. It should therefore be possible to inuence
expressive perceptual processes and thus shape the musical mind by developing a kinesthetic awareness of the
sensory-motor relationships, i.e., integrating the sensations of joint mobility, muscular stability, and posture as
a whole. If such indirect procedures would contribute to reinforcing musculoskeletal health and the quality of
the performance in the musical domain, they may also be applied in a reverse way for learning dance and sport
skills or for patients in clinical rehabilitation by means of experimental manipulations of auditory feedback.
As a promising perspective of this study, we started to develop a complementary approach for assessing
the eects of harsh timbre degradation on cellists’ motor behavior. By means of our statistical framework of
functional analyses, we expect to close the perceptual loop that links cellists’ timbre quality to their postural
control. e methodological aspects of such a work are based on the use of an electric silent cello and the setup
of a multimodal platform combining a motion capture system and spatial rendering to study sound/gesture
interactions. We think that augmenting the perceptual information, especially through ne sound synthesis
techniques applied to gestural sonication, might provide a suitable means to strengthen the understanding of
the body schema related to cognitive interpretation and physical expression of structures within music or dance
performance. Such an approach has the potential to guide research on the design of skill training or rehabilita-
tion scenarios in the context of real-world applications, and it is particularly well-suited for (but not limited to)
musicians and dancers.
Methods
Participants. Seven highly skilled cellists (males = 4; females = 3; mean age =
40.5 ±11.1
) were recruited
on a voluntary basis from the Music Conservatory and the Opera of Marseille to participate in a 3-h experiment
that, as they were told, consisted of ‘ “exploring cellists’ sound/gesture relationships”. Before the experiment, each
musician signed a consent form that advised them of the precise the nature of the postural conditions and in
which they agreed to the publication of the information/image(s) collected during the experiment in an online
open-access publication. e musicians were also given an honorarium for their participation. All the proce-
dures of the protocol were approved by a local ethics board at the ISM-Aix-Marseille University and were carried
out according to the relevant guidelines expressed in the 1964 Declaration of Helsinki.
Design and apparatus. e design of our experiment was based on four postural conditions of gradual
diculty129. For each condition, the cellists were asked to play a score composed of dierent technical patterns
as expressively as possible. e full score was executed three times by postural condition, according to two tempi
[45/70 bpm] and bowing modes [detached/legato]. e postural conditions and repetitions of factor combina-
tions were randomly presented to each participant. At the end of each postural session, we collected the par-
ticipants’ impressions regarding their diculties in terms of motion and sound production by means of a short
questionnaire. In this paper, we focus on the two extreme experimental conditions (cf Fig.1): the natural perfor-
mance (entitled [N]: Normal) and the fully constrained condition (entitled [SCH]: Static Chest and Head). is
fully constrained condition consisted of impairing the cellists by two immobilization devices that reduced their
primary postural control in a noninvasive way: a six-point safety race harness that restrained the torso displace-
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ments and an adjusted neck collar that limited the freedom of head movements. We installed this equipment on
the musicians so that their shoulder mobility was not aected.
e cellists’ movements were recorded by an infrared motion capture system (Vicon 8, fps=125 Hz) that
tracked the three-dimensional positions of the reective markers positioned on the performer’s body and the
instrument. We followed the anatomical “Plug-in-Gait” (Vicon Motion Systems. Plug-in-Gait product guide.
Oxford: Vicon Motion Systems, 2010, https ://www.c-m otio n.com/downl oad/IORGa itFil es/p igma nualv er1.pdf)
standard to distribute the marker locations on the instrumentalist’s body. For this study, we focused the kinematic
analyses on a subset of seven key markers covering the cellists’ postural chain (torso/head) and the instrumental
chain responsible for the bowing gestures produced by the right arm. Some of these markers were virtually com-
puted from the Plug-in-Gait anatomical landmarks located on each segment, in accordance with the Dempster
model convention130 (cf Supplementary Table1). e acoustic signals produced by the instrument were recorded
by a DPA 4096 microphone placed under the cello bridge and connected to a MOTU interface (Ultralite MIC3,
fps = 44.1 kHz). Both recording systems were synchronized by a manual clap.
Stimuli and procedure. e stimuli were extracted from the cellists’ post-experimental feedback, which
identied a part of the performed score as frequently degraded in the constrained postural situation. Actually,
several notes belonging to this passage sounded harsher and shriller in agreement with the cellists’ comments
regarding their performance, in particular, their impression of producing “tighter and tenser sounds”, or “sounds
lacking depth and natural resonance”. Such harshness phenomena (i.e., degraded, metallic sound color) occurred
during the execution of quick syncopated patterns requiring excellent synchronization between the two arms
and were quite consistent among cellists on the rst note of the sequence (cf Fig.1). is dotted sixteenth of pitch
E4 is a key note that provides the motion impulse to the musical phrase through a large bow-pulling gesture
on the rst (A) cello string. Spectrogram analyses of this note between the normal and constrained postural
situations revealed salient signal dierences, which were thoroughly explored and connected to the musicians’
perception in a previous work48. We assessed the qualitative harshness phenomenon judgments according to
esthetic criteria of classical music by means of perceptual tests administered to a population of 15 trained cel-
lists, both teachers and advanced students. None of these cellists had participated in the experiment and had no
knowledge of the constrained postural conditions.
For this paper, we used the same corpus as in our previous work, which was built from perceptual evaluations
of harshness between the normal and constrained performances of the seven cellists. is corpus was composed
of the eight most salient pairs of round/harsh (good/poor quality) sounds of the E4 note, extracted from the
cellists’ performances in the normal and constrained contexts (mean note duration =
310 ±60
ms
∀
[N/SCH]).
Each round[N]/harsh[SCH] note pair belonged to a given cellist performing in slow tempo (45 bpm) and legato
bowing mode. e pairs of samples also belonged to dierent cellists and could thus be considered independent.
Motion analyses. Motion analyses were based on the anatomic displacements of the cellists’ joints associ-
ated with each sound of the corpus and on their bow velocity over time. To assess ne coordination features, we
designed a kinematic model describing the temporal evolution of these body joints (cf Fig.2a). e model was
composed of a linkage of six main rotary joints (cf Table1) articulating seven segments related to the body trunk
and the right arm (pelvis, abdomen, chest, head, upper arm, forearm, hand). Each corporeal segment was
assumed to be a rigid link, and the six articulations were approximated from the skeleton geometry as spherical
joints of three-dimensional degrees of freedom (DOFs)131,132. We computed 18 DOFs (6 joints
×
3 angles) as
joint-related triplets of anatomic angles {
ψn,θn,φn
},
n∈[1...6]
(cf Table1) by performing Cardan/Euler con-
versions of their segment-related marker coordinates132,133. For each joint, the method consisted of computing
the way the distal segment of the join was spatially rotated with respect to its proximal segment (cf Supplemen-
tary Figure1). In geometric terms, this approach merely dened a rotation matrix between two bases {

ip,

jp,

k
p
}
and {

id,

jd,

k
d
} attached to the joint proximal and distal segments, respectively (cf Supplementary Table2). Such
a matrix represents a succession of three rotations needed to transform a joint proximal basis into its relative
distal basis: rst rotation around X by an angle
ψ
(roll), second rotation around Y by an angle
θ
(pitch), and third
rotation around Z by an angle
φ
(yaw). As six rotation matrices should be computed to model all the DOFs, we
iterated the process along the six reference body hinges of the cellists’ motor chain. In addition to these joint
single-axis rotations, we also dened two composite angles for characterizing the global torso rotation (
ψ12
) and
the global forearm pronation/supination (
ψ56
). Note that angle
θ5
was removed because of the redundancy with
the external/internal rotation of the shoulder (
ψ4
); most biomechanics literature actually expresses the elbow
joint by only two DOFs: exion/extension (
φ5
) and pronation/supination (
ψ5
)134. At the end of this chain of
anatomic angles, the bow velocity was computed as the velocity vector norms of the bow “frog” marker (cf Sup-
plementary Table1) along the duration of each note composing the corpus:
Bowvel
=

(v2
x+v2
y+v2
z
)
, where
the triplet (
vx,vy,vz
) refers to the derivatives of the spatial coordinates of the bow frog at a given time.
Acoustic analyses. Acoustic analyses were based on the computation of ve acoustic descriptors over time
(cf Table2), which had been determined to be signicant in our previous work48 for discriminating between
round and harsh cello sounds. e extraction process for note E4 relied on a pitch-tracking algorithm adapted
from the MIR toolbox (Music Information Retrieval)135 of MATLAB soware. We developed a dedicated work-
ow in MATLAB to compute the ve acoustic descriptors over time by following the MPEG-7 standards136:
HSV (Harmonic Spectral Variations) relates to the sound spectral ux as a time-varying spectral content of its
harmonic components83; it was obtained from the spectral variation of harmonic amplitudes between adjacent
temporal frames. ATS (Attack Time Slope) corresponds to the attack time slope of the sound signal; it was deter-
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mined from the logarithmic rise time of the signal energy during the attack phase. MFCCratio is a ratio between
the two rst MFCCs (Mel-Frequency Cepstral Coecients)85, which we designed to highlight specic variations
of the sound spectral envelope in a perceptual way; the coecients were classically obtained through a DCT
(Discrete Cosine Transform) applied to the logarithmic spectral envelope. SC (Spectral Centroid) corresponds
to an amplitude-weighted mean of the harmonic spectral peaks; it was obtained through a decomposition in
subbands centered on the signal harmonics137. TRIratio describes the spectral energy distribution in three fre-
quency bands as an energy ratio between each band and the total number of harmonics. e rst band contains
the fundamental frequency, the second band contains the medium partials (two, three, four) and the last band
contains the higher partials (ve and more). e three tristimulus coordinates were obtained by spectral centroid
computations for each band87.
Statistical framework. Our statistical framework was designed with the aim of carrying out functional
comparisons of the cellists’ sound-gesture interactions between the normal and constrained conditions. is
process can be divided into ve steps, which are described below by referring to the schema components of
Fig.2b. All the calculations were performed with the help of MATLAB soware and the FDA toolbox138.
Functional data analyses (FDA). In contrast with the classic PCA approach, functional data analysis considers
the entire sequence of measurements a function or a single entity rather than a series of individual data points76.
To represent our motion features (anatomic angles, bow velocity) and acoustic descriptors as time-varying func-
tions, the FDA methodology consisted of decomposing each time-series of variables as a linear combination
of B-spline basis functions. We chose an equally spaced 6-order B-spline basis because it was better suited for
numerical calculations than polynomials that are less stable. Furthermore, B-spline functions were very useful
for smoothing acoustic data of noisier natures than kinematic data while eciently accommodating changes in
local behavior. A semi-sampled spline basis was sucient to keep a ne-grained denition of each curve. e
B-spline mathematical decomposition is also required to align the
n=16
time series (eight {normal/constraint}
data pairs) of motion and acoustic descriptors to the duration of the longest series beforehand. is duration was
normalized between 0 and 1 to be consistent with the FDA time-warping mechanism.
Functional principal component analyses (FPCA). FPCA was carried out based on the spline-based representa-
tion of time-point data. is technique has the major advantage of producing functional principal components
that can be interpreted in the same domain as the original observations (kinematic and acoustic). Actually, this
technique models each descriptor time-series
fi
as a linear combination of weighted deviations from its mean
dataset f
i
(t
)
:
where
ξk(t)
are the functional principal components (FPCs), also called eigenfunctions, that captured the K rst
main hidden modes of variations. e coecients
cik
correspond to score projections as in classical PCA but
assess the extent to which the shape of each individual behavior
fi
of the dataset matches with the global mean
trend
fi
(
t)
.
ǫi
is the prediction error between the observations
fi(t)
and their model as a sum of projections on
the K principal modes.
In this study, for each kinematic or acoustic descriptor, we performed an FPCA on the set of its spline-
based time-series
fi(t),i∈[1, 16]
, without considering, for the moment, a separation between the normal and
constrained conditions. e acoustic descriptors were processed by adding a small amount of smoothing to
the B-spline model to more easily capture the main variation trends while avoiding distortion of the data. e
deviation patterns obtained by FPCA, especially those related to the acoustic descriptors, took into account
this compromise between data smoothness and the largest proportion of explained variance. According to the
statistics literature68,70, FPCA should be interpreted through graphs that present the ensemble mean curve of
the original observations (
fi
(
t)
) and the functions obtained by adding or subtracting a suitable multiple of each
FPC (
ξk(t)
) to or from this mean. Generally, this multiple corresponds to the percentage p of explained variance,
which can be written in this way:
fi
(
t
)±
p
×ξ
k
(
t)
. We followed this methodology in the paper to explain the
K=2
main modes of variation resulting from our analyses through two gures describing their detailed eects
on both motion and acoustic sides (cf Figs.3 and 4). In these graphs, the decision to add or subtract a functional
component to the mean curve was made according to the mean sign of the FPC scores of each postural condition.
Statistical comparisons of the functional principal components (FPCs). e functional principal component
scores returned by the FPCA could be used to compare the behavior of each kinematic or acoustic variable
between the two postural conditions. We carried out these comparisons by means of two-tailed paired Student’s
t-tests on the eight normal (N) and constrained (SCH) score samples of each variable. e eects were consid-
ered signicant for p-values equal to or less than .05, and the proportion of signicance was indicated by a num-
ber of stars related to p-values:
p<0.05∗,p<0.01∗∗,p<0.001∗∗∗
. For the rst functional behavior (referred
to as major mode), we retained the FPC scores that signicantly and directly separated the postural conditions.
For the secondary functional behavior (referred to as minor mode), we performed a Varimax rotation of the PCA
structure for prior insignicant score discrimination and retained the rotated scores if their t-test comparisons
highlighted signicant postural dierences. Varimax rotation is a procedure of variance distribution and rep-
resents a convenient way to focus on the structure of the second variation mode to facilitate interpretation. As
a consequence of this process, the eigenfunctions capturing the rst and second behavioral dierences may not
(3)
fi(t)=fi(t)+
K

k=1
cikξk(t)+ǫi,cik =ξk(t)fi(t)
dt
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be perfectly orthogonal. In practice, however, the functional units related to each of the two motor behaviors
enabled clearly distinct interpretations.
Functional principal component regressions (FPCR). When the FPC scores of an analysis variable could be sig-
nicantly discriminated between the two postural conditions, we needed to conduct further analyses to compute
the functional principal components corresponding to each intergroup variation (i.e., normal and constrained).
Actually, the eigenfunctions returned by FPCA did not integrate the criteria for separating the postural condi-
tions. Such a problem could be resolved by applying an inverse methodology of functional principal component
regression (FPCR). is technique also allowed us to rebuild the original set of curves from the scores computed
by FPCA and nally assess the tting accuracy of our model68,74. Starting from a design matrix Z of the signicant
PC scores, FPCR determines K regression functions
βk
to t at best the shape of the time series
fi(t),i∈[1, 16]
:
where the function
β0
corresponds to the mean curve of the time series, and
βk
,
k∈[
1,
K]
stands for unbundled
eigenfunctions (
ξN
k
and
ξSCH
k
), which could not be dierentiated in the FPCA context (cf Eq.3). e score matrix
Z enabled such separation between the two postural conditions [N/SCH] by dividing each group of eight
zik
scores into
K=2
columns.
Multiple regressions and correlations of FPC scores. Standard statistical techniques were used to highlight the
main functional units shared by the cellists between the normal and constrained conditions. We determined
how their motor coordination inuenced the variations in bow velocity by carrying out two multivariate linear
regressions, one for each functional principal component. In this design, the signicant FPC scores of anatomic
angles were considered predictors of the bow velocity FPC scores. is approach resulted in two models of
functional motor units, which are presented in the bottom right part of Figs.3e and 4e. Each model is also char-
acterized by a linear relationship (cf Eqs.1 and 2) between the most signicant anatomic variables involved in
the coordination chain.
Two kinds of correlation analyses were nally performed in both motion and acoustic domains. First, we
extracted the important joint coupling chains of motor coordination by means of crossed correlations between
the signicant anatomic FPC scores. Second, we assessed functional sound-gesture interactions by computing
standard Pearson correlations between the FPC scores of bow velocity and those of each acoustic descriptor. e
most relevant correlations of these analyses provided a better understanding of how cellists’ motor programs
inuence their functional sound features in subtle ways.
Data availability
e datasets generated and analyzed during the current study are available from the corresponding author on
reasonable request.
Received: 10 December 2019; Accepted: 27 July 2020
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Acknowledgements
We acknowledge the ISM (Institut des Sciences du Mouvement) of Marseille for providing the technological
environment of the motion capture system and support related to the computations of anatomical Cardan/Euler
angles. is work is part of the “SoniMove” project (ANR-14-CE24-0018).
Author contributions
All authors participated to the design of the experiment and reviewed the manuscript. J.R. and S.Y. conducted the
experiment. With the help of ISM, J.R. conducted the functional motion analyses. M.A. contributed to statistical
analyses and R.K.M. contributed to acoustical analyses.
Competing interests
e authors declare no competing interests.
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