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RESEARCH ARTICLE
A brief and efficient stimulus set to create the
inverted U-shaped relationship between
rhythmic complexity and the sensation of
groove
Jan StupacherID
1,2
*, Markus Wrede
3
, Peter Vuust
1
1Department of Clinical Medicine, Center for Music in the Brain, Aarhus University & The Royal Academy of
Music Aarhus, Aalborg, Denmark, 2Institute of Psychology, University of Graz, Graz, Austria, 3Department
of Clinical Medicine, Aarhus University, Aarhus, Denmark
*stupacher@clin.au.dk
Abstract
When listening to music, we often feel a strong desire to move our body in relation to the
pulse of the rhythm. In music psychology, this desire to move is described by the term
groove. Previous research suggests that the sensation of groove is strongest when a rhythm
is moderately complex, i.e., when the rhythm hits the sweet spot between being too simple
to be engaging and too complex to be interpretable. This means that the relationship
between rhythmic complexity and the sensation of groove can be described by an inverted
U-shape (Matthews 2019). Here, we recreate this inverted U-shape with a stimulus set that
was reduced from 54 to only nine rhythms. Thereby, we provide an efficient toolkit for future
studies to induce and measure different levels of groove sensations. Pleasure and move-
ment induction in relation to rhythmic complexity are emerging topics in music cognition and
neuroscience. Investigating the sensation of groove is important for understanding the
neurophysiological mechanisms underlying motor timing and reward processes in the gen-
eral population, and in patients with conditions such as Parkinson’s disease, Huntington’s
disease and motor impairment after stroke. The experimental manipulation of groove also
provides new approaches for research on social bonding in interpersonal movement interac-
tions that feature music. Our brief stimulus set facilitates future research on these topics by
enabling the creation of efficient and concise paradigms.
Introduction
In music psychology, the experience of groove is often defined as a pleasurable state of wanting
to move one’s body in relation to the pulse of a musical rhythm [1–4]. Recent findings suggest
that we feel a strong desire to move our bodies when listening to music with a moderate
amount of rhythmic complexity, whereas in comparison, low and high amounts of rhythmic
complexity decrease our desire to move [5,6]. Consequently, the relationship between rhyth-
mic complexity and the sensation of groove can be described by an inverted U-shape. Besides
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OPEN ACCESS
Citation: Stupacher J, Wrede M, Vuust P (2022) A
brief and efficient stimulus set to create the
inverted U-shaped relationship between rhythmic
complexity and the sensation of groove. PLoS ONE
17(5): e0266902. https://doi.org/10.1371/journal.
pone.0266902
Editor: Jessica Adrienne Grahn, University of
Western Ontario, CANADA
Received: November 18, 2021
Accepted: March 29, 2022
Published: May 19, 2022
Copyright: ©2022 Stupacher et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: All relevant data are
within the paper and its Supporting information file.
Funding: The Center for Music in the Brain is
funded by the Danish National Research
Foundation (DNRF 117, awarded to PV). JS is
supported by an Erwin Schro¨dinger fellowship
from the Austrian Science Fund (FWF) [J-4288].
This research was funded in whole, or in part, by
the Austrian Science Fund (FWF) [J-4288, awarded
to JS]. For the purpose of open access, the author
has applied a CC BY public copyright license to any
rhythmic complexity, Matthews and colleagues [5] investigated the influence of harmonic com-
plexity on the sensation of groove and found that wanting to move ratings were similar for low
and moderately complex harmonies, but dropped for a highly complex harmony. The present
study tests whether these effects of rhythmic and harmonic complexity can be replicated with a
subset of nine stimuli from the original set of 54 stimuli used by Matthews and colleagues [5].
Rhythmic complexity, and the related affective and behavioral responses, play important
roles in recent research on music-supported movement therapies, social bonding, and neuro-
physiological mechanisms underlying motor timing and reward processes. Predicting how
music unfolds and develops over time is a rewarding, pleasurable process [7,8] that involves
neural auditory-motor interactions [9,10]. With music that is rated as high-groove, neural
auditory-motor interactions are more affected than with low-groove music [4]. Music that
facilitates the sensation of groove might therefore be especially effective in therapeutic pro-
grams for improving body movements in individuals with conditions such as Parkinson’s dis-
ease, Huntington’s disease and motor impairment after stroke [11,12]. Importantly, in
patients with motor impairments, the most groove-inducing rhythms might be shifted from
moderate to low rhythmic complexities when compared with healthy control participants [13].
A similar shift of the inverted U-shape towards simpler rhythms could also occur for cochlear
implant users—but research on this topic is lacking.
Rhythmic complexity is also important for social bonding in interpersonal movement inter-
actions that feature music. A clear perception of the temporal structure of music is crucial for
providing a meaningful social context in which the movements of oneself and others can be
interpreted and evaluated. Interestingly, recent findings suggest that a moderate level of rhyth-
mic complexity may be favorable for social bonding when moving together with music: The
feeling of social closeness tends to follow an inverted U-shape in relation to rhythmic complex-
ity [14]. Although the inverted U-shape of rhythmic complexity can also be found in social
interactions, it remains an open question whether and how groove experiences differ in indi-
vidual and social contexts.
Combined with neuroimaging, groove research can help us understand the role of motor
and reward networks when making and listening to music [4,15,16]. In neuroimaging, but
also in behavioral studies, one of the outstanding questions is how rhythmic and harmonic
complexity contribute to motor behavior, reward and pleasure. To facilitate future research on
all of the previously mentioned topics, we present a brief stimulus set of nine rhythms that
reproduces the effects of rhythmic and harmonic complexity found in an experiment by Mat-
thews and colleagues [5] with a stimulus set of 54 rhythms.
Method
Participants
Data were collected in an online questionnaire completed by 174 participants. Five partici-
pants reported a history of motor-related neurological diseases and were excluded. The result-
ing 169 participants (116 female, 53 male) had a mean age of 25.1 years (SD = 6.1). One
hundred fifty-one participants were Danish; the rest of the participants came from 13 different
countries (Austria [n = 1], Belgium [1], Canada [1], France [2], Germany [3], Iceland [1], Lith-
uania [1], Mexico [1], Norway [2], South Korea [1], Sweden, UK [2], and Uruguay [1]).
Twenty-five participants reported playing an instrument and singing, 75 participants reported
playing an instrument but not singing, 14 participants reported singing but not playing an
instrument, and 55 participants reported not playing an instrument and not singing. The sam-
ple size was comparable to Matthews and colleagues’ [5] sample of 201 participants. The study
was conducted in accordance with the guidelines from the Declaration of Helsinki and the
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Author Accepted Manuscript version arising from
this submission.
Competing interests: The authors have declared
that no competing interests exist.
Danish Code of Conduct for Research Integrity and Aarhus University’s Policy for research
integrity, freedom of research and responsible conduct of research. All collected data included
no personally identifiable information.
Stimuli
Nine audio clips were selected based on subjective musicality by author MW from a set of 54
stimuli used by Matthews and colleagues [5]. The audio clips were ten seconds long and con-
sisted of rhythmic patterns played with one chord in a piano timbre. Every rhythmic pattern
consisted of five onsets per bar, which were repeated for four bars in total. The rhythmic and
harmonic complexity of the patterns had three levels. Rhythmic complexity varied between low,
moderate and high levels of syncopation (Fig 1A). The chords were in D major and varied
between low harmonic complexity (D major triad and two inversions), moderate harmonic
complexity (four note chords with extensions), and high harmonic complexity (flat ninth inter-
val between chord note and extension). For more information about the stimuli, see Matthews
et al. [5]. Roughness was calculated with the MIR-toolbox [17] to estimate harmonic complexity
of the selected stimuli. Pulse clarity (MIR toolbox) and syncopation index [5,18] were calcu-
lated to estimate rhythmic complexity. Mean roughness was lowest for low harmonic complexity
(188), followed by moderate (213), and high (266) harmonic complexity. Pulse clarity (PC) was
highest and syncopation index (SI) was lowest for low rhythmic complexity (PC: 0.72, SI: 0),
followed by moderate (PC: 0.31, SI: 4), and high (PC: 0.28, SI: 18) rhythmic complexity. For
details on the calculations of the syncopation indices, see Fig 1B and 1C. The nine stimuli can
be found online at https://researchbox.org/487.
Procedure
Each audio clip was presented once in randomized order. After each stimulus, participants
rated the groove of the audio clip on a continuous slider ranging from “not groovy” on the left
to “very groovy” on the right. The numerical values ranged from 1 on the left side to 101 on
the right side, but participants could not see these values. Groove was defined as “wanting to
move in time with the music” [1,2,4]. In contrast to Matthews et al. [5] who asked, “How
much does this musical pattern make you want to move?” the present study directly men-
tioned the term groove and connected it to the urge to move with a musical rhythm.
Results and discussion
In line with previous research by Matthews et al. [5] and Witek et al. [6], groove ratings fol-
lowed an inverted U-shape when plotted against rhythmic complexity, i.e. syncopation (Fig 2).
The strongest sensation of groove was reported for patterns with a moderate amount of rhyth-
mic complexity (M= 61.2, SD = 23.7), followed by low (M= 41.3, SD = 24.4) and high
(M= 20.1, SD = 20.5) rhythmic complexity. The manipulation of harmonic complexity also led
to similar results as in Matthews et al. (2019): Groove ratings were highest for low harmonic
complexity (M= 47.3, SD = 29.0) followed by moderate (M= 43.5, SD = 27.4) and high
(M= 31.8, SD = 26.4) harmonic complexity.
An ANOVA on groove ratings with the within-subject factors rhythmic complexity and har-
monic complexity revealed main effects of rhythmic complexity (F(2,1344) = 686.30, p<.001,
η
2
= .46) and harmonic complexity (F(2,1344) = 105.43, p<.001, η
2
= .07) as well as an interac-
tion between the two factors (F(4,1344) = 7.05, p<.001, η
2
= .01). With the large effect size of
η
2
= .46, the factor rhythmic complexity may be more important for the sensation of groove
than harmonic complexity, with a much smaller effect size of η
2
= .07. This finding is in accor-
dance with Matthews et al. [5], who suggest that “rhythm plays a primary role in generating
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the sensation of groove, with harmony providing a modulatory role through its effect on plea-
sure”. It is important to note that the inverted U-shape of rhythmic complexity might be more
prominent in a sample of professional musicians and less prominent in non-musicians in
comparison to our sample of mixed musical expertise [5].
Fig 1. Description of the rhythms with metric weights and syncopation measures. A) Low, moderate and high rhythmic complexity (RC) stimuli. Each onset is
represented by a dot (●) with the corresponding metric weight noted below. The eight-note hi-hat (×) is part of each of the three stimuli. B and C) Calculations of the
syncopation index following Fitch and Rosenfeld (2007) and Matthews et al. (2019) for the moderate and high rhythmic complexity stimuli. A syncopation occurs when
a rest (here at the eight-note level) is preceded by the onset of a note of lesser weight. The summed up differences between syncopated notes and rests make the
syncopation index.
https://doi.org/10.1371/journal.pone.0266902.g001
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The interaction between the two factors was unpacked with Bonferroni-corrected paired t-
tests (see Fig 2). Differences in groove ratings between low and moderate harmonic complexity
were nonsignificant in stimuli with low and high rhythmic complexity, but significant in sti-
muli with moderate rhythmic complexity. All other pairwise comparisons between harmonic
complexity levels within each rhythmic complexity level were significant (p <.001). Data of the
individual participants can be found in S1 Table. In accordance with findings of Matthews
et al. [5], our study provides further evidence for the assumption of an inverted U-shape rela-
tionship between rhythmic complexity and the sensation of groove. This inverted U-shape can
be explained using the theory of predictive coding of music, in which it is proposed that music
perception and action are shaped by bottom-up sensory input on one hand, and top-down
predictive brain models on the other hand [19,20]. According to the predictive coding of
rhythm [20], a listener compares an internally generated predictive model with the actual sen-
sory input. Music with moderate rhythmic complexity is regular enough for a listener to create
a predictive mental model of beat and meter that is possible to move in time to, whereas the
syncopations within the rhythm result in prediction errors. These prediction errors can be
reduced either by updating the model to better align with the sensory input, or by changing
the input, for example by moving one’s body in time with the beat to add a proprioceptive
dimension. In these ways, reducing prediction errors increases top-down engagement,
embodiment, pleasure, and reward. If the rhythms are very simple, however, the predictions
and the input match almost perfectly, leading to few prediction errors, and therefore fewer
Fig 2. Groove ratings as a function of rhythmic and harmonic complexity. Dots represent mean groove ratings.
Boxplots: The centerline represents the median. The lower and upper ends of the boxes correspond to the first and
third quartiles. Whiskers represent lowest and highest values within 1.5 ×interquartile range (IQR) from the lower and
upper quartiles, respectively. Circles represent values outside 1.5 ×IQR. ns = nonsignificant,�p<.001.
https://doi.org/10.1371/journal.pone.0266902.g002
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updates of the predictive model and less top-down engagement. If the rhythms are very com-
plex, the listener is unable to create an appropriate predictive model at all, precluding the pos-
sibility of updating the model. Compared to moderately complex rhythms, both very simple
and very complex rhythms may therefore reduce top-down engagement, pleasure, and embod-
ied experiences associated with updating and maintaining the predictive model.
Syncopation is one of the most discussed musical features related to groove [5,6,16,21–
23], but it is of course not the only one. Other rhythmic and sonic features connected to the
sensation of groove are energy in bass frequencies [24,25], event density [22,26] cf. [25],
beat salience / pulse clarity [26] cf. [22,25], and tempo [1] cf. [22] cf. [27]. Microtiming—
intended and expressive onset deviations from the metric grid in the range of a few tens of mil-
liseconds—is another often-discussed feature of groove. However, empirical studies come to
contradictory conclusions with positive, negative, and null effects of microtiming deviations
on groove ratings (see e.g., [28] for an overview). The brief stimulus set presented here can be
used to investigate how syncopation interacts with the above-mentioned features in evoking
the sensation of groove.
As the current musical stimuli are synthesized, their (micro)rhythmic and sonic features
can be easily adapted for future experiments. Their synthesized nature also minimizes poten-
tial effects of familiarity that can occur with popular music [29]. However, the high control
and internal validity associated with synthesized stimuli, a fully crossed randomized design,
and individual data collection come with a decrease in ecological validity. Future experiments
could therefore build on the recent findings by comparing synthesized versus performed ver-
sions of the stimulus set, and individual versus collective listening environments.
The application-oriented conclusion of the present study is that the inverted U-shaped rela-
tionship between rhythmic complexity and the sensation of groove can be shown efficiently
with a set of nine stimuli that are only rated once. The effects of harmonic complexity on
groove ratings measured with this small stimulus set are also similar to the effects of the origi-
nal study with 54 stimuli [5]. This is especially important for future studies on rhythm percep-
tion and the sensation of groove with time constraints and complex designs. The brief
stimulus set facilitates efficient combinations of groove paradigms and clinical applications,
such as Parkinson’s, Huntington’s, and stroke therapies, or cochlear implant research. Partici-
pants in most of these groups particularly profit from short paradigms. Furthermore, the stim-
ulus set’s conciseness is ideal for large-scale online experiments comparing participants who,
for example, differ in cultural background, musical expertise, dance training, motor skills,
empathy, or age. These types of groove research paradigms will help us to better understand
the interplay between timing processes, movement, social behavior, and pleasure in music lis-
tening, music making, and dance.
Supporting information
S1 Table. Individual groove ratings of participants. The table shows all combinations of low,
moderate, and high rhythmic complexities (LR, MR, and HR, respectively) with low, moder-
ate, and high harmonic complexities (LH, MH, and HH, respectively). Ratings were given on a
continuous scale from 1 on the left to 101 on the right. Participants could not see these values.
(PDF)
Author Contributions
Conceptualization: Jan Stupacher, Markus Wrede, Peter Vuust.
Data curation: Markus Wrede.
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Formal analysis: Jan Stupacher.
Methodology: Jan Stupacher, Markus Wrede.
Supervision: Jan Stupacher.
Writing – original draft: Jan Stupacher.
Writing – review & editing: Jan Stupacher.
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