The nature and perception of fluctuations in human musical rhythms

Stochastic properties of musical time series

Musical sequences are correlated dynamical processes that may differ depending on musical styles. We aim to quantify the correlations through power spectral analysis of pitch sequences in a large corpus of musical compositions as well as improvised performances. Using a multitaper method we extend the power spectral estimates down to the smallest possible frequencies optimizing the tradeoff between bias and variance. The power spectral densities reveal a characteristic behavior; they typically follow inverse power laws (1/f β-noise), yet only down to a cutoff frequency, where they end in a plateau. Correspondingly the pitch autocorrelation function exhibits slow power law decays only up to a cutoff time, beyond which the correlations vanish. We determine cutoff times between 4 and 100 quarter note units for the compositions and improvisations of the corpus, serving as a measure for the degree of persistence and predictability in music. The histogram of exponents β for the power law regimes has a pronounced peak near β = 1 for classical compositions, but is much broader for jazz improvisations.

Tapping strength variability in sensorimotor experiments on rhythmic tapping

We report psychophysical experiments and time series analyses to investigate sensorimotor tapping strength fluctuations in human periodic tapping with and without a metronome. The power spectral density of tapping strength fluctuations typically decays in an inverse power law (1/fβ-noise) associated with long-range correlations, i.e., with a slow power-law decay of tapping strength autocorrelations and scale-free behavior. The power-law exponents β are scattered around β=1 ranging from 0.67 to 1.8. A log-linear representation of the power spectral densities reveals rhythmic peaks at frequencies f=0.25 (and f=0.5) and a tendency to slightly accentuate every fourth (and second) stroke when subjects try to synchronize their tapping with a metronome.

A review of psychological and neuroscientific research on musical groove

When listening to music, we naturally move our bodies rhythmically to the beat, which can be pleasurable and difficult to resist. This pleasurable sensation of wanting to move the body to music has been called "groove." Following pioneering humanities research, psychological and neuroscientific studies have provided insights on associated musical features, behavioral responses, phenomenological aspects, and brain structural and functional correlates of the groove experience. Groove research has advanced the field of music science and more generally informed our understanding of bidirectional links between perception and action, and the role of the motor system in prediction. Activity in motor and reward-related brain networks during music listening is associated with the groove experience, and this neural activity is linked to temporal prediction and learning. This article reviews research on groove as a psychological phenomenon with neurophysiological correlates that link musical rhythm perception, sensorimotor prediction, and reward processing. Promising future research directions range from elucidating specific neural mechanisms to exploring clinical applications and socio-cultural implications of groove.

Asymmetric Effects of Different Training-Testing Mismatch Types on Myoelectric Regression via Deep Learning

This paper investigates how predictions of a convolutional neural network (CNN) suited for myoelectric simultaneous and proportional control (SPC) are affected when training and testing conditions differ. We used a dataset composed of electromyogram (EMG) signals and joint angular accelerations measured from volunteers drawing a star. This task was repeated multiple times using different combinations of motion amplitude and frequency. CNNs were trained with data from a given combination and tested under different combinations. Predictions were compared between situations in which training and testing conditions matched versus when there was a training-testing mismatch. Changes in predictions were assessed through three metrics: normalized root mean squared error (NRMSE), correlation, and slope of the linear regression between targets and predictions. We found that predictive performance declined differently depending on whether the confounding factors (amplitude and frequency) increased or decreased between training and testing. Correlations dropped as the factors decreased, whereas slopes deteriorated when factors increased. NRMSEs worsened when factors increased or decreased, with more accentuated deterioration for decreasing factors. We argue that worse correlations could be related to differences in EMG signal-to-ratio (SNR) between training and testing, which affected the noise robustness of the CNNs' learned internal features. Slope deterioration could be a result of the networks' inability to predict accelerations outside the range seen during training. These two mechanisms may also asymmetrically increase NRMSE. Finally, our findings open further possibilities to develop strategies to mitigate the negative impact of confounding factor variability on myoelectric SPC devices.

Research in Computational Expressive Music Performance and Popular Music Production: A Potential Field of Application?

In music, the interpreter manipulates the performance parameters in order to offer a sonic rendition of the piece that is capable of conveying specific expressive intentions. Since the 1980s, there has been growing interest in expressive music performance (EMP) and its computational modeling. This research field has two fundamental objectives: understanding the phenomenon of human musical interpretation and the automatic generation of expressive performances. Rule-based, statistical, machine, and deep learning approaches have been proposed, most of them devoted to the classical repertoire, in particular to piano pieces. On the contrary, we introduce the role of expressive performance within popular music and the contemporary ecology of pop music production based on the use of digital audio workstations (DAWs) and virtual instruments. After an analysis of the tools related to expressiveness commonly available to modern producers, we propose a detailed survey of research into the computational EMP field, highlighting the potential and limits of what is present in the literature with respect to the context of popular music, which by its nature cannot be completely superimposed to the classical one. In the concluding discussion, we suggest possible lines of future research in the field of computational expressiveness applied to pop music.

Spectral fingerprints of nonequilibrium dynamics: The case of a Brownian gyrator

The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally relevant model of such a system-the so-called Brownian gyrator-a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under nonequilibrium conditions, while no net rotation takes place under equilibrium ones. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in nonequilibrium. We show that indeed one can conclusively distinguish between equilibrium and nonequilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a nonequilibrium dynamics.

Toward Understanding the Brain Dynamics of Music: Learning and Conscious Performance of Lyrics and Melodies With Variable Rhythms and Beats

A neural network architecture models how humans learn and consciously perform musical lyrics and melodies with variable rhythms and beats, using brain design principles and mechanisms that evolved earlier than human musical capabilities, and that have explained and predicted many kinds of psychological and neurobiological data. One principle is called factorization of order and rhythm: Working memories store sequential information in a rate-invariant and speaker-invariant way to avoid using excessive memory and to support learning of language, spatial, and motor skills. Stored invariant representations can be flexibly performed in a rate-dependent and speaker-dependent way under volitional control. A canonical working memory design stores linguistic, spatial, motoric, and musical sequences, including sequences with repeated words in lyrics, or repeated pitches in songs. Stored sequences of individual word chunks and pitch chunks are categorized through learning into lyrics chunks and pitches chunks. Pitches chunks respond selectively to stored sequences of individual pitch chunks that categorize harmonics of each pitch, thereby supporting tonal music. Bottom-up and top-down learning between working memory and chunking networks dynamically stabilizes the memory of learned music. Songs are learned by associatively linking sequences of lyrics and pitches chunks. Performance begins when list chunks read word chunk and pitch chunk sequences into working memory. Learning and performance of regular rhythms exploits cortical modulation of beats that are generated in the basal ganglia. Arbitrary performance rhythms are learned by adaptive timing circuits in the cerebellum interacting with prefrontal cortex and basal ganglia. The same network design that controls walking, running, and finger tapping also generates beats and the urge to move with a beat.

Coordination and Consonance Between Interacting, Improvising Musicians

Joint action (JA) is ubiquitous in our cognitive lives. From basketball teams to teams of surgeons, humans often coordinate with one another to achieve some common goal. Idealized laboratory studies of group behavior have begun to elucidate basic JA mechanisms, but little is understood about how these mechanisms scale up in more sophisticated and open-ended JA that occurs in the wild. We address this gap by examining coordination in a paragon domain for creative joint expression: improvising jazz musicians. Coordination in jazz music subserves an aesthetic goal: the generation of a collective musical expression comprising coherent, highly nuanced musical structure (e.g., rhythm, harmony). In our study, dyads of professional jazz pianists improvised in a "coupled," mutually adaptive condition, and an "overdubbed" condition that precluded mutual adaptation, as occurs in common studio recording practices. Using a model of musical tonality, we quantify the flow of rhythmic and harmonic information between musicians as a function of interaction condition. Our analyses show that mutually adapting dyads achieve greater temporal alignment and produce more consonant harmonies. These musical signatures of coordination were preferred by independent improvisers and naive listeners, who gave higher quality ratings to coupled interactions despite being blind to condition. We present these results and discuss their implications for music technology and JA research more generally.

Dynamic Functional Connectivity between order and randomness and its evolution across the human adult lifespan

Functional Connectivity (FC) during resting-state or task conditions is not static but inherently dynamic. Yet, there is no consensus on whether fluctuations in FC may resemble isolated transitions between discrete FC states rather than continuous changes. This quarrel hampers advancing the study of dynamic FC. This is unfortunate as the structure of fluctuations in FC can certainly provide more information about developmental changes, aging, and progression of pathologies. We merge the two perspectives and consider dynamic FC as an ongoing network reconfiguration, including a stochastic exploration of the space of possible steady FC states. The statistical properties of this random walk deviate both from a purely "order-driven" dynamics, in which the mean FC is preserved, and from a purely "randomness-driven" scenario, in which fluctuations of FC remain uncorrelated over time. Instead, dynamic FC has a complex structure endowed with long-range sequential correlations that give rise to transient slowing and acceleration epochs in the continuous flow of reconfiguration. Our analysis for fMRI data in healthy elderly revealed that dynamic FC tends to slow down and becomes less complex as well as more random with increasing age. These effects appear to be strongly associated with age-related changes in behavioural and cognitive performance.

Microtiming Deviations and Swing Feel in Jazz

Jazz music that swings has the fascinating power to elicit a pleasant sensation of flow in listeners and the desire to synchronize body movements with the music. Whether microtiming deviations (MTDs), i.e. small timing deviations below the bar or phrase level, enhance the swing feel is highly debated in the current literature. Studies on other groove related genres did not find evidence for a positive impact of MTDs. The present study addresses jazz music and swing in particular, as there is some evidence that microtiming patterns are genre-specific. We recorded twelve piano jazz standards played by a professional pianist and manipulated the natural MTDs of the recordings in systematic ways by quantizing, expanding and inverting them. MTDs were defined with respect to a grid determined by the average swing ratio. The original and manipulated versions were presented in an online survey and evaluated by 160 listeners with various musical skill levels and backgrounds. Across pieces the quantized versions (without MTDs) were rated slightly higher and versions with expanded MTDs were rated lower with regard to swing than the original recordings. Unexpectedly, inversion had no impact on swing ratings except for two pieces. Our results suggest that naturally fluctuating MTDs are not an essential factor for the swing feel.

Scaling behaviour in music and cortical dynamics interplay to mediate music listening pleasure

The pleasure of music listening regulates daily behaviour and promotes rehabilitation in healthcare. Human behaviour emerges from the modulation of spontaneous timely coordinated neuronal networks. Too little is known about the physical properties and neurophysiological underpinnings of music to understand its perception, its health benefit and to deploy personalized or standardized music-therapy. Prior studies revealed how macroscopic neuronal and music patterns scale with frequency according to a 1/f^α relationship, where a is the scaling exponent. Here, we examine how this hallmark in music and neuronal dynamics relate to pleasure. Using electroencephalography, electrocardiography and behavioural data in healthy subjects, we show that music listening decreases the scaling exponent of neuronal activity and-in temporal areas-this change is linked to pleasure. Default-state scaling exponents of the most pleased individuals were higher and approached those found in music loudness fluctuations. Furthermore, the scaling in selective regions and timescales and the average heart rate were largely proportional to the scaling of the melody. The scaling behaviour of heartbeat and neuronal fluctuations were associated during music listening. Our results point to a 1/f resonance between brain and music and a temporal rescaling of neuronal activity in the temporal cortex as mechanisms underlying music appreciation.

Neural entrainment is associated with subjective groove and complexity for performed but not mechanical musical rhythms

Both movement and neural activity in humans can be entrained by the regularities of an external stimulus, such as the beat of musical rhythms. Neural entrainment to auditory rhythms supports temporal perception, and is enhanced by selective attention and by hierarchical temporal structure imposed on rhythms. However, it is not known how neural entrainment to rhythms is related to the subjective experience of groove (the desire to move along with music or rhythm), the perception of a regular beat, the perception of complexity, and the experience of pleasure. In two experiments, we used musical rhythms (from Steve Reich’s Clapping Music) to investigate whether rhythms that are performed by humans (with naturally variable timing) and rhythms that are mechanical (with precise timing), elicit differences in (1) neural entrainment, as measured by inter-trial phase coherence, and (2) subjective ratings of the complexity, preference, groove, and beat strength of rhythms. We also combined results from the two experiments to investigate relationships between neural entrainment and subjective perception of musical rhythms. We found that mechanical rhythms elicited a greater degree of neural entrainment than performed rhythms, likely due to the greater temporal precision in the stimulus, and the two types only elicited different ratings for some individual rhythms. Neural entrainment to performed rhythms, but not to mechanical ones, correlated with subjective desire to move and subjective complexity. These data, therefore, suggest multiple interacting influences on neural entrainment to rhythms, from low-level stimulus properties to high-level cognition and perception.

Origins of 1/f noise in human music performance from short-range autocorrelations related to rhythmic structures

1/f fluctuations have been described in numerous physical and biological processes. This noise structure describes an inverse relationship between the intensity and frequency of events in a time series (for example reflected in power spectra), and is believed to indicate long-range dependence, whereby events at one time point influence events many observations later. 1/f has been identified in rhythmic behaviors, such as music, and is typically attributed to long-range correlations. However short-range dependence in musical performance is a well-established finding and past research has suggested that 1/f can arise from multiple continuing short-range processes. We tested this possibility using simulations and time-series modeling, complemented by traditional analyses using power spectra and detrended fluctuation analysis (as often adopted more recently). Our results show that 1/f-type fluctuations in musical contexts may be explained by short-range models involving multiple time lags, and the temporal ranges in which rhythmic hierarchies are expressed are apt to create these fluctuations through such short-range autocorrelations. We also analyzed gait, heartbeat, and resting-state EEG data, demonstrating the coexistence of multiple short-range processes and 1/f fluctuation in a variety of phenomena. This suggests that 1/f fluctuation might not indicate long-range correlations, and points to its likely origins in musical rhythm and related structures.

Multifractal analysis reveals music-like dynamic structure in songbird rhythms

Music is thought to engage its listeners by driving feelings of surprise, tension, and relief through a dynamic mixture of predictable and unpredictable patterns, a property summarized here as “expressiveness”. Birdsong shares with music the goal to attract its listeners’ attention and might use similar strategies to achieve this. We here tested a thrush nightingale’s (Luscinia luscinia) rhythm, as represented by song amplitude envelope (containing information on note timing, duration, and intensity), for evidence of expressiveness. We used multifractal analysis, which is designed to detect in a signal dynamic fluctuations between predictable and unpredictable states on multiple timescales (e.g. notes, subphrases, songs). Results show that rhythm is strongly multifractal, indicating fluctuations between predictable and unpredictable patterns. Moreover, comparing original songs with re-synthesized songs that lack all subtle deviations from the “standard” note envelopes, we find that deviations in note intensity and duration significantly contributed to multifractality. This suggests that birdsong is more dynamic due to subtle note timing patterns, often similar to musical operations like accelerando or crescendo. While different sources of these dynamics are conceivable, this study shows that multi-timescale rhythm fluctuations can be detected in birdsong, paving the path to studying mechanisms and function behind such patterns.

Correlated microtiming deviations in jazz and rock music

Musical rhythms performed by humans typically show temporal fluctuations. While they have been characterized in simple rhythmic tasks, it is an open question what is the nature of temporal fluctuations, when several musicians perform music jointly in all its natural complexity. To study such fluctuations in over 100 original jazz and rock/pop recordings played with and without metronome we developed a semi-automated workflow allowing the extraction of cymbal beat onsets with millisecond precision. Analyzing the inter-beat interval (IBI) time series revealed evidence for two long-range correlated processes characterized by power laws in the IBI power spectral densities. One process dominates on short timescales (t < 8 beats) and reflects microtiming variability in the generation of single beats. The other dominates on longer timescales and reflects slow tempo variations. Whereas the latter did not show differences between musical genres (jazz vs. rock/pop), the process on short timescales showed higher variability for jazz recordings, indicating that jazz makes stronger use of microtiming fluctuations within a measure than rock/pop. Our results elucidate principles of rhythmic performance and can inspire algorithms for artificial music generation. By studying microtiming fluctuations in original music recordings, we bridge the gap between minimalistic tapping paradigms and expressive rhythmic performances.

Multiple scaling behaviour and nonlinear traits in music scores

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis (DFA). We find different fluctuation profiles that correspond to distinct autocorrelation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear autocorrelations by estimating the DFA of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.

The Effects of Pharmacological Compounds on Beat Rate Variations in Human Long QT-Syndrome Cardiomyocytes

Healthy human heart rate fluctuates overtime showing long-range fractal correlations. In contrast, various cardiac diseases and normal aging show the breakdown of fractal complexity. Recently, it was shown that human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) intrinsically exhibit fractal behavior as in humans. Here, we investigated the fractal complexity of hiPSC-derived long QT-cardiomyocytes (LQT-CMs). We recorded extracellular field potentials from hiPSC-CMs at baseline and under the effect of various compounds including β-blocker bisoprolol, ML277, a specific and potent I_Ks current activator, as well as JNJ303, a specific I_Ks blocker. From the peak-to-peak-intervals, we determined the long-range fractal correlations by using detrended fluctuation analysis. Electrophysiologically, the baseline corrected field potential durations (cFPDs) were more prolonged in LQT-CMs than in wildtype (WT)-CMs. Bisoprolol did not have significant effects to the cFPD in any CMs. ML277 shortened cFPD in a dose-dependent fashion by 11 % and 5–11 % in WT- and LQT-CMs, respectively. JNJ303 prolonged cFPD in a dose-dependent fashion by 22 % and 7–13 % in WT- and LQT-CMs, respectively. At baseline, all CMs showed fractal correlations as determined by short-term scaling exponent α. However, in all CMs, the α was increased when pharmacological compounds were applied indicating of breakdown of fractal complexity. These findings suggest that the intrinsic mechanisms contributing to the fractal complexity are not altered in LQT-CMs. The modulation of I_Ks channel and β1-adrenoreceptors by pharmacological compounds may affect the fractal complexity of the hiPSC-CMs.

Irregular Liesegang-type patterns in gas phase revisited. II. Statistical correlation analysis

We present a statistical analysis of Liesegang-type patterns formed in a gaseous HCl-NH3 system by ammonium chloride precipitation along glass tubes, as described in Paper I [J. C. Torres-Guzmán et al., J. Chem. Phys. 144, 174701 (2016)] of this work. We focus on the detection and characterization of short and long-range correlations within the non-stationary sequence of apparently irregular precipitation bands. To this end we applied several techniques to estimate spatial correlations stemming from different fields, namely, linear auto-correlation via the power spectral density, detrended fluctuation analysis (DFA), and methods developed in the context of random matrix theory (RMT). In particular RMT methods disclose well pronounced long-range correlations over at least 40 bands in terms of both, band positions and intensity values. By using a variant of the DFA we furnish proof of the nonlinear nature of the detected long-range correlations.

Bach Is the Father of Harmony: Revealed by a 1/f Fluctuation Analysis across Musical Genres

Harmony is a fundamental attribute of music. Close connections exist between music and mathematics since both pursue harmony and unity. In music, the consonance of notes played simultaneously partly determines our perception of harmony; associates with aesthetic responses; and influences the emotion expression. The consonance could be considered as a window to understand and analyze harmony. Here for the first time we used a 1/f fluctuation analysis to investigate whether the consonance fluctuation structure in music with a wide range of composers and genres followed the scale free pattern that has been found for pitch, melody, rhythm, human body movements, brain activity, natural images and geographical features. We then used a network graph approach to investigate which composers were the most influential both within and across genres. Our results showed that patterns of consonance in music did follow scale-free characteristics, suggesting that this feature is a universally evolved one in both music and the living world. Furthermore, our network analysis revealed that Bach’s harmony patterns were having the most influence on those used by other composers, followed closely by Mozart.

Fluctuations of hi-hat timing and dynamics in a virtuoso drum track of a popular music recording

Long-range correlated temporal fluctuations in the beats of musical rhythms are an inevitable consequence of human action. According to recent studies, such fluctuations also lead to a favored listening experience. The scaling laws of amplitude variations in rhythms, however, are widely unknown. Here we use highly sensitive onset detection and time series analysis to study the amplitude and temporal fluctuations of Jeff Porcaro’s one-handed hi-hat pattern in “I Keep Forgettin’”—one of the most renowned 16th note patterns in modern drumming. We show that fluctuations of hi-hat amplitudes and interbeat intervals (times between hits) have clear long-range correlations and short-range anticorrelations separated by a characteristic time scale. In addition, we detect subtle features in Porcaro’s drumming such as small drifts in the 16th note pulse and non-trivial periodic two-bar patterns in both hi-hat amplitudes and intervals. Through this investigation we introduce a step towards statistical studies of the 20th and 21st century music recordings in the framework of complex systems. Our analysis has direct applications to the development of drum machines and to drumming pedagogy.

Improvisation and the self-organization of multiple musical bodies

Understanding everyday behavior relies heavily upon understanding our ability to improvise, how we are able to continuously anticipate and adapt in order to coordinate with our environment and others. Here we consider the ability of musicians to improvise, where they must spontaneously coordinate their actions with co-performers in order to produce novel musical expressions. Investigations of this behavior have traditionally focused on describing the organization of cognitive structures. The focus, here, however, is on the ability of the time-evolving patterns of inter-musician movement coordination as revealed by the mathematical tools of complex dynamical systems to provide a new understanding of what potentiates the novelty of spontaneous musical action. We demonstrate this approach through the application of cross wavelet spectral analysis, which isolates the strength and patterning of the behavioral coordination that occurs between improvising musicians across a range of nested time-scales. Revealing the sophistication of the previously unexplored dynamics of movement coordination between improvising musicians is an important step toward understanding how creative musical expressions emerge from the spontaneous coordination of multiple musical bodies.

The causal inference of cortical neural networks during music improvisations

We present an EEG study of two music improvisation experiments. Professional musicians with high level of improvisation skills were asked to perform music either according to notes (composed music) or in improvisation. Each piece of music was performed in two different modes: strict mode and "let-go" mode. Synchronized EEG data was measured from both musicians and listeners. We used one of the most reliable causality measures: conditional Mutual Information from Mixed Embedding (MIME), to analyze directed correlations between different EEG channels, which was combined with network theory to construct both intra-brain and cross-brain networks. Differences were identified in intra-brain neural networks between composed music and improvisation and between strict mode and "let-go" mode. Particular brain regions such as frontal, parietal and temporal regions were found to play a key role in differentiating the brain activities between different playing conditions. By comparing the level of degree centralities in intra-brain neural networks, we found a difference between the response of musicians and the listeners when comparing the different playing conditions.

Embodiment of intersubjective time: relational dynamics as attractors in the temporal coordination of interpersonal behaviors and experiences

This paper addresses the issue of “being together,” and more specifically the issue of “being together in time.” We provide with an integrative framework that is inspired by phenomenology, the enactive approach and dynamical systems theories. To do so, we first define embodiment as a living and lived phenomenon that emerges from agent-world coupling. We then show that embodiment is essentially dynamical and therefore we describe experiential, behavioral and brain dynamics. Both lived temporality and the temporality of the living appear to be complex, multiscale phenomena. Next we discuss embodied dynamics in the context of interpersonal interactions, and briefly review the empirical literature on between-persons temporal coordination. Overall, we propose that being together in time emerges from the relational dynamics of embodied interactions and their flexible co-regulation.

Long-range correlation properties in timing of skilled piano performance: the influence of auditory feedback and deep brain stimulation

Unintentional timing deviations during musical performance can be conceived of as timing errors. However, recent research on humanizing computer-generated music has demonstrated that timing fluctuations that exhibit long-range temporal correlations (LRTC) are preferred by human listeners. This preference can be accounted for by the ubiquitous presence of LRTC in human tapping and rhythmic performances. Interestingly, the manifestation of LRTC in tapping behavior seems to be driven in a subject-specific manner by the LRTC properties of resting-state background cortical oscillatory activity. In this framework, the current study aimed to investigate whether propagation of timing deviations during the skilled, memorized piano performance (without metronome) of 17 professional pianists exhibits LRTC and whether the structure of the correlations is influenced by the presence or absence of auditory feedback. As an additional goal, we set out to investigate the influence of altering the dynamics along the cortico-basal-ganglia-thalamo-cortical network via deep brain stimulation (DBS) on the LRTC properties of musical performance. Specifically, we investigated temporal deviations during the skilled piano performance of a non-professional pianist who was treated with subthalamic-deep brain stimulation (STN-DBS) due to severe Parkinson's disease, with predominant tremor affecting his right upper extremity. In the tremor-affected right hand, the timing fluctuations of the performance exhibited random correlations with DBS OFF. By contrast, DBS restored long-range dependency in the temporal fluctuations, corresponding with the general motor improvement on DBS. Overall, the present investigations demonstrate the presence of LRTC in skilled piano performances, indicating that unintentional temporal deviations are correlated over a wide range of time scales. This phenomenon is stable after removal of the auditory feedback, but is altered by STN-DBS, which suggests that cortico-basal ganglia-thalamocortical circuits play a role in the modulation of the serial correlations of timing fluctuations exhibited in skilled musical performance.

What musicians do to induce the sensation of groove in simple and complex melodies, and how listeners perceive it

Groove is the experience of wanting to move when hearing music, such as snapping fingers or tapping feet. This is a central aspect of much music, in particular of music intended for dancing. While previous research has found considerable consistency in ratings of groove across individuals, it remains unclear how groove is induced, that is, what are the physical properties of the acoustic signal that differ between more and less groove-inducing versions. Here, we examined this issue with a performance experiment, in which four musicians performed six simple and six complex melodies in two conditions with the intention of minimizing and maximizing groove. Analyses of rhythmical and temporal properties from the performances demonstrated some general effects. For example, more groove was associated with more notes on faster metrical levels and syncopation, and less groove was associated with deadpan timing and destruction of the regular pulse. We did not observe that deviations from the metrical grid [i.e., micro-timing (MT)] were a predictor of groove. A listener experiment confirmed that the musicians' manipulations had the intended effects on the experience of groove. A Brunswikian lens model was applied, which estimates the performer-perceiver communication across the two experiments. It showed that the communication achievement for simple melodies was 0.62, and that the matching of performers' and listeners' use of nine rhythmical cues was 0.83. For complex melodies with an already high level of groove, the corresponding values were 0.39 and 0.34, showing that it was much more difficult to "take out" groove from musical structures designed to induce groove.

Synchronization in human musical rhythms and mutually interacting complex systems

Though the music produced by an ensemble is influenced by multiple factors, including musical genre, musician skill, and individual interpretation, rhythmic synchronization is at the foundation of musical interaction. Here, we study the statistical nature of the mutual interaction between two humans synchronizing rhythms. We find that the interbeat intervals of both laypeople and professional musicians exhibit scale-free (power law) cross-correlations. Surprisingly, the next beat to be played by one person is dependent on the entire history of the other person's interbeat intervals on timescales up to several minutes. To understand this finding, we propose a general stochastic model for mutually interacting complex systems, which suggests a physiologically motivated explanation for the occurrence of scale-free cross-correlations. We show that the observed long-term memory phenomenon in rhythmic synchronization can be imitated by fractal coupling of separately recorded or synthesized audio tracks and thus applied in electronic music. Though this study provides an understanding of fundamental characteristics of timing and synchronization at the interbrain level, the mutually interacting complex systems model may also be applied to study the dynamics of other complex systems where scale-free cross-correlations have been observed, including econophysics, physiological time series, and collective behavior of animal flocks.

How do online social networks grow?

Online social networks such as Facebook, Twitter and Gowalla allow people to communicate and interact across borders. In past years online social networks have become increasingly important for studying the behavior of individuals, group formation, and the emergence of online societies. Here we focus on the characterization of the average growth of online social networks and try to understand which are possible processes behind seemingly long-range temporal correlated collective behavior. In agreement with recent findings, but in contrast to Gibrat's law of proportionate growth, we find scaling in the average growth rate and its standard deviation. In contrast, Renren and Twitter deviate, however, in certain important aspects significantly from those found in many social and economic systems. Whereas independent methods suggest no significance for temporally long-range correlated behavior for Renren and Twitter, a scaling analysis of the standard deviation does suggest long-range temporal correlated growth in Gowalla. However, we demonstrate that seemingly long-range temporal correlations in the growth of online social networks, such as in Gowalla, can be explained by a decomposition into temporally and spatially independent growth processes with a large variety of entry rates. Our analysis thus suggests that temporally or spatially correlated behavior does not play a major role in the growth of online social networks.

The microfluidic jukebox

Music is a form of art interweaving people of all walks of life. Through subtle changes in frequencies, a succession of musical notes forms a melody which is capable of mesmerizing the minds of people. With the advances in technology, we are now able to generate music electronically without relying solely on physical instruments. Here, we demonstrate a musical interpretation of droplet-based microfluidics as a form of novel electronic musical instruments. Using the interplay of electric field and hydrodynamics in microfluidic devices, well controlled frequency patterns corresponding to musical tracks are generated in real time. This high-speed modulation of droplet frequency (and therefore of droplet sizes) may also provide solutions that reconciles high-throughput droplet production and the control of individual droplet at production which is needed for many biochemical or material synthesis applications.

Dynamic musical communication of core affect

Is there something special about the way music communicates feelings? Theorists since Meyer (1956) have attempted to explain how music could stimulate varied and subtle affective experiences by violating learned expectancies, or by mimicking other forms of social interaction. Our proposal is that music speaks to the brain in its own language; it need not imitate any other form of communication. We review recent theoretical and empirical literature, which suggests that all conscious processes consist of dynamic neural events, produced by spatially dispersed processes in the physical brain. Intentional thought and affective experience arise as dynamical aspects of neural events taking place in multiple brain areas simultaneously. At any given moment, this content comprises a unified "scene" that is integrated into a dynamic core through synchrony of neuronal oscillations. We propose that (1) neurodynamic synchrony with musical stimuli gives rise to musical qualia including tonal and temporal expectancies, and that (2) music-synchronous responses couple into core neurodynamics, enabling music to directly modulate core affect. Expressive music performance, for example, may recruit rhythm-synchronous neural responses to support affective communication. We suggest that the dynamic relationship between musical expression and the experience of affect presents a unique opportunity for the study of emotional experience. This may help elucidate the neural mechanisms underlying arousal and valence, and offer a new approach to exploring the complex dynamics of the how and why of emotional experience.

Thalamocortical mechanisms for integrating musical tone and rhythm

Studies over several decades have identified many of the neuronal substrates of music perception by pursuing pitch and rhythm perception separately. Here, we address the question of how these mechanisms interact, starting with the observation that the peripheral pathways of the so-called "Core" and "Matrix" thalamocortical system provide the anatomical bases for tone and rhythm channels. We then examine the hypothesis that these specialized inputs integrate acoustic content within rhythm context in auditory cortex using classical types of "driving" and "modulatory" mechanisms. This hypothesis provides a framework for deriving testable predictions about the early stages of music processing. Furthermore, because thalamocortical circuits are shared by speech and music processing, such a model provides concrete implications for how music experience contributes to the development of robust speech encoding mechanisms.

Long-range temporal correlations in resting-state α oscillations predict human timing-error dynamics

Human behavior is imperfect. This is notably clear during repetitive tasks in which sequences of errors or deviations from perfect performance result. These errors are not random, but show patterned fluctuations with long-range temporal correlations that are well described using power-law spectra P(f)∝1/f(β), where β is the power-law scaling exponent describing the decay in temporal correlations. The neural basis of temporal correlations in such behaviors is not known. Interestingly, long-range temporal correlations are a hallmark of amplitude fluctuations in resting-state neuronal oscillations. Here, we investigated whether the temporal dynamics in brain and behavior are related. Thirty-nine subjects' eyes-open rest EEG was measured. Next, subjects reproduced without feedback a 1 s interval by tapping with their right index finger. In line with previous reports, we found evidence for the presence of long-range temporal correlations both in the amplitude modulation of resting-state oscillations in multiple frequency bands and in the timing-error sequences. Frequency scaling exponents of finger tapping and amplitude modulation of oscillations exhibited large individual differences. Neuronal dynamics of resting-state alpha-band oscillations (9-13 Hz) recorded at precentral sites strongly predicted scaling exponents of tapping behavior. The results suggest that individual variation in resting-state brain dynamics offer a neural explanation for individual variation in the error dynamics of human behavior.

Note onset deviations as musical piece signatures

A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.

Fractal dynamics in chaotic quantum transport

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

Affect and non-uniform characteristics of predictive processing in musical behaviour

The important roles of prediction and prior experience are well established in music research and fit well with Clark's concept of unified perception, cognition, and action arising from hierarchical, bidirectional predictive processing. However, in order to fully account for human musical intelligence, Clark needs to further consider the powerful and variable role of affect in relation to prediction error.

Unravelling daily human mobility motifs

Human mobility is differentiated by time scales. While the mechanism for long time scales has been studied, the underlying mechanism on the daily scale is still unrevealed. Here, we uncover the mechanism responsible for the daily mobility patterns by analysing the temporal and spatial trajectories of thousands of persons as individual networks. Using the concept of motifs from network theory, we find only 17 unique networks are present in daily mobility and they follow simple rules. These networks, called here motifs, are sufficient to capture up to 90 per cent of the population in surveys and mobile phone datasets for different countries. Each individual exhibits a characteristic motif, which seems to be stable over several months. Consequently, daily human mobility can be reproduced by an analytically tractable framework for Markov chains by modelling periods of high-frequency trips followed by periods of lower activity as the key ingredient.