Does expressive timing in music performance scale proportionally with tempo?

Summary Evidence is presented that expressive timing in music is not relationally invariant with global tempo. Our results stem from an analysis of repeated performances of Beethoven's variations on a Paisiello theme. Recordings were made of two pianists playing the pieces at three tempi. In contrast with the relational-invariance hypothesis (see Repp, 1994), between-tempo correlations were in general lower than within-tempo correlations. Analyses of variance of log-transformed inter-onset intervals (IOIs) showed significant interactions between tempo and IOI, i. e., evidence against a proportional relation between timing and tempo. Complex, but consistent, nonproportional patterns were shown in the analyses of the timing of the grace notes in the piece. The analysis suggests that timing aspects of music are closely linked to the musical structure and can be studied and manipulated only respecting this relation — not as a global timing pattern or tempo curve. Finally, it is shown that methodological issues of data collection and analysis had a significant influence on the results.     

The effect of tempo on pedal timing in piano performance

The temporal coordination of hand and foot actions in piano performance is an interesting instance of highly practiced, perceptually guided complex motor behavior. To gain some insight into the nature of this coordination, ten pianists were asked to play two excerpts from the piano literature that required repeated use of the damper pedal to connect successive chords. Each excerpt was played at three prescribed tempos on a Yamaha Disklavier and was recorded in MIDI format. The question of interest was whether and how changes in tempo would affect the timing of pedal releases and depressions within the periods defined by successive manual chord onsets. Theoretical possibilities ranged from absolute invariance (variable phase relationships) to relative invariance of pedal timing (constant phase relationships). The results show that, typically, the timing of pedal actions is neither absolutely nor relatively invariant: As the tempo increases, both pedal releases and depressions usually occur a little sooner and pedal changes (release-depression sequences) are executed a little more quickly, but these effects are proportionally smaller than the changes in manual (and pedal) period duration. Since this may be due to unequal changes in peripheral hand and foot kinematics with tempo, it remains possible that there is invariance of either kind at the level of central motor commands. However, it is the peripheral timing that produces the acoustic consequences musicians try to achieve.     

Variability of timing in expressive piano performance increases with interval duration

In simple motor tasks such as finger tapping at different constant rates, within-trial variability of response interonset intervals (IOIs) increases with IOI duration (which varies between trials). In expressive piano performance, the rate of key depressions is not constant, in part due to compositional structure and in part due to expressive timing, so that IOIs of many different durations occur within a single “trial.” Nevertheless, across repeated performances of the same music (Schumann’s “Träumerei” and Debussy’s “La fille aux cheveux de lin”) at the same intended tempo, the standard deviations of individual IOIs tend to increase linearly with their average duration. This is also true when the variation is due to expressive timing alone and when unintended differences in basic tempo between performances are taken into account. In the music studied here, at least, there was no evidence of compensatory timing. The results suggest that the pianists employed a continuously variable tempo governed by a flexible internal timekeeper whose variability follows a generalized Weber’s law (for IOIs longer than about 300 msec).     

Evidence for tempo-specific timing in music using a web-based experimental setup

Perceptual invariance has been studied and found in several domains of cognition, including those of speech, motor behavior, and object motion. It has also been the topic of several studies in music perception. However, the existing perceptual studies present rather inconclusive evidence with regard to the perceptual invariance of expressive timing under tempo transformation in music performance. The current study used a novel experimental methodology that took advantage of new technologies, such as an online Internet setup, high-quality audio, and state-of-the-art tempo-transformation techniques. The results show that listeners could detect which was the original performance when asked to compare 2 recordings, 1 of which was tempo-transformed to make both similar in overall tempo. This result is taken as support for the tempo-specific timing hypothesis--which predicts that a tempo-transformed performance will sound less natural than an original performance--and as counterevidence for the relationally invariant timing hypothesis, which predicts that a tempo-transformed performance will sound equally natural.     

Mapping musical thought to musical performance

Expressive timing methods are described that map pianists' musical thoughts to sounded performance. In Experiment 1, 6 pianists performed the same musical excerpt on a computer-monitored keyboard. Each performance contained 3 expressive timing patterns: chord asynchronies, rubato patterns, and overlaps (staccato and legato). Each pattern was strongest in experienced pianists' performances and decreased when pianists attempted to play unmusically. In Experiment 2 pianists performed another musical excerpt and notated their musical intentions on an unedited score. The notated interpretations correlated with the presence of the 3 methods: The notated melody preceded other events in chords (chord asynchrony); events notated as phase boundaries showed greatest tempo changes (rubato); and the notated melody showed most consistent amount of overlap between adjacent events (staccato and legato). These results suggest that the mapping of musical thought to musical action is rule-governed, and the same rules produce different interpretations.     

Testing a Bifactor Model of Relational and Physical Aggression in Early Childhood

Different approaches have been used to classify children as relationally aggressive, physically aggressive, or both relationally and physically aggressive (co-occurring aggression). The goal of the current study (N = 164, 50.9% boys, M _age = 47.75 months, SD = 7.37) was to test a bifactor model of aggression, which allows for aggression to be assessed dimensionally, and postulates a co-occurring aggression factor as well as unique relational and physical aggression factors, during early childhood. Aggression was measured using reliable observer and teacher reports of physical and relational aggression subscales. The two-factor model was an adequate fit to the data but the bifactor model was a significant improvement in model fit compared to the two-factor model. Alternative statistics for evaluating bifactor models were used in the current study. The measurement invariance (e.g., configural invariance, metric invariance, and scalar invariance) of the bifactor model was tested across gender and results from the bifactor model using teacher report showed that the model was invariant across gender. Lastly, the criterion validity of the model was examined by evaluating the relations between the bifactor model and observations of physical and relational aggression and results generally supported the validity of the bifactor model. Overall, results suggest that a bifactor model of aggression may be a useful method for studying aggression in early childhood.     

Perceived tempo change is dependent on base tempo and direction of change: Evidence for a generalized version of Schulze's (1978) internal beat model

Assumptions of a theory, still influential, of tempo perception by Schulze (1978) are reconsidered in view of counter-evidence from other time-perception and timing studies. Specifically, it is shown that the role of base tempo of stimuli and the orientation of tempo change (acceleration versus deceleration) have to be incorporated in them. Therefore, Schulze's assumptions were extended so as to include the two stimulus parameters. A generalized version of Schulze's internal beat model, one of three formal elaborations of the theory, was tested in an experiment which required subjects (N = 17) to tell the direction of change (acceleration or deceleration) in metronomic tone sequences presented at tempi of 1, 2, or 4 Hz, the amount of tempo change being varied in steps of 2% between –10% (acceleration) and + 10%, including zero change. Psychometric curves obtained from logistic regression analysis showed the limitation of the original assumptions and supported the proposed generalization of Schulze's model. The validity of the theoretical interpretation of the data was discussed with respect to some methodological constraints in the experiment, such as the presentation of the different tempo conditions and the time length of the metronomic stimuli used, and with respect to their applicability to the performance of expressive drift (rubato versus accelerando) in music.     

Perceiving action identity: how pianists recognize their own performances

Can skilled performers, such as artists or athletes, recognize the products of their own actions? We recorded 12 pianists playing 12 mostly unfamiliar musical excerpts, half of them on a silent keyboard. Several months later, we played these performances back and asked the pianists to use a 5-point scale to rate whether they thought they were the person playing each excerpt (1 = no, 5 = yes). They gave their own performances significantly higher ratings than any other pianist's performances. In two later follow-up tests, we presented edited performances from which differences in tempo, overall dynamic (i.e., intensity) level, and dynamic nuances had been removed. The pianists' ratings did not change significantly, which suggests that the remaining information (expressive timing and articulation) was sufficient for self-recognition. Absence of sound during recording had no significant effect. These results are best explained by the hypothesis that an observer's action system is most strongly activated during perception of self-produced actions.     

Control of Expressive and Metronomic Timing in Pianists

In 12 tasks, each including 10 repetitions, 6 skilled pianists performed or responded to a musical excerpt. In the first 6 tasks, expressive timing was required; in the last 6 tasks, metronomic timing. The pianists first played the music on a digital piano (Tasks 1 and 7), then played it without auditory feedback (Tasks 2 and 8), then tapped on a response key in synchrony with one of their own performances (Tasks 3 and 9), with an imagined performance (Tasks 4 and 10), with a computer-generated performance (Tasks 5 and 11), and with a computer-generated sequence of clicks (Tasks 6 and 12). The results demonstrated that pianists are capable of generating the expressive timing pattern of their performance in the absence of auditory and kinaesthetic (piano keyboard) feedback. They can also synchronize their finger taps quite well with expressively timed music or clicks (while imagining the music), although they tend to underestimate long interonset intervals and to compensate on the following tap. Expressive timing is thus shown to be generated from an internal representation of the music. In metronomic performance, residual expressive timing effects were evident. Those did not depend on auditory feedback, but they were much reduced or absent when kinaesthetic feedback from the piano keyboard was eliminated. Thus, they seemed to arise from the pianist's physical interaction with the instrument. Systematic timing patterns related to expressive timing were also observed in synchronization with a metronomic computer performance and even in synchronization with metronomic clicks. These results shed light on intentional and unintentional, structurally governed processes of timing control in music performance.     

Individual differences in the biomechanical effect of loudness and tempo on upper-limb movements during repetitive piano keystrokes

The present study addressed the effect of loudness and tempo on kinematics and muscular activities of the upper extremity during repetitive piano keystrokes. Eighteen pianists with professional music education struck two keys simultaneously and repetitively with a combination of four loudness levels and four tempi. The results demonstrated a significant interaction effect of loudness and tempo on peak angular velocity for the shoulder, elbow, wrist and finger joints, mean muscular activity for the corresponding flexors and extensors, and their co-activation level. The interaction effect indicated greater increases with tempo when eliciting louder tones for all joints and muscles except for the elbow velocity showing a greater decrease with tempo. Multiple-regression analysis and K-means clustering further revealed that 18 pianists were categorized into three clusters with different interaction effects on joint kinematics. These clusters were characterized by either an elbow-velocity decrease and a finger-velocity increase, a finger-velocity decrease with increases in shoulder and wrist velocities, or a large elbow-velocity decrease with a shoulder-velocity increase when increasing both loudness and tempo. Furthermore, the muscular load considerably differed across the clusters. These findings provide information to determine muscles with the greatest potential risk of playing-related disorders based on movement characteristics of individual pianists.     

Conscientiousness and Extraversion relate to responsiveness to tempo in dance

Previous research has shown broad relationships between personality and dance, but the relationship between personality and specific structural features of music has not been explored. The current study explores the influence of personality and trait empathy on dancers’ responsiveness to small tempo differences between otherwise musically identical stimuli, measured by difference in the amount in acceleration of key joints. Thirty participants were recorded using motion capture while dancing to excerpts from six popular songs that were time-stretched to be slightly faster or slower than their original tempi. Analysis revealed that higher conscientiousness and lower extraversion both correlated with greater responsiveness to tempo change. Partial correlation analysis revealed that conscientiousness remained significantly correlated with responsiveness when extraversion was controlled, but not vice versa. No effect of empathy was found. Implications are discussed.     

Timing in solo and duet piano performances

Perhaps some of the most refined forms of timing arise in musical performance, particularly in the coordination between musicians playing together. Studies of timing in solo and duet piano performances are described, in which the musicians gave repeat performances of the music. In both solo and duet performances there was expressive use of timing, modulating the tempo of the music and the phase relationship between the voices, and the expressive forms were similar in successive performances of the piece. There was also evidence of separate timing control of the metre and of the production of notes and rests. Thus timing in musical performance is best modelled by assuming two levels of timekeeper, one pacing the metre and the other contained in the movement trajectories of note production, computed by motor procedure in relation to the metre. It is argued that expressive forms are derived from an interpretation of the music rather than memorized; and that coordination between voices in the music is achieved at the level of the metre.     

The influence of proximal motor strategies on pianists' upper-limb movement variability

Repetitive movements are considered a risk factor for developing practice-related musculoskeletal disorders. Intra-participant kinematic variability might help musicians reduce the risk of injury during repetitive tasks. No research has studied the effects of proximal motion (i.e., trunk and shoulder movement) on upper-limb movement variability in pianists. The first objective was to determine the effect of proximal movement strategies and performance tempo on both intra-participant joint angle variability of upper-limb joints and endpoint variability. The second objective was to compare joint angle variability between pianist's upper-limb joints. As secondary objectives, we assessed the relationship between intra-participant joint angle variability and task range of motion (ROM) and documented inter-participant joint angle variability. The upper body kinematics of 9 expert pianists were recorded using an optoelectronic system. Participants continuously performed two right-hand chords (lateral leap motions) while changing movements based on trunk motion (with and without) and shoulder motion (counter-clockwise, back-and-forth, and clockwise) at two tempi (slow and fast). Trunk and shoulder movement strategies collectively influenced variability at the shoulder, elbow and, to a lesser extent, the wrist. Slow tempi led to greater variability at wrist and elbow flexion/extension compared to fast tempi. Endpoint variability was influenced only along the anteroposterior axis. When the trunk was static, the shoulder had the lowest joint angle variability. When trunk motion was used, elbow and shoulder variability increased, and became comparable to wrist variability. ROM was correlated with intra-participant joint angle variability, suggesting that increased task ROM might result in increased movement variability during practice. Inter-participant variability was approximately six times greater than intra-participant variability. Pianists should consider incorporating trunk motion and a variety of shoulder movements as performance strategies while performing leap motions at the piano, as they might reduce exposure to risks of injury.     

Skill acquisition in music performance: relations between planning and temporal control

We investigated the acquisition of music performance skills in novice and expert pianists. Temporal disruptions in novice performances coincided with constraints in planning capacities. Child and adult pianists ranging in age (9-26 years), training (3-15 years) and sight-reading ability learned to perform a novel musical piece in eleven practice trials. Computer-detected pitch and timing errors revealed: (1) gradual improvements in performance tempo and pitch accuracy with skill level and practice, generally fitting a power function; (2) a relative-timing/pitch accuracy trade-off and high incidence of simultaneous pitch/time errors; (3) improvements in relative timing (temporal continuity, underlying beat, metrical structure) with skill and practice; and (4) increased anticipatory behavior and a greater range of planning with skill and practice. A strong positive relationship between the mastery of temporal constraints and planning abilities within performance suggests that these two cognitive indicators are closely related and may arise from segmentation processes during performance. Examination of sequence timing may explicate planning abilities that underlie many complex skills.     

The perception of tempo in music

Tempo is one factor that is frequently associated with the expressive nature of a piece of music. Composers often indicate the tempo of a piece of music through the use of numerical markings (beats min(-1)) and subjective terms (adagio, allegro). Three studies were conducted to assess whether listeners were able to make consistent judgments about tempo that varied from piece to piece. Listeners heard short extracts of Scottish music played at a range of tempi and were asked to make a two-alternative forced choice of "too fast" or "too slow" for each extract. The responses for each study were plotted as proportion of too fast responses as a function of tempo for each piece, and cumulative normal curves were fitted to each data set. The point where these curves cross 0.5 is the tempo at which the music sounds right to the listeners, referred to as the optimal tempo. The results from each study show that listeners are capable of making consistent tempo judgments and that the optimal tempo varies across extracts. The results also revealed that rhythm plays a role, but not the only role in making temporal judgments.     

Detectability of duration and intensity increments in melody tones: A partial connection between music perception and performance

Two experiments demonstrate positional variation in the relative detectability of, respectively, local temporal and dynamic perturbations in an isochronous and isodynamic sequence of melody tones, played on a computer-controlled piano. This variation may reflect listeners’ expectations of expressive performance microstructure (thetop-down hypothesis), or it may be due to psychoacoustic (pitch-related) stimulus factors (thebottom-up hypothesis). Percent correct scores for increments in tone duration correlated significantly with the average timing profile of pianists’ expressive performances of the music, as predicted specifically by the top-down hypothesis. For intensity increments, the analogous perception-performance correlation was weak and the bottom-up factors of relative pitch height and/or direction of pitch change accounted for some of the perceptual variation. Subjects’ musical training increased overall detection accuracy but did not affect the positional variation in accuracy scores in either experiment. These results are consistent with the top-down hypothesis for timing, but they favor the bottom-up hypothesis for dynamics. The perception-performance correlation for timing may also be viewed as being due to complex stimulus properties such as tonal motion and tension/relaxation that influence performers and listeners in similar ways.     

Probing the cognitive representation of musical time: structural constraints on the perception of timing perturbations.

To determine whether structural factors interact with the perception of musical time, musically literate listeners were presented repeatedly with eight-bar musical excerpts, realized with physically regular timing on an electronic piano. On each trial, one or two randomly chosen time intervals were lengthened by a small amount, and the score. The resulting detection accuracy profile across all positions in each musical excerpt showed pronounced dips in places where lengthening would typically occur in an expressive (temporally modulated) performance. False alarm percentages indicated that certain tones seemed longer a priori, and these were among the ones whose actual lengthening was easiest to detect. The detection accuracy and false alarm profiles were significantly correlated with each other and with the temporal microstructure of expert performances, as measured from sound recordings by famous artists. Thus the detection task apparently tapped into listeners' musical thought and revealed their expectations about the temporal microstructure of music performance. These expectations, like the timing patterns of actual performances, derive from the cognitive representation of musical structure, as cued by a variety of systemic factors (grouping, meter, harmonic progression) and their acoustic correlates. No simple psycho-acoustic explanation of the detection accuracy profiles was evident. The results suggest that the perception of musical time is not veridical but "warped" by the structural representation. This warping may provide a natural basis for performance evaluation: expected timing patterns sound more or less regular, unexpected ones irregular. Parallels to language performance and perception are noted.     

Learning expressive percussion performance under different visual feedback conditions

A study was conducted to test the effect of two different forms of real-time visual feedback on expressive percussion performance. Conservatory percussion students performed imitations of recorded teacher performances while receiving either high-level feedback on the expressive style of their performances, low-level feedback on the timing and dynamics of the performed notes, or no feedback. The high-level feedback was based on a Bayesian analysis of the performances, while the low-level feedback was based on the raw participant timing and dynamics data. Results indicated that neither form of feedback led to significantly smaller timing and dynamics errors. However, high-level feedback did lead to a higher proficiency in imitating the expressive style of the target performances, as indicated by a probabilistic measure of expressive style. We conclude that, while potentially disruptive to timing processes involved in music performance due to extraneous cognitive load, high-level visual feedback can improve participant imitations of expressive performance features.