Perceiving musical tension in long chord sequences

We attempted to predict perceived musical tension in longer chord sequences by hierarchic and sequential models based on Lerdahl and Jackendoff's and Lerdahl's cognitive theories and on Parncutt's sensory-psychoacoustical theory. Musicians and nonmusicians were asked to rate the perceived tension of chords which were drawn either from a piece composed for the study (Exp. 1) or from a Chopin Prelude (Exps. 2–4). In Exps. 3 and 4, several experimental manipulations were made to emphasize either the global or the local structure of the piece and to verify how these manipultions would affect the respective contribution of the models in the ratings. In all experiments, musical tension was only weakly influenced by global harmonic structure. Instead, it mainly seemed to be determined locally, by harmonic cadences. The hierarchic model of Lerdahl and Jackendoff provided the best fit to tension ratings, not because it accounted for global hierarchic effects, but because it captured the local effect of cadences. By reacting to these local structures, tension ratings fit quite well with a hierarchic model, even though the participants were relatively insensitive to the global structure of the pieces. As a main outcome, it is argued that musical events were perceived through a short perceptual window sliding from cadence to cadence along a sequence. Received: 24 March 1997 / Accepted: 10 May 1998     

Influence of tonal and temporal expectations on chord processing and on completion judgments of chord sequences

Pitch and time are two principal form-bearing dimensions in Western tonal music. Research on melody perception has shown that listeners develop expectations about "What" note is coming next and "When" in time it will occur. Our study used sequences of chords (i.e., simultaneously sounding notes) to investigate the influence of these expectations on chord processing (Experiments 1 and 4) and subjective judgments of completion (Experiments 2 and 3). Both tasks showed an influence of tonal relations and temporal regularities: expected events occurring at the expected moment were processed faster and led to higher completion judgments. However, pitch and time dimensions interacted only for completion judgments. The present outcome suggests that for chord perception the influence of pitch and time might depend on the required processing: with a more global judgment favoring interactive influences in contrast to a task focusing on local chord processing.     

Exploring task-set reconfiguration with random task sequences

Switching between two different tasks normally results in an impairment in people's performance known as a switch cost, typically measured as an increase in reaction time (RT) and errors compared to a situation in which no task switch is required. Researchers in task switching have suggested that this switch cost is the behavioural manifestation of the task set reconfiguration processes that are necessary to perform the upcoming task. However, an examination of the literature in task switching reveals apparently contradictory results about the nature of task set reconfiguration processes. In Experiment 1, we addressed this issue by comparing participants' performance in two different experimental conditions: predictable task switching and random task switching. In the predictable switch condition the switch cost completely vanished after the first repetition of the new task. However, in the random switch condition, while the difference between switch and repetition trials was not significant, we observed a significant reduction in RT between the first and second repetition of the new task. In Experiment 2, we further investigated the pattern of task set reconfiguration in the random switch situation. The results showed a progressive reduction of participants' response latencies across repetitions of the same task. The present study demonstrates that, whereas the results in predictable switching conditions are compatible with an exogenous-reconfiguration hypothesis, random task switching produces a more gradual, decay-like switch cost reduction with task repetition.     

Effects of random reinforcement sequences

Rats were exposed to a random sequence of reinforcement on two levers, such that there was no way to predict from the previous reinforcement which lever would deliver reinforcement next. The rats showed a tendency to repeat the choice that had just produced reinforcement, despite the absence of an overall contingency that differentially reinforced such repetition. However, this tendency decreased with continued exposure to the schedule. Runs of successive reinforcements on a lever increased the probability of pressing that lever, but only slightly, and only in the earlier phases of training. The more quickly a press was made after reinforcement the more likely it was to be on the lever that had delivered that reinforcement. Repetition of choice followed by reinforcement should be viewed as a naturally occurring behavior in the rat, but not necessarily as a behavior that will continue without differential reinforcement of repetition.     

Perception of musical tension in short chord sequences: The influence of harmonic function,sensory dissonance,horizontal motion,and musical training

This study investigates the effect of four variables (tonal hierarchies, sensory chordal consonance, horizontal motion, and musical training) on perceived musical tension. Participants were asked to evaluate the tension created by a chord X in sequences of three chords {C major → X → C major} in a C major context key. The X chords could be major or minor triads major-minor seventh, or minor seventh chords built on the 12 notes of the chromatic scale. The data were compared with Krumhansl’s (1990) harmonic hierarchy and with predictions of Lerdahl’s (1988) cognitive theory, Hutchinson and Knopoff’s (1978) and Parncutt’s (1989) sensory-psychoacoustical theories, and the model of horizontal motion defined in the paper. As a main outcome, it appears that judgments of tension arose from a convergence of several cognitive and psychoacoustics influences, whose relative importance varies, depending on musical training.     

Searching for patterns in random sequences.

In a probability-guessing paradigm, participants predict which of two events will occur on each trial. Participants generally frequency match even though frequency matching is nonoptimal with random sequences. The optimal strategy is to guess the most frequent event, maximizing. We hypothesize that frequency matching results from a search for patterns, even in random sequences. Using both callisotomy patients and patients with frontal brain damage, Wolford, Miller, and Gazzaniaga (2000) found frequency matching in the left hemisphere but maximizing in the right hemisphere. In this paper, we show that a secondary task that competes for left hemisphere resources moves the participants toward maximizing but that a right-hemisphere task preserves frequency matching. We also show that a misunderstanding of randomness contributes to frequency matching.     

Hierarchical motion organization in random dot configurations

Motion organization has 2 aspects: the extraction of a (moving) frame of reference and the hierarchical organization of moving elements within the reference frame. Using a discrimination of relative motions task, the authors found large differences between different types of motion (translation, divergence, and rotation) in the degree to which each can serve as a moving frame of reference. Translation and divergence are superior to rotation. There are, however, situations in which rotation can serve as a reference frame. This is due to the presence of a second factor, structural invariants (SIs). SIs are spatial relationships persisting among the elements within a configuration such as a collinearity among points or one point coinciding with the center of rotation for another (invariant radius). The combined effect of these 2 factors--motion type and SIs-influences perceptual motion organization.     

Perceived motion is influenced by random dynamic information

Distortions of the local spatial-frequency power spectrum caused by motion blur may be used by the visual system to improve motion analysis (e.g., Barlow and Olshausen, 2004 Journal of Vision 4415-426). We tested this hypothesis by measuring the error of perceived motion direction of moving patterns in the presence of random noncoherent motion manipulated to create different spatial power spectra. The results showed that error increased when the background power spectrum was similar to the motion power spectrum; however, when the background power spectrum had an anisotropy consistent with motion blur, the error was reduced. Shifting the power spectrum away from the motion power spectrum reduced the error.     

Visible persistence is reduced by fixed-trajectory motion but not by random motion.

Despite the sluggish temporal response of the human visual system, moving objects appear clear and without blur, which suggests that visible persistence is reduced when objects move. It has been argued that spatiotemporal proximity alone can account for this modulation of visible persistence and that activation of a motion mechanism per se is not necessary. Experiments are reported which demonstrate that there is a motion-specific influence on visible persistence. Specifically, points moving in constant directions, or fixed trajectories, show less persistence than points moving with the same spatial and temporal displacements but taking random walks, randomly changing direction each frame. Subjects estimated the number of points present in the display for these two types of motion conditions. Under conditions chosen to produce 'good' apparent motion, ie small temporal and spatial increments, the apparent number of points for the fixed-trajectory condition was significantly lower than the apparent number in the random-walk condition. The traditional explanation of the suppression of persistence based on the spatiotemporal proximity of objects cannot account for these results. The enhanced suppression of persistence observed for a target moving in a consistent direction depends upon the activation of a directionally tuned motion mechanism extended over space and time.     

Beliefs about what types of mechanisms produce random sequences

Although many researchers use Wagenaar's framework for understanding the factors that people use to determine whether a process is random, the framework has never undergone empirical scrutiny. This paper uses Wagenaar's framework as a starting point and examines the three properties of his framework—independence of events, fixed alternatives, and equiprobability. We find strong evidence to suggest that independence of events is indeed used as a cue toward randomness. Equiprobability has an effect on randomness judgments. However, it appears to work only in a limited role. Fixedness of alternatives is a complex construct that consists of multiple sub‐concepts. We find that each of these sub‐concepts influences randomness judgments, but that they exert forces in different directions. Stability of outcome ratios increases randomness judgments, while knowledge of outcome ratios decreases randomness judgments. Future directions for development of a functional framework for understanding perceptions of randomness are suggested. Copyright © 2008 John Wiley & Sons, Ltd.     

Sensitivity to shearing and compressive motion in random dots

The sensitivity of the visual system to motion of differentially moving random dots was measured. Two kinds of one-dimensional motion were compared: standing-wave patterns where dot movement amplitude varied as a sinusoidal function of position along the axis of dot movement (longitudinal or compressional waves) and patterns of motion where dot movement amplitude varied as a sinusoidal function orthogonal to the axis of motion (transverse or shearing waves). Spatial frequency, temporal frequency, and orientation of the motion were varied. The major finding was a much larger threshold rise for shear than for compression when motion spatial frequency increased beyond 1 cycle deg-1. Control experiments ruled out the extraneous cues of local luminance or local dot density. No conspicuous low spatial-frequency rise in thresholds for any type of differential motion was seen at the lowest spatial frequencies tested, and no difference was seen between horizontal and vertical motion. The results suggest that at the motion threshold spatial integration is greatest in a direction orthogonal to the direction of motion, a view consistent with elongated receptive fields most sensitive to motion orthogonal to their major axis.     

Discrimination of intentional and random motion paths by pigeons

Twelve pigeons (Columba livia) were trained on a go/no-go schedule to discriminate between two kinds of movement patterns of dots, which to human observers appear to be "intentional" and "non-intentional" movements. In experiment 1, the intentional motion stimulus contained one dot (a "wolf") that moved systematically towards another dot as though stalking it, and three distractors ("sheep"). The non-intentional motion stimulus consisted of four distractors but no stalker. Birds showed some improvement of discrimination as the sessions progressed, but high levels of discrimination were not reached. In experiment 2, the same birds were tested with different stimuli. The same parameters were used but the number of intentionally moving dots in the intentional motion stimulus was altered, so that three wolves stalked one sheep. Despite the enhanced difference of movement patterns, the birds did not show any further improvement in discrimination. However, birds for which the non-intentional stimulus was associated with reward showed a decline in discrimination. These results indicated that pigeons can discriminate between stimuli that do and do not contain an element that human observer see as moving intentionally. However, as no feature-positive effect was found in experiment 1, it is assumed that pigeons did not perceive or discriminate these stimuli on the basis that the intentional stimuli contained a feature that the non-intentional stimuli lacked, though the convergence seen in experiment 2 may have been an effective feature for the pigeons. Pigeons seem to be able to recognise some form of multiple simultaneously goal-directed motions, compared to random motions, as a distinctive feature, but do not seem to use simple "intentional" motion paths of two geometrical figures, embedded in random motions, as a feature whose presence or absence differentiates motion displays. Electronic Publication     

Stereo and motion cues in preattentive vision processing--some experiments with random-dot stereographic image sequences

Low-level preattentive vision processing is of special interest since it seems the logical starting point of all vision processing. Exploration of the human visual processing system at this level is, however, extremely difficult, but can be facilitated by the use of stroboscopic presentation of sequences of random-dot stereograms, which contain only local spatial and temporal information and therefore limit the processing of these images to the low level. Four experiments are described in which such sequences were used to explore the relationships between various cues (optical flow, stereo disparity, and accretion and deletion of image points) at the low level. To study these relationships in more depth, especially the resolution of conflicting information among the cues, some of the image sequences presented information not usually encountered in 'natural' scenes. The results indicate that the processing of these cues is undertaken as a set of cooperative processes.     

Signal recognition models compared for random and Markov presentation sequences

Models of two-category signal recognition are compared to data from a variety of experimental conditions. For recognition, one of two signals (S₁, S₂) which vary slightly on some simple physical dimension is presented on each trial, and 0 is to identify (I₁, I₂ ) which signal was presented. In general, Os show a decrease in both Pr(I₁ /S₂) and Pr(I₂/S₁) for either greater Pr(S₂) or, sequentially, for greater S₂ recency. These effects are described as probability and sequential contrast, respectively. The memory state model (MS) describes a three-state threshold process with responses determined by a simple first-order Markov process which depends on the sensory state and response on the immediately preceding trial. The memory trace regression model (MTR) assumes that O compares the observed signal event with the memory trace of the previous signal event. When the difference is large, the sign of the difference determines the response; when it is small, the response depends on the preceding response. The memory trace is assumed to regress toward the mean signal value. Both models accurately predict the observed bias changes as a function of signal probabilities and of the subsequence of events on the previous trial. The response axioms of the MTR model are modified to predict the results for individual Os for Markov chains of signal events. The response axioms of the MS model are modified to predict responding when information is given to O concerning signal probabilities. Although both models do well under all conditions, the MS model uses fewer parameters and correctly predicts the direction of higher order sequential dependencies.     

Time course of chord priming

The time course of chord priming was explored in four experiments. In chord priming, a chord (a typical combination of simultaneously sounded tones) primes other chords that are musically related. In the present study, the prime duration and the stimulus onset asynchrony (SOA) between the prime chord and the chord to be judged were varied. Priming occurred at an SOA and prime duration as short as 50 msec, the shortest tested. When the prime duration was held constant at 50 msec, priming occurred at an SOA as long as 2,500 msec, the longest tested, and the magnitude of the priming effect did not diminish. To eliminate a possible role of sensory memory in maintaining the priming effect during the silence following the prime, a 250-msec noise mask was presented immediately following the 50-msec prime. The interpolated noise mask did not eliminate priming, thereby supporting the view that chord priming is the consequence of associative activation.     

Consistency of vertebral motion and individual characteristics in gait sequences

Vertebral motion reveals complex patterns, which are not yet understood in detail. This applies to vertebral kinematics in general but also to specific motion tasks like gait. For gait analysis, most of existing publications focus on averaging characteristics of recorded motion signals. Instead, this paper aims at analyzing intra- and inter-individual variation specifically and elaborating motion parameters, which are consistent during gait cycles of particular persons. For this purpose, a study design was utilized, which collected motion data from 11 asymptomatic test persons walking at different speed levels (2, 3, and 4 km/h). Acquisition of data was performed using surface topography. The motion signals were preprocessed in order to separate average vertebral orientations (neutral profiles) from basic gait cycles. Subsequently, a k-means clustering technique was applied to figure out, whether a discrimination of test persons was possible based on the preprocessed motion signals. The paper shows that each test sequence could be assigned to the particular test person without additional prior information. In particular, the neutral profiles appeared to be highly consistent intra-individually (across the gait cycles as well as speed levels), but substantially different between test persons. A full discrimination of test persons was achieved using the neutral profiles with respect to flexion/extension data. Based on this, these signals can be considered as individual characteristics for the particular test persons.     

Perceptual integrality of major chord components

In the present study, an accuracy, rather than a reaction time, version of the Garner paradigm was used to evaluate the integrality or separability of major chord components. Tuned (prototype, or P) and mistuned (nonprototype, or NP) sets of root position C-major triads were constructed by holding the C constant in all stimuli and varying the E and G frequencies in 2- and 4-Hz steps. The P stimuli represent small systematic mistunings in the E and G notes relative to an equal-tempered C-major chord. The NP stimuli represent an equivalent range of frequency variation, but relative to a significantly out-of-tune C-major triad. In different experimental sessions, asame-different (AX) task was used to separately evaluate discrimination performance for the E and G frequencies as a function of whether the nontarget frequency (G or E) was fixed or varied in either a correlated or an orthogonal fashion (with the C frequency always held constant). Compared with a fixed baseline condition where only the target frequency changed, both chord components exhibited a significant redundancy gain in the correlated conditions and, to varying degrees, significant interference effects in the orthogonal condition, indicating that the chord components function largely in an integral fashion. Relative to the discrimination of G, discrimination of the E frequency was less influenced by variation in the nontarget (G) frequency, showing that attention, to some degree, could be selectively allocated to the E chord component. In addition, the results were consistent with previous findings that the functional prototype for the major chord category seems to act as a perceptual anchor, rather than as a magnet, and appears to be located in the physiologically defined area of just temperament, as opposed to the more experientially defined area ofequal temperament.     

Time course of chord priming.

The time course of chord priming was explored in four experiments. In chord priming, a chord (a typical combination of simultaneously sounded tones) primes other chords that are musically related. In the present study, the prime duration and the stimulus onset asynchrony (SOA) between the prime chord and the chord to be judged were varied. Priming occurred at an SOA and prime duration as short as 50 msec, the shortest tested. When the prime duration was held constant at 50 msec, priming occurred at an SOA as long as 2,500 msec, the longest tested, and the magnitude of the priming effect did not diminish. To eliminate a possible role of sensory memory in maintaining the priming effect during the silence following the prime, a 250-msec noise mask was presented immediately following the 50-msec prime. The interpolated noise mask did not eliminate priming, thereby supporting the view that chord priming is the consequence of associative activation.