Perceiving the numerosity of rapidly occurring auditory events in metrical and nonmetrical contexts

Humans can sense small numbers of objects in a box by touch alone

Everyday experiences suggest that a container, such as a box of chocolate sprinkles, can convey pertinent information about the nature of its content. Despite the familiarity of the experience, we do not know whether people can perceive the number of objects in the container from touch alone and how accurately they can do so. In three experiments, participants handled containers holding between one and five objects and verbally estimated their number. Containers were small cardboard jewelry boxes, and objects were round beads of varying diameter and weight. Any useful visual and auditory cues were precluded. Experiment 1 demonstrated very accurate performance, provided the objects were of sufficient weight. Experiment 2 demonstrated that withholding information about the possible number of objects inside the container does not affect accuracy at a group level but does produce occasional overestimations at an individual level. Experiment 3 demonstrated that removing the weight cue leads to systematic underestimations but does not eliminate people's ability to distinguish between different numbers of objects in the container. This study contributes to a growing picture that container haptics is surprisingly capable.

Manipulation of Attention Affects Subitizing Performance: A Systematic Review and Meta-analysis

Subitizing is the fast and accurate enumeration of small sets. Whether attention is necessary for subitizing remains controversial considering (1) subitizing is claimed to be "pre-attentive", and (2) existing experimental methods and results are inconsistent. To determine whether manipulations to attention demonstratively affect subitizing, the current study comprises a systematic review and meta-analysis. Results from fourteen studies (22 experiments, 35 comparisons) suggest that changes to attentional demands interferes with enumeration of small sets; leading to slower response times, lower accuracy, and poorer Weber acuity (p <.010; p <.001; p <.001; respectively)-notwithstanding a potential publication bias. A unifying framework is proposed to explain the role of attention in visual enumeration, with progressively greater attentional involvement from estimation to subitizing to counting. Our findings suggest attention is integral for subitizing and highlights the need to emphasise attentional mechanisms into neurocognitive models of numerosity processing. We also discuss the possible role of attention in numerical processing difficulties (e.g., dyscalculia).

Effect of Tempo on Temporal Expectation Driven by Rhythms in Dual-Task Performance

Temporal expectation is the ability to focus attention at a particular moment in time to optimize performance, which has been shown to be driven by regular rhythms. However, whether the rhythm-based temporal expectations rely upon automatic processing or require the involvement of controlled processing has not been clearly established. Furthermore, whether the mechanism is affected by tempo remains unknown. To investigate this research question, the present study used a dual-task procedure. In a single task, the participants were instructed to respond to a visual target preceded by a regular or an irregular visual rhythm under a fast (500 ms) or slow (3,500 ms) tempo. The dual-task simultaneously combined a working memory (WM) task. The results showed temporal expectation effects in which the participants responded faster to the regular than to the irregular conditions in a single task. Moreover, this effect persisted under dual-task interference in the fast tempo condition but was impaired in the slow tempo condition. These results revealed that rhythmic temporal expectation induced by fast tempo was dependent on automatic processing. However, compared with the faster tempo, temporal expectation driven by a slower tempo might involve more controlled processing.

Beat perception in polyrhythms: Time is structured in binary units

In everyday life, we group and subdivide time to understand the sensory environment surrounding us. Organizing time in units, such as diurnal rhythms, phrases, and beat patterns, is fundamental to behavior, speech, and music. When listening to music, our perceptual system extracts and nests rhythmic regularities to create a hierarchical metrical structure that enables us to predict the timing of the next events. Foot tapping and head bobbing to musical rhythms are observable evidence of this process. In the special case of polyrhythms, at least two metrical structures compete to become the reference for these temporal regularities, rendering several possible beats with which we can synchronize our movements. While there is general agreement that tempo, pitch, and loudness influence beat perception in polyrhythms, we focused on the yet neglected influence of beat subdivisions, i.e., the least common denominator of a polyrhythm ratio. In three online experiments, 300 participants listened to a range of polyrhythms and tapped their index fingers in time with the perceived beat. The polyrhythms consisted of two simultaneously presented isochronous pulse trains with different ratios (2:3, 2:5, 3:4, 3:5, 4:5, 5:6) and different tempi. For ratios 2:3 and 3:4, we additionally manipulated the pitch of the pulse trains. Results showed a highly robust influence of subdivision grouping on beat perception. This was manifested as a propensity towards beats that are subdivided into two or four equally spaced units, as opposed to beats with three or more complex groupings of subdivisions. Additionally, lower pitched pulse trains were more often perceived as the beat. Our findings suggest that subdivisions, not beats, are the basic unit of beat perception, and that the principle underlying the binary grouping of subdivisions reflects a propensity towards simplicity. This preference for simple grouping is widely applicable to human perception and cognition of time.

Numerosity Identification Used to Assess Tactile Stimulation Methods for Communication

Finger-Braille is a tactile communication method used by people who are Deafblind. Individuals communicate Finger-Braille messages with combinations of taps on three fingers of each of the hands of the person receiving the communication. Devices have been developed to produce Finger-Braille symbols using different tactile stimulation methods. Before engaging in communication studies based on technologically-mediated Finger-Braille, we evaluated the relative efficacy of these methods by comparing two devices similarly constructed; the first based on widely employed eccentric rotating-mass vibrating motors and the other using specifically designed tapping actuators. We asked volunteers to identify the numerosity of presented items and for each device we measured (1) error-rate, (2) reaction time, (3) confidence ratings, and (4) a comparison of confidence ratings to actual performance. The four measures obtained for each device showed a net advantage of the tapping stimulation method over the method of vibrations. In this article, we conclude that the tapping stimulation method is recommended for use in the design of tactile communication devices based on Finger-Braille and fingerspelling methods reliant on finger tapping actions. The results did not demonstrate clear evidence for tactile subitising with passively experienced stimulation on the fingers.

Groupitizing Improves Estimation of Numerosity of Auditory Sequences

Groupitizing is a recently described phenomenon of numerosity perception where clustering items of a set into smaller "subitizable" groups improves discrimination. Groupitizing is thought to be rooted on the subitizing system, with which it shares several properties: both phenomena accelerate counting and decrease estimation thresholds irrespective of stimulus format (for both simultaneous and sequential numerosity perception) and both rely on attention. As previous research on groupitizing has been almost completely limited to vision, the current study investigates whether it generalizes to other sensory modalities. Participants estimated the numerosity of a series of tones clustered either by proximity in time or by similarity in frequency. We found that compared with unstructured tone sequences, grouping lowered auditory estimation thresholds by up to 20%. The groupitizing advantage was similar across different grouping conditions, temporal proximity and tone frequency similarity. These results mirror the groupitizing effect for visual stimuli, suggesting that, like subitizing, groupitizing is an a-modal phenomenon.

Representing Numerosity Through Vibration Patterns

It can be useful to display information about numerosity haptically. For instance, to display the time of day or distances when visual or auditory feedback is not possible or desirable. Here, we investigated the possibility of displaying numerosity information by means of a sequence of vibration pulses. From previous studies on numerosity perception in vision, haptics and audition it is known that numerosity judgment can be facilitated by grouping. Therefore, we investigated whether perception of the number of vibration pulses in a sequence can be facilitated by temporally grouping the pulses. We found that indeed temporal grouping can lead to considerably smaller errors and lower error rates indicating that this facilitated the task, but only when participants knew in advance whether the pulses would be temporally grouped. When grouped and ungrouped series of pulses were presented randomly interleaved, there was no difference in performance. This means that temporally grouping vibration sequences can allow the sequence to be displayed at a faster rate while it remains possible to perceive the number of vibration pulses accurately if the users is aware of the temporal grouping.

Small numerosity advantage for sequential enumeration on RSVP stimuli: an object individuation-based account

Although there is a large literature demonstrating rapid and accurate enumeration of small sets of simultaneously presented items (i.e., subitizing), it is unclear whether this small numerosity advantage (SNA) can also manifest in sequential enumeration. The present study thus has two aims: to establish a robust processing advantage for small numerosities during sequential enumeration using a rapid serial visual presentation (RSVP) paradigm, and to examine the underlying mechanism for a SNA in sequential enumeration. The results indicate that a small set of items presented in fast sequences can be enumerated accurately with a high precision and a SOA (stimulus onset asynchrony)-sensitive capacity limit, essentially generalizing the large literature on small numerosity advantage from spatial domain to temporal domain. A resource competition hypothesis was proposed and confirmed in further experiments. Specifically, sequential enumeration and other cognitive process, such as visual working memory (VWM), compete for a shared resource of object individuation by which items are segregated as individual entities. These results implied that the limited resource of object individuation can be allocated within time windows of flexible temporal scales during simultaneous and sequential enumerations. Taken together, the present study calls for attention to the dynamic aspect of the enumeration process and highlights the pivotal role of object individuation in underlying a wide range of mental operations, such as enumeration and VWM.

If it looks, sounds, or feels like subitizing, is it subitizing? A modulated definition of subitizing

Research in cognitive psychology has focused mainly on the visual modality as the input interface for mental processes. We suggest that integrating studies from different modalities can aid in resolving theoretical controversies. We demonstrate this in the case of subitizing. Subitizing, the quick and accurate enumeration of small quantities, has been studied since the 19th century. Nevertheless, to date, the underlying mechanism is still debated. Two mechanisms have been suggested: a domain-general mechanism-attention, and a domain-specific mechanism-pattern recognition. Here, we review pivotal studies in the visual, tactile, and auditory modalities. The accumulative findings shed light on the theoretical debate. Accordingly, we suggest that subitizing is a subprocess of counting that occurs in the presence of facilitating factors, such as attentional resources and familiar patterns.

Perceptual limits in a simulated "Cocktail party"

Numerosity judgments of simultaneous talkers were examined. Listeners were required to report the number of talkers heard when this number varied (1 to 13). Spatial location of talkers (1 or 6 locations), duration of talker voices (0.8 s, 5.0 s, and 15.0 s), and gender arrangement of talkers also were manipulated in four experiments. In all experiments, the proportion of correct numerosity judgments monotonically decreased as talker numbers increased. Perceptual limits, defined as talker numbers with proportion correct scores of 0.5, varied between 3 to 5 talkers, on average, depending on listening conditions, and were significantly higher for spatially separated talkers, for the longer voices, and for the mixed gender voices (Experiments 1, 2, and 3). In addition, Experiment 4 found that average numerosity response times increased monotonically over a range of one to four talkers. These results support the idea that, before counting talkers, listeners perceptually segregate talkers to render numerosity judgments. They also suggest that our functional auditory world for simultaneous voices may consist of, at most, three to five talkers depending on listening situations. In light of these results, possible causes for such perceptual limits are discussed.

Preattentive and attentive responses to changes in small numerosities of tones in adult humans

The brain hosts a primitive number sense to non-symbolically represent numerosities of objects or events. Small exact numerosities (~4 or less) can be individuated in parallel. In contrast, large numerosities (more than ~4) can only be approximated. However, whether small numerosities can be approximated without their parallel individuation remains unclear. Parallel individuation is suggested to be an attentive process and numerical approximation an automatic process. We, therefore, tested whether small numerosities can be represented preattentively. We recorded adult humans׳ event-related potentials (ERPs) and behavioral responses to 300-ms sequences of six tones (each of either 440 Hz or 660 Hz in frequency). Mostly, a sequence was of 3 tones of each frequency. Occasionally (P=0.1), the numerosities were 4 and 2 (minor changes) or 5 and 1 (major changes). Mismatch negativity (MMN), but no later attention-related positive-polarity ERPs, was observed to the major but not to the minor changes during a visual non-numerical task. In a following attentive task, behavioral responses even to major changes resulted in a very low hit rates (0.11 for major and 0.023 for minor changes) and yet an above-zero false-alarm rate (0.052). The findings support a view that small numerosities of objects can be automatically approximated independently of their attentive individuation.

Estimating group size from human speech: Three's a conversation, but four's a crowd

Much previous research has examined various aspects of auditory processing, including the localization of sounds, and the influence of lexical and indexical information on language processing. In the present set of experiments we explored the ability of listeners to estimate the number of speakers in a group solely from the information in an auditory signal. The bound on accurately estimating the number of simultaneous speakers is 3. We suggest that subitization-the ability to estimate numerosity of visual and auditory elements without explicitly counting these elements-rather than the capacity of short-term memory, may underlie this limitation. The cognitive constraint on estimating the number of simultaneous speakers may have implications for a wide variety of seemingly unrelated psychological phenomena.

Number As a Primary Perceptual Attribute: A Review

Although humans are the only species to possess language-driven abstract mathematical capacities, we share with many other animals a nonverbal capacity for estimating quantities or numerosity. For some time, researchers have clearly differentiated between small numbers of items--less than about four--referred to as the subitizing range, and larger numbers, where counting or estimation is required. In this review, we examine more recent evidence suggesting a further division, between sets of items greater than the subitizing range, but sparse enough to be individuated as single items; and densely packed stimuli, where they crowd each other into what is better considered as a texture. These two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws and show different dependencies on eccentricity and on luminance levels. But provided the elements are not too crowded (less than about two items per square degree in central vision, less in the periphery), there is little evidence that estimation of numerosity depends on mechanisms responsive to texture. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills.

Sensorimotor synchronization: a review of recent research (2006-2012)

Sensorimotor synchronization (SMS) is the coordination of rhythmic movement with an external rhythm, ranging from finger tapping in time with a metronome to musical ensemble performance. An earlier review (Repp, 2005) covered tapping studies; two additional reviews (Repp, 2006a, b) focused on music performance and on rate limits of SMS, respectively. The present article supplements and extends these earlier reviews by surveying more recent research in what appears to be a burgeoning field. The article comprises four parts, dealing with (1) conventional tapping studies, (2) other forms of moving in synchrony with external rhythms (including dance and nonhuman animals' synchronization abilities), (3) interpersonal synchronization (including musical ensemble performance), and (4) the neuroscience of SMS. It is evident that much new knowledge about SMS has been acquired in the last 7 years.

Perceiving sequential dependencies in auditory streams

This study examined the ability of human listeners to detect the presence and judge the strength of a statistical dependency among the elements comprising sequences of sounds. The statistical dependency was imposed by specifying transition matrices that determined the likelihood of occurrence of the sound elements. Markov chains were constructed from these transition matrices having states that were pure tones/noise bursts that varied along the stimulus dimensions of frequency and/or interaural time difference. Listeners reliably detected the presence of a statistical dependency in sequences of sounds varying along these stimulus dimensions. Furthermore, listeners were able to discriminate the relative strength of the dependency in pairs of successive sound sequences. Random variation along an irrelevant stimulus dimension had small but significant adverse effects on performance. A much greater decrement in performance was found when the sound sequences were concurrent. Likelihood ratios were computed based on the transition matrices to specify Ideal Observer performance for the experimental conditions. Preliminary modeling efforts were made based on degradations of Ideal Observer performance intended to represent human observer limitations. This experimental approach appears to be useful for examining auditory "stream" formation and maintenance over time based on the predictability of the constituent sound elements.

Anticipatory phase correction in sensorimotor synchronization

Studies of phase correction in sensorimotor synchronization often introduce timing perturbations that are unpredictable with regard to direction, magnitude, and position in the stimulus sequence. If participants knew any or all of these parameters in advance, would they be able to anticipate perturbations and thus regain synchrony more quickly? In Experiment 1, we asked musically trained participants to tap in synchrony with short isochronous tone sequences containing a phase shift (PS) of -100, -40, 40, or 100 ms and provided advance information about its direction, position, or both (but not about its magnitude). The first two conditions had little effect, but in the third condition participants shifted their tap in anticipation of the PS, though only by about ±40 ms on average. The phase correction response to the residual PS was also enhanced. In Experiment 2, we provided complete advance information about PSs of various magnitudes either at the time of the immediately preceding tone ("late") or at the time of the tone one position back ("early") while also varying sequence tempo. Anticipatory phase correction was generally conservative and was impeded by fast tempo in the "late" condition. At fast tempi in both conditions, advancing a tap was more difficult than delaying a tap. The results indicate that temporal constraints on anticipatory phase correction resemble those on reactive phase correction. While the latter is usually automatic, this study shows that phase correction can also be controlled consciously for anticipatory purposes.

Temporal evolution of the phase correction response in synchronization of taps with perturbed two-interval rhythms

Human sensorimotor synchronization is flexible but subject to temporal constraints. Previous research has shown that musicians tend to lose synchrony with target tones in an isochronous sequence when the sequence rate exceeds 8-10 Hz, presumably because phase correction ceases to function. The present study investigated directly the time required for an immediate phase correction response (PCR). Musicians tapped in synchrony with cyclic two-interval (short-long) rhythms, using the two hands in alternation. Perturbations were applied to the long interval, and the compensatory shift of the next tap (the PCR) was measured following the short interval, whose duration was varied from 100 to 300 ms. The PCR was found to increase gradually within this range, being nearly absent at 100 ms. Similar results were obtained when participants tapped only with the second tone in each rhythmic group, which confirms that the PCR is based on the preceding tone rather than on the preceding tap-tone asynchrony, and also when the second tone was omitted in the pacing sequence, which indicates that the PCR occurs automatically even when there is no synchronization target for the critical tap. These results extend earlier findings regarding rate limits of synchronization and also provide further support for an event-based phase resetting account of the PCR.

Decomposing rhythm processing: electroencephalography of perceived and self-imposed rhythmic patterns

Perceiving musical rhythms can be considered a process of attentional chunking over time, driven by accent patterns. A rhythmic structure can also be generated internally, by placing a subjective accent pattern on an isochronous stimulus train. Here, we investigate the event-related potential (ERP) signature of actual and subjective accents, thus disentangling low-level perceptual processes from the cognitive aspects of rhythm processing. The results show differences between accented and unaccented events, but also show that different types of unaccented events can be distinguished, revealing additional structure within the rhythmic pattern. This structure is further investigated by decomposing the ERP into subcomponents, using principal component analysis. In this way, the processes that are common for perceiving a pattern and self-generating it are isolated, and can be visualized for the tasks separately. The results suggest that top-down processes have a substantial role in the cerebral mechanisms of rhythm processing, independent of an externally presented stimulus.

A filled duration illusion in music: Effects of metrical subdivision on the perception and production of beat tempo

This study replicates and extends previous findings suggesting that metrical subdivision slows the perceived beat tempo (Repp, 2008). Here, musically trained participants produced the subdivisions themselves and were found to speed up, thus compensating for the perceived slowing. This was shown in a synchronization-continuation paradigm (Experiment 1) and in a reproduction task (Experiment 2a). Participants also judged the tempo of a subdivided sequence as being slower than that of a preceding simple beat sequence (Experiment 2b). Experiment 2 also included nonmusician participants, with similar results. Tempo measurements of famous pianists’ recordings of two variation movements from Beethoven sonatas revealed a strong tendency to play the first variation (subdivided beats) faster than the theme (mostly simple beats). A similar tendency was found in musicians’ laboratory performances of a simple theme and variations, despite instruc-tions to keep the tempo constant (Experiment 3a). When playing melodic sequences in which only one of three beats per measure was subdivided, musicians tended to play these beats faster and to perceive them as longer than adjacent beats, and they played the whole sequence faster than a sequence without any subdivisions (Experiments 3b and 3c). The results amply demonstrate a filled duration illusion in rhythm perception and music performance: Intervals containing events seem longer than empty intervals and thus must be shortened to be perceived as equal in duration.

Rhythmic sensorimotor coordination is resistant but not immune to auditory stream segregation

In a recent study of musicians' sensorimotor synchronization with auditory sequences composed either of beat and subdivision tones differing in pitch or of beat tones only, Repp (2009) found that the phase correction response (PCR) to perturbed beats was inhibited by the presence of subdivisions regardless of whether beats and subdivisions formed integrated or segregated perceptual streams. The present study used a different paradigm in which perturbed subdivisions triggered the PCR. At the slower of two sequence tempi, the PCR was equally large in integrated and segregated conditions, but at the faster tempo stream segregation reduced the PCR substantially. This new finding indicates that although the PCR is strongly resistant to auditory stream segregation, it is not totally immune to it.

Discontinuity in the enumeration of sequentially presented auditory and visual stimuli

The seeking of discontinuity in enumeration was recently renewed because Cowan [Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87-185; Cowan, N. (2005). Working memory capacity. Hove: Psychology Press] suggested that it allows evaluating the limit of the focus of attention, currently estimated at four items. A strong argument in favour of a general constraint of the cognitive system is that similar discontinuities should be observed in modalities different from the classic simultaneous presentation of visual objects. Recently, data were provided on tactile stimuli, but the authors diverged in their conclusion about the existence of such discontinuity [Gallace, A., Tan, H. Z., & Spence, C. (2006). Numerosity judgments for tactile stimuli distributed over the body surface. Perception, 35(2), 247-266; Riggs, K. J., Ferrand, L., Lancelin, D., Fryziel, L., Dumur, G., & Simpson, A. (2006). Subitizing in tactile perception. Psychological Science, 17(4), 271-272]. Following a similar rationale, our study aimed at evaluating discontinuity in the enumeration of auditory and visual stimuli presented sequentially. The clear and similar discontinuity observed in error rates, response times and given responses for both modalities favours the general capacity limit view, but also questions the size of this capacity, because the discontinuity occurred here at size 2. However, the masking of stimuli in sensory memory could not be entirely discarded.