For the Last Time: Temporal Sensitivity and Perceived Timing of the Final Stimulus in an Isochronous Sequence

in Timing & Time Perception
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An isochronous sequence is a series of repeating events with the same inter-onset-interval. A common finding is that as the length of a sequence increases, so does temporal sensitivity to irregularities — that is, the detection of deviations from isochrony is better with a longer sequence. Several theoretical accounts exist in the literature as to how the brain processes sequences for the detection of irregularities, yet there remains to be a systematic comparison of the predictions that such accounts make. To compare the predictions of these accounts, we asked participants to report whether the last stimulus of a regularly-timed sequence appeared ‘earlier’ or ‘later’ than expected. Such task allowed us to separately analyse bias and performance. Sequences lengths (3, 4, 5 or 6 beeps) were either randomly interleaved or presented in separate blocks. We replicate previous findings showing that temporal sensitivity increases with longer sequence in the interleaved condition but not in the blocked condition (where performance is higher overall). Results also indicate that there is a consistent bias in reporting whether the last stimulus is isochronous (irrespectively of how many stimuli the sequence is composed of). Such result is consistent with a perceptual acceleration of stimuli embedded in isochronous sequences. From the comparison of the models’ predictions we determine that the improvement in sensitivity is best captured by an averaging of successive estimates, but with an element that limits performance improvement below statistical optimality. None of the models considered, however, provides an exhaustive explanation for the pattern of results found.

For the Last Time: Temporal Sensitivity and Perceived Timing of the Final Stimulus in an Isochronous Sequence

in Timing & Time Perception



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    Predictions for the Percept Averaging (PA, equations 1 and 2), Multiple Look (ML, equation 6), Internal Reference (IR, equation 9), and Diminishing Return (DR, equation 11) models for JND N with a sequence of N stimuli expressed as a function of JND 2 = 1 ms. Each model has a single free parameter that has been varied to show the range of patterns that can be captured by the models. The value of the parameters for the DR model has been tuned (as discussed in the results section) to capture statistical optimality obtaining a value of c = 0.8.

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    Examples of trials with different sequence length. (a) Sequence of three stimuli (two intervals) where the final stimulus is presented later than expected (+ Anisochrony). (b) Sequence of four stimuli (three intervals) where the final stimulus is presented earlier than expected (− Anisochrony). (c) Sequence of five stimuli (four intervals) where the final stimulus is presented later than expected (+ Anisochrony). (d) Sequence of six stimuli (five intervals) where the final stimulus is presented earlier than expected (− Anisochrony).

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    Proportion of ‘later’ responses as a function of the anisochrony of the final interval in the sequence for (a) 2, (b) 3, (c) 4, and (d) 5 intervals for interleaved and blocked presentation. Error bars represent the standard error of the mean.

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    JND values as a function of sequence length for (a) interleaved and (b) blocked presentation. (c) JND values calculated on the proportion of ‘later’ responses across sequence lengths for blocked and interleaved conditions. The asterisk indicates a significant difference according to the ANOVA presented in the text. Error bars represent the standard error of the mean.

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    PSE values as a function of sequence length for (a) interleaved and (b) blocked presentation. (c) PSE values calculated on the proportion of ‘later’ responses across sequence length for interleaved and blocked presentation. The asterisk indicates a significant difference from 0 according to single-sample t-tests and between conditions according to the ANOVA (details presented in the text). Error bars represent the standard error of the mean.

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    Empirical results and predictions of the Percept Averaging (PA), Multiple Look (ML), Internal-Reference (IR), and Diminishing Returns (DR) model (see results section). The predictions of the PA (Schulze, 1978; 1989) and ML Models (Drake & Botte, 1993; Miller & McAuley, 2005) visually capture the increase in temporal sensitivity as a function of sequence length across the two conditions. The IR model (Dyjas et al., 2012) captures the flat course of JND for the blocked condition but cannot accurately capture the obvious increase in temporal sensitivity for the interleaved condition. The DR Model (Ten Hoopen et al., 2011) captures the negatively accelerating course of the JND only for the interleaved condition but does not correctly account for flat course of JND in the blocked condition, as the fit for several participants predicts worse performance due to the presence of low-performance conditions.

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    Comparison of the models fit to the empirical data captured by the sum of squared errors for the Percept Averaging (PA; Correlated and Uncorrelated), Multiple Look (ML), Internal Reference (IR), and Diminishing Returns (DR) models. The dark grey bar represents the interleaved condition whilst the light grey indicates the blocked condition. A two-way r.m. ANOVA on the data with factors models and interleaved/blocked is significant for the factor model [F(4, 96) = 39.37, p < 0.0001, η p 2 = 0.62] whereas the factor blocked/interleaved and interaction are not significant. Error bars represent the standard error of the mean across participants.


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