Perceptual Timing Judgment Tasks

All participants completed both visual and auditory tasks, in separate blocks, counterbalanced across participants. Each trial started with a 500-ms blank period (with no stimulus, besides the fixation point). Then, a visual or auditory test stimulus was presented. The duration of the test stimulus was one of five logarithmically spaced intervals of time, between 300 and 900 ms (i.e., 300, 395, 520, 684, 900 ms). Before beginning each block, participants were presented with five or more visual (or auditory) reference stimuli with duration 520 ms (the geometric mean of the test stimuli durations). They were instructed to remember the reference duration and to make subsequent judgments regarding test stimuli relative to the reference duration (the PSE values in Additional file 1: Fig. S6 confirm that participants indeed complied with this instruction). Before beginning the task, participants were allowed to continue to experience the reference stimulus repeatedly, until they were confident that they had remembered the reference duration. Once the block began, participants could no longer experience the reference stimulus.
Participants reported their choice on each trial after the stimulus had ended by pressing one of two keyboard buttons. The button-choice contingency was counterbalanced across participants: half the participants pressed the “F” button with their left index finger and the “J” button with their right index finger to indicate longer and shorter test durations, respectively, while the other half responded with the reverse mapping. Participants were instructed to make each response as quickly and accurately as possible. To ensure an equal number of consecutive stimulus pairs, while retaining a long-term pseudorandom structure, the order of stimulus presentation was determined by a pseudorandom 5⁴ de Bruijn sequence. This creates an optimally short (pseudorandom) sequence of stimuli (625 trials total) in which each contiguous subsequence of 4 stimuli (from the 5 possible stimulus intervals) occurs exactly once [68 (link)]. Accordingly, each individual stimulus occurred 125 times, each possible pair occurred 25 times, each possible triplet occurred 5 times, and each quadruplet occurred once (per block).