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FIGURE 9.2 Results from Fortin and Masse's (2000) experiment 2. Mean produced intervals, not including breaks (± SE), as a function of break location.

effects in time production, where increasing the delay between the start of an interval and presentation of a tone to be discriminated lengthened produced intervals (Rousseau et al., 1984). More precisely, Rousseau et al. (1984) proposed that pulses are emitted and transferred to a counter. Two possible states are assumed in pulse transfer, ON or OFF, so accumulation proceeds in an all-or-nothing mode. Pulse accumulation is under attentional control, so this process is ON when attention is selectively allocated to timing. During an interval production, the proportion of time that pulse transfer is ON is represented by a p parameter. (1 - p) is the proportion of time OFF, when attention is not allocated to timing. An increase of (1 - p) accounts for longer intervals when the tone to be discriminated was delayed, because during this delay, attention was diverted from timing to monitor the auditory channel for tone detection.

Note that effects of location of intervening elements on timing are not specific to temporal production. They have also been observed with time discrimination tasks (e.g., Buffardi, 1971; Casini and Macar, 1997; Israeli, 1930), and an interpretation of attentional time-sharing during pulse accumulation has been considered recently by Casini and Macar (1997) to explain such effects.

Fortin and Masse's (2000) study showed effects of location with no concurrent task by varying the time of occurrence of empty breaks during time production. The time-sharing interpretation of break location in a production task is illustrated in Figure 9.3. In this figure, interval production starts with a first key press (kp1). When no break is expected, as in practice trials, pulse accumulation proceeds until a criterion number of pulses corresponding to the target duration is reached (A), which triggers the second key press, ending the interval (kp2A). When the prebreak duration is 800 msec, accumulation is slower until the break onset (dashed part of the accumulation function) because attentional shifts increase the proportion of time where pulse transfer is OFF. Accumulation is completely interrupted during the break (flat part of the function) and resumes after the break at its usual rate until the criterion is reached (B), which triggers the end of production (kp2B). The time

FIGURE 9.3 Pulse accumulation during a time interval production. Produced interval is the time between kp1 and kp2A when no break is expected, in a trial with no break. The time between kp1 and kp2B is the temporal production in a trial with a break, which occurs 800 msec after the beginning of the interval production. In a trial with a break, productions are lengthened by pulse loss in the prebreak duration (dotted line) and by the interruption during the break period (solid horizontal line between break onset and offset).

FIGURE 9.3 Pulse accumulation during a time interval production. Produced interval is the time between kp1 and kp2A when no break is expected, in a trial with no break. The time between kp1 and kp2B is the temporal production in a trial with a break, which occurs 800 msec after the beginning of the interval production. In a trial with a break, productions are lengthened by pulse loss in the prebreak duration (dotted line) and by the interruption during the break period (solid horizontal line between break onset and offset).

between the two key presses in production with the break (kpl and kp2B) is longer than with no break (kpl and kp2A). Two factors contribute to longer productions in trials with breaks. The most obvious is the duration of the break itself, during which time is elapsing, but timing is interrupted in accordance with instructions. The second factor is the rate of accumulation before break onset, which is slowed down by attentional shifts during the prebreak period. In summary, accumulation is interrupted (1) during the experiment-controlled break itself, and (2) during brief attentional shifts caused by anticipating the experiment-controlled break.

The time-sharing interpretation of the break location effect is illustrated in Figure 9.4. Note that for the sake of simplicity, in that figure, as in the following figures, the break period is no longer included. The two main periods of interest during which the accumulation process operates in these experiments, the prebreak and postbreak periods, are represented with dotted and solid lines respectively. In Figure 9.4, the abscissa represents time, and white arrows represent key presses executed by the participants. The time between key presses corresponds to produced intervals as defined previously: time between the first and second key presses from which the break period (time between break onset and offset in Figure 9.3) has been removed. For example, when a break occurs 800 msec after the first key press, the produced interval, defined as the sum of prebreak and postbreak durations, will be the time between kpl and kp2B1. When a break occurs 1300 msec after the first key press, the produced interval will be the time between kpl and kp2B2. Productions are longer when break location is 1300 msec than when it is 800 msec because the longer period of time-sharing (dotted line) before the break causes an extra loss in pulse accumulation. After the break, accumulation resumes at its normal rate in both location conditions (solid lines of accumulation functions). The criterion is reached later when the break occurs later because a larger amount of temporal information

FIGURE 9.4 Pulse accumulation in time production during the prebreak and postbreak periods. Note that the break period itself is not represented. Accumulation in time production starts at the first key press (kpl), is slower during the prebreak period (parts of accumulation function shown with dotted lines), and resumes at its usual rate (parts of accumulation functions shown with solid lines) after the break. Production is shown when a break is expected for 800 msec (time between kpl and kp2S1) or 1300 msec (time between kpl and kp2B2). Production is longer when a break is expected for 1300 than 800 msec because if accumulation is slower for a longer period, the criterion would be reached later.

FIGURE 9.4 Pulse accumulation in time production during the prebreak and postbreak periods. Note that the break period itself is not represented. Accumulation in time production starts at the first key press (kpl), is slower during the prebreak period (parts of accumulation function shown with dotted lines), and resumes at its usual rate (parts of accumulation functions shown with solid lines) after the break. Production is shown when a break is expected for 800 msec (time between kpl and kp2S1) or 1300 msec (time between kpl and kp2B2). Production is longer when a break is expected for 1300 than 800 msec because if accumulation is slower for a longer period, the criterion would be reached later.

was lost in the prebreak period. Consequently, produced intervals are longer at a later break location.

While the time-sharing interpretation can account for the break location effect, it is based on an expectancy assumption. It is not the break itself, but its expectation, that induces time-sharing. Experiments 3 and 4 from Fortin and Masse's (2000) study provided a test of the expectancy assumption. In these experiments, trials with and without breaks were mixed within blocks of trials.

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