## Introduction

The hallmark of short-interval timing is the scalar property. This property is demonstrated by a constant coefficient of variability (standard deviation divided by the mean of distributions from timing experiments) and is a version of Weber's law. In particular, the distribution of timing data is the same for different target intervals when the data are normalized on x- and y-axes. For the x-axis normalization, time is expressed as a percentage of the different target intervals. For the y-axis normalization, response rate is expressed as a percentage of the maximum rates obtained for each target interval. This empirical feature of timing data will be referred to as the linear-timing hypothesis throughout this chapter. This property has been observed in humans (Rakitin et al., 1998; Wearden, 1991; Wearden et al., 1997) and many other animals (Church et al., 1994; Fetterman and Killeen, 1995; Richelle and Lejeune, 1984). For example, in a fixed-interval procedure, food is available for the first response after the fixed interval elapses. Temporal anticipation is documented by the increase in response rate as a function of time. When different fixed intervals are tested, the temporal anticipation functions superimpose when the x- and y-axes are normalized. In contrast, when the data are plotted in absolute rather than relative terms, the data fail to superimpose.

The linear-timing hypothesis has been supported by many experiments using a wide variety of target intervals (e.g., 30, 300, 3000 sec; Dews, 1970), and it has played an important role in the development of research in timing (Allan, 1998; Gibbon, 1991). The linear-timing hypothesis predicts that sensitivity to time is constant (i.e., linear) across a wide range of intervals. A more precise statement of the linear-timing hypothesis is that timing estimates consist of a linear component plus random error. If evaluating the fit of a theoretical function to data reveals nonrandom discrepancies from the average estimate, then the implication is that the function is an unacceptable description of the data. Therefore, it is possible to elaborate the linear-timing hypothesis at two levels of detail. According to the most basic description, the linear-timing hypothesis requires that psychological estimates of time increase as a constant proportion of physical estimates of time. According to a more detailed description, the linear-timing hypothesis predicts that departures from the linear prediction are expected to be random.

A well-established exception to the linear-timing hypothesis is known to occur when relatively short intervals (i.e., in the range of milliseconds) are examined (e.g., Church et al., 1976; Crystal, 1999; Fetterman and Killeen, 1992). In particular, the coefficient of variation of time estimates is relatively large for relatively short intervals. This may be interpreted as a generalized Weber function or an absolute threshold (Church et al., 1976; Crystal, 1999; Fetterman and Killeen, 1992). Another exception to the linear-timing hypothesis occurs when relatively long intervals are examined (e.g., Brunner et al., 1992; Crystal, 2002; Gibbon et al., 1997b; Lejeune and Wearden, 1991; Zeiler, 1991; Zeiler and Powell, 1994). In particular, the coefficient of variation of time estimates is relatively large for relatively long intervals. The objective of this chapter is to review evidence that interval timing is characterized by several temporal regions of improved sensitivity to time. These local maxima in sensitivity to time represent an empirical challenge to the linear-timing hypothesis. The evidence for local maxima in sensitivity to time comes from studies of (a) short-interval timing (i.e., timing of milliseconds, seconds, and minutes), (b) long-interval timing (i.e., timing of hours), and (c) circadian timing (i.e., timing of intervals of approximately 24 h). The chapter concludes with a discussion of implications for theories of timing.

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