There is general agreement among the quantitative models for time (see Allan, 1998) that mean perceived time ( μ t ) is a power function of clock time with an exponent close to 1.0,and that variability in perceived time (s t ) is proportional to mean perceived time,The proportionalityconstant g is known as the Weber fraction, and the proportionality relation is often referred to as scalar variability. This scalar property between the standard deviation and the mean results in distributions of perceived time that superpose when the temporal axis is normalized with respect to the mean of the distribution. This superposition in relative time reflects a re-scaling in time, a scale-invariant error distribution for perceived time. Many psychophysical procedures have been developed for the study of time perception (see Allan, 1979Allan, , 1998. One relatively new procedure is temporal bisection. In the prototypic temporal bisection task, two referents, one short (S ) and the other long (L), are explicitly identified either by familiarizing the subject with the referents at the beginning of a block of trials (e.g., Allan, 1999;Wearden, 1991;Wearden & Ferrara, 1995Wearden, Rogers, & Thomas, 1997) or periodically throughout a block of trials (e.g., Allan & Gibbon, 1991;Penney, Allan, Meck, & Gibbon, 1998). On probe trials, a temporal interval t, S £ t £ L, is presented, and the subject is required to indicate whether t is more similar to S (R S ) or to L (R L ). Temporal bisection yields a psychometric function relating the proportion of long responses, P(R L ), to probe duration t. The value of t at which R S and R L occur with equal frequency, P(R L ) 5 0.5, is often referred to as the bisection point (T 1/2 ). One interpretation of T 1/2 is that it is the value of t that is equally confusable with S and L. For bisection, the scalar property predicts superposition of psychometric functions for all L-to-S ratios when plotted against t normalized by the bisection point (i.e., t / T 1/2 ).A number of psychophysical models for temporal bisection have been proposed. These models differ with regard to the source of the scalar variability and the nature of the decision rule for categorizing t as R L or R S . In his now classic paper on temporal bisection, derived the bisection function for a similarity ratio decision rule. For this rule, the decision to respond R S or R L is made by comparing the similarity of the perceived value of t with memories of the two referents, S and L. This comparison is based on a ratio of the similarity of t to S relative to the similarity of t to L. If that ratio is less than a criterion b, the response is R L . Gibbon combined the similarity ratio rule with two sources for scalar variability, perception or memory. In the "referent known exactly model" (RKE), he assumed no variability in the memory for the referents and placed scalar variability in the perception of the probes. In contrast, in the "stimulusThe preparation of this paper was supported by a grant to L.G.A. from the Natural Sciences ...