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How is it that counting to ourselves helps us to estimate an interval of time? To address this question, we develop a generalized clock-counter model of duration discrimination that allows error in both the timing and the counting processes. We show that in order to minimize variability in temporal judgments, it is usually to the subject's advantage to segment the interval to be judged into subintervals. The optima] duration of the subintervals will depend on the parameters of the fundamental error equations that relate variance to the duration and number of the subintervals; in most cases, however, the optimal duration will be independent of the duration of the interval to be timed. The canonical form of the Weber function derived from our analysis takes as special cases the forms predicted by various other models of temporal discrimination. For long intervals it reduces to Weber's law, with the constant in that law solely a function of counting error.

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