Responses of 26 rats were reinforced following a signal of a certain duration, but not following signals of shorter or longer durations. This led to a positive temporal generalization gradient with a maximum at the reinforced duration in six experiments. Spacing of the nonreinforced signals did not influence the gradient, but the location of the maximum and breadth of the gradient increased with the duration of the reinforced signal. Reduction of reinforcement, either by partial reinforcement or reduction in the probability of a positive signal, led to a decrease in the height of the generalization gradient. There were large, reliable individual differences in the height and breadth of the generalization gradient. When the conditions of reinforcement were reversed (responses reinforced following all signals longer or shorter than a single nonreinforced duration), eight additional rats had a negative generalization gradient with a minimum at a signal duration shorter than the single nonreinforced duration. A scalar timing theory is described that provided a quantitative fit of the data. This theory involved a clock that times in linear units with an accurate mean and a negligible variance, a distribution of memory times that is normally distributed with an accurate mean and a scalar standard deviation, and a rule to respond if the clock is "close enough" to a sample of the memory time distribution. This decision is based on a ratio of the discrepancy between the clock time and the remembered time, to the remembered time. When this ratio is below a (variable) threshold, subjects respond. When three timing parameters--coefficient of variation of the memory time, the mean and the standard deviation of the threshold--were set at their median values, a theory with two free parameters accounted for 96% of the variance. The two parameters reflect the probability of attention to time and the probability of a response given inattention. These parameters were not influenced by stimulus manipulations but were affected by manipulations of reinforcement rate and by individual differences.