This article presents properties of the clock–counter model with a periodic generator employed as the source of regularly emitted pulses. The pacemaker and accumulator mechanisms are often considered in research in neurobiology and cognitive science: neurons or their groups serve as oscillators, and the number of spikes emitted while a stimulus lasts becomes an estimate of the length of the stimulus. The article integrates three approaches: a theoretical model to present the general concept, a working implementation of this model to perform intensive simulation experiments, and the analytical description of the behavior of the model. Oscillators that exhibit some degree of regularity have been compared to the Poisson ones, and the corresponding probability distributions have been presented that describe the number of pulses accumulated over time. Several continuous and discrete interpulse distributions have been investigated, and the influence of generator parameters on the possible outcomes of the measurement have been described. Particular attention has been paid to the relationship between measurement variability and the mean number of pulses observed. Issues concerning practical realizations of periodic generators: discrete time, dependence of the generator start time on the stimulus, and relation to Weber’s law have been discussed as well.