Organisms use circadian clocks to generate 24 hour cycles of gene expression. However, the clock can also interact with other pathways to generate shorter period oscillations with more than one peak per day. It remains unclear how these different frequencies are generated. We examined this problem by studying the coupling of the clock to a circuit controlling the expression of a key photosynthetic gene in the cyanobacterium Synechococcus elongatus. Using single cell time-lapse microscopy, we found genes that are activated with two peaks of expression every circadian cycle. We also observed two peaks of growth rate at the single cell level, suggesting a role for frequency doubling in modulating growth. Using genetic perturbations and mathematical modelling, I will show how this frequency doubling can be generated and modulated. These dynamics are enabled by a simple circuit. Owing to its simplicity, this circuit could be a general motif allowing frequency doubling oscillations in other organisms.