The theoretical description of synchronization phenomena often relies on coupled units of continuous t    ime noisy Markov
chains with a small number of states in each unit. It is sometimes assumed, either explicitly or implicitly, that coupled
discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators.
We explore condi    tions that justify this assumption by coarse graining continuous phase units. In particular, we determine
the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.