Phonological dependencies in natural language tend to relate elements which are phonologically similar, and corresponding learning biases have been found in laboratory experiments. This paper interprets the learning facts in terms of "modularity bias", a preference for grammars which minimize interaction between phonological subsystems. Simulations of two experiments with human participants show that human-like modularity bias can emerge from the interaction of two general principles, the Bayesian Occam's Razor and the parametric parsimony of modular grammars.