  We consider a system hierarchically modular, if besides its hierarchical
structure it shows a sequence of scale separations from the point of view of
some functionality or property. Starting from regular, deterministic objects
like the Vicsek snowflake or the deterministic scale free network by Ravasz et
al. we first characterize the hierarchical modularity by the periodicity of
some properties on a logarithmic scale indicating separation of scales. Then we
introduce randomness by keeping the scale freeness and other important
characteristics of the objects and monitor the changes in the modularity. In
the presented examples sufficient amount of randomness destroys hierarchical
modularity. Our findings suggest that the experimentally observed hierarchical
modularity in systems with algebraically decaying clustering coefficients
indicates a limited level of randomness.
