|Abstract:||Phonologists focus on a few processes at the time. This practice is motivated by the intuition that phonological processes factorize into clusters with no interactions across clusters (e.g., obstruent voicing does not interact with vowel harmony). To formalize this intuition, we factorize a full-blown representation into under-specified representations, each encoding only the information needed by the corresponding phonological cluster. And we require a grammar for the original full-blown representations to factorize into grammars that handle the under-specified representations separately, independently of each other. Within a harmony-based implementation of constraint-based phonology, HG is shown to follow axiomatically from this grammar factorizability assumption.