A factorial typology in OT (Optimality Theory, Prince and Smolensky 1993) is the set of all grammars and languages predicted by a given set of constraints. If there are n constraints, there will be n!=1*2*...*n ("n factorial") different grammars (producing usually less than n! different languages, since several rankings of the constraints often converge on the same language). Building on the descriptive work of Kubozono 2012, this talk will develop a factorial typology of the lexical and postlexical tone system of Japanese, focusing on the tonal microvariation in the Kagoshima dialects (Ito and Mester 2018). In the process, various prosodic issues of general import will arise, such as the prosodic hierarchy, syllables vs. moras as counting units and accent carriers, and the interplay of lexical and postlexical processes in a stratal organization of grammar (Kiparsky 2015).