Harmonic Serialism (HS; McCarthy 2007b, 2008a,b, 2009) and Optimality Theory with Candidate Chains (OT-CC; McCarthy 2007a,c) make assumptions about production of candidates by Gen significantly different from classic OT (Prince and Smolensky 2004). There are important differences in the ability of Gen to supply candidates recursively and the degree of “freedom of analysis” given to Gen.

On the one hand, classic OT is a parallel model and Gen yields output candidates only once. As a corollary, classic OT necessarily allows Gen to generate candidates entirely different from a given input. On the other hand, HS and OT-CC are serial theories and endow Gen with the ability to generate candidates recursively. But they impose a restriction on Gen: gradualness. It dictates that each step may contain at most...

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