In the analysis of free variation in phonology, we often encounter the effects of intersecting constraint families: there are two independent families of constraints, each of which has a quantifiable effect on the outcome. A challenge for theories is to account for the patterns that emerge from such intersection. We address three cases: Tagalog nasal substitution, French liaison/elision, and Hungarian vowel harmony, using corpus data. We characterize the patterns we find as across-the-board effects in both dimensions, restrained by floor and ceiling limits. We analyze these patterns using several formal frameworks, and find that an accurate account is best based on harmonic grammar (in one of its two primary quantitative implementations). Our work also suggests that certain lexical distinctions treated as discrete by classical phonological theory (e.g. ‘h-aspiré’ vs. ordinary vowel-initial words of French) are in fact gradient and require quantitative treatment.


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pp. 497-548
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