Ternary rhythmic systems differ from binary systems in stressing every third syllable in a word, rather than every second. Consider the following examples from Cayuvava (Key 1961), where stress is on every third syllable counting from the end of the word:

(1) a. à.ri.hi.hí.be.e ‘I have already put the top on’

b. ma.rà.ha.ha.é.i.ki ‘their blankets’

c. i.ki.tà.pa.re.ré.pe.ha ‘the water is clean’

Ternary rhythm is well-established for only a small group of languages, including Chugach Alutiiq, Cayuvava and Estonian, and possibly Winnebago. Nevertheless the stress patterns of these languages are sufficiently complex to warrant an ongoing debate about the implications for metrical theory (see Prince 1980, Levin 1985, 1988, Halle & Vergnaud 1987, Halle 1990, Hammond 1990, Dresher & Lahiri 1991, Rice 1992, Hewitt 1992, Kager 1993, 1994, Halle & Idsardi 1995, Hayes 1995, Ishii 1996, Elenbaas 1999, among others).

The reason for a fresh look at ternarity is the rise of Optimality Theory (henceforth OT; Prince & Smolensky 1993, McCarthy & Prince 1993a), a theory abandoning most devices on which rule-based accounts of ternarity were based. It abandons serial derivations and together with it directional foot assignment, a core device in parametric theories of word stress, as well as special parsing modes for ternary rhythm (Weak Local Parsing; Hayes 1995). Derivational mechanisms and parameters are replaced by universal and violable constraints, stating well-formedness on output forms, and ranked in language-particular hierarchies.

The issue then arises whether OT is able to predict the ternary patterns in a descriptively adequate fashion. The first goal of this paper is to argue that adequate and insightful analyses are indeed possible in OT for two ternary stress languages: Cayuvava and Chugach Alutiiq. We argue that these analyses require no ternarity-inducing mechanisms, such as ternary feet or special parsing modes. Instead ternarity emerges by LICENSING, involving interactions of the anti-lapse constraint *LAPSE (banning long sequences of unstressed syllables; Selkirk 1984) with standard foot- alignment constraints (ALL-FT-X, ALIGN-Y; McCarthy & Prince 1993b). Our analysis incorporates Ishii's (1996) insight that ternarity is a kind of underparsing, which is licensed by an anti-lapse constraint, and induced by standard foot alignment.