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.

A central idea in rule-based phonology is the serial derivation (Chomsky & Halle 1968). In a serial derivation, an underlying form passes through a number of intermediate representations on its way to the surface:

[Scheme here]

Implementational details can differ: the order of rules might be stipulated or it might be derived from universal principles; the steps might be called ‘rules’, ‘cycles’ or ‘levels’; the steps might involve applying rules or enforcing constraints. But, details aside, the defining characteristic of a serial derivation, in the sense I will employ here, is the pre-eminence of the chronological metaphor: the underlying form is transformed into a succession of distinct, accessible intermediate representations on its way to the surface. I will call any theory with this property ‘serialism’.

Semitic languages such as Hebrew and Arabic are known for what has become characterised as their discontiguous or non-concatenative morphology. In the overwhelming majority of the literature, in both ‘traditional’ and generative grammar, semantically related words in such languages are described as sharing a common ROOT, usually consisting of three consonants. Such consonantal roots are viewed as actual morphemes with lexical status. Words are formed by affixation to roots; the most common type of such affixation is the interleaving of vowels between the consonants of a root. Within current phonology, the morphological status of roots was originally expressed through a multi-tiered representation, where a root occupied a distinguished tier (e.g. McCarthy 1979, 1981). More recently the notion of root has been challenged by Bat- El (1994a), who argues, based on properties of the process of denominal verb formation (DVF) in Modern Hebrew (MH), that the concept of root can be eliminated.

In this paper, I present further arguments that there is no need to refer to roots in the process of DVF in MH. I also show that under such a view a unified, comprehensive treatment of DVF in MH is possible within Optimality Theory (OT; Prince & Smolensky 1993). This analysis goes beyond that originally presented in Bat-El (1994a), in that it has the power to predict the surface pattern of biliteral denominal verbs, whose outputs exhibit variation.

The first influential linguistic research on natural sign languages of the deaf is contained in a monograph by Stokoe (1960).I would like to thank Harry van der Hulst for useful comments on this review. That work demonstrated that sign language (American Sign Language in this case) could be shown to have a level of structure that corresponds to the phonological level, in that it consists of a finite list of meaningless units that combine to form all the lexical items of the language. By substituting just one of these units with another, minimal pairs could be identified. Stokoe further categorised these units into three broad types: handshape, location and movement, a categorisation which has persisted in most subsequent work. The fact that this seminal work addressed phonology rather than any other level of linguistic structure is a significant one, precisely because the physical modality of transmission is so different from that of spoken language. Despite this fact, and despite the obvious iconicity of much of the lexicon, sign languages do in fact have an abstract submorphemic level of structure.

Since Stokoe's discovery, linguists have been trying to describe that structure, and to compare it with that of spoken languages, developing approaches which are more and more informed by theoretical work on phonology of spoken languages. Two inherent problems have challenged researchers in this field: (i) to pinpoint the similarities and differences between the phonology of spoken languages and that of sign languages; and (ii) to understand the mutual relevance of sign language phonology and general phonological theory. Brentari's book about the phonology of American Sign Language (ASL) is the most recent attempt to rise to these challenges.