The Problem

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Bruce Hayes March 29, 2017

Faithfulness and Componentiality in Metrics*

  1. The Problem

The field of generative metrics attempts to characterize the tacit knowledge of fluent participants in a metrical tradition. An adequate metrical analysis will characterize the set of phonological structures constituting well-formed verse in a particular tradition and meter. Structures that meet this criterion are termed metrical. An adequate analysis will also specify differences of complexity or tension among the metrical lines. Example (1) illustrates these distinctions with instances of (in order) a canonical line, a complex line, and an unmetrical line, for English iambic pentameter.

  1. a. The li- / on dy- / ing thrust- / eth forth / his paw Shakespeare, R3 5.1.29

b. Let me / not to / the mar- / riage of / true minds Shakespeare, Sonnet 116

c. Ode to / the West / Wind by / Percy / Bysshe Shelley Halle and Keyser (1971, 139)

The goals of providing explicit accounts of metricality and complexity were laid out in the work of Halle and Keyser (1966) and have been pursued in various ways since then.
From its inception, generative metrics has been constraint-based: formal analyses consist of static conditions on well formedness that determine the closeness of match between a phonological representation and a rhythmic pattern. The idea that the principles of metrics are static constraints rather than derivational rules has been supported by Kiparsky (1977), who demonstrated that paradoxes arise under a view of metrics that somehow derives the phonological representation from the rhythmic one or vice versa.
The idea that grammars consist of well-formedness constraints has become widespread in linguistic theory. An important approach to constraint-based grammars in current work is Optimality Theory (= “OT”, Prince and Smolensky 1993), whose basic ideas have been applied with success in several areas of linguistics. One might expect that metrics would be easier to accommodate in the OT world view than any other area, given that metrics has been constraint-based for over 35 years. Surprisingly, problems arise when one attempts to do this.
To begin, OT is, at least at first blush, a derivational theory: it provides a means to derive outputs from inputs. But in metrics, the idea of inputs and outputs has no obvious role to play; rather, we want to classify lines and other structures according to their metricality and complexity.
Second, there is the problem of marked winners: as we will see, many existing lines or other verse structures violate Markedness constraints. Why shouldn’t these marked winners lose out to less marked alternatives? Hayes and MacEachern (1998) attempt to explain this by supposing that whenever a winning candidate violates a Markedness constraint, there are still higher-ranking Markedness constraints that are violated by all of the rival candidates. However, as we will see, this cannot be true in general.
In phonology, the reason marked winners can occur is plain: they obey Faithfulness constraints that are violated by all of their less-marked rivals. But it is not immediately clear how Faithfulness can be implemented in metrics: in a patently non-derivational system, where are the underlying forms that surface candidates can be faithful to?

Third, the problem of marked winners arises again when we consider metrical complexity. Intuitively, in certain cases we want to say that the Markedness violations of a winner give rise to a complexity penalty. However, as we will see, in many other cases, Markedness violations can occur with inducing any penalty at all. What distinguishes the two cases?

Last, there is a problem of the missing remedy. OT defines the output of any derivation as the most harmonic candidate, the form created by GEN that wins the candidate competition. Thus, in principle, every unmetrical form ought to have a well-formed counterpart, an alternative that wins the competition that the unmetrical form loses. But this fails to correspond to the experience of poets and listeners; unmetrical forms like (1)c usually sound wrong without suggesting any specific alternative.1
All of these problems would have a quick and easy solution under a recent proposal made by Golston (1998); see also Golston and Riad (2000). These authors suggest that the unmetrical lines are simply those that violate high-ranked Markedness constraints, and complex lines are those which violate medium-ranked Markedness constraints. This solution is a radical one, since it claims that in metrics—unlike any other component of grammar—there are no effects of constraint conflict. In other grammatical components, it is commonplace for a candidate to win (and sound perfect) even when it violates a high ranked constraint, when all rivals violate even higher-ranked constraints. Moreover, Hayes and Kaun (1996) and Hayes and MacEachern (1998) give evidence for constraint-conflict effects in metrics, so I believe that the strategy of a special version of OT just for metrics would not work in any event.
My own proposal for solving the problems outlined above draws from several sources.

  • Following the principle of the Richness of the Base (Prince and Smolensky 1993:191, Smolensky 1996), an OT grammar can be used to delimit a set of well-formed representations, rather than derive one set of representations from another.

  • To derive marked winners, I adopt metrical Faithfulness constraints, which are ranked against Markedness constraints and determine which forms emerge as metrical in spite of their Markedness violations. The problem of finding the required underlying representations can be solved by fiat, simply by adopting the surface form of each metrical entity as its underlying form (Keer and Baković 1997, Baković and Keer 2001).

  • With Faithfulness constraints in place, the problem of metrical complexity can be addressed by using the stochastic approach to gradient well formedness developed in Hayes and MacEachern (1998), Hayes (2000), and Boersma and Hayes (2001).

  • Finally, to solve the missing-remedy problem, I assume (following Kiparsky 1977) that the metrical grammar is componential, and that candidate representations should be evaluated independently in each component. To be well formed, an output must win the competition for every component. This permits grammars that rule out forms absolutely, without suggesting an alternative.

The data with which I will test my proposals involve two problems that (in my opinion) received only partial solutions in earlier work: free variation in quatrain structure (Hayes and MacEachern 1998) and the distribution of mismatched lexical stress in sung verse (Hayes and Kaun 1996).

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