2.1 Non-finality and two-way contrasts

In discussing two-way contrasts in syllable weight, I focus on default-to-same-side systems – unbounded systems where stress has the same directional orientation whether or not a form contains heavy syllables.Footnote ⁵ When heavy syllables are absent in a form, stress falls on the light syllable at a given edge. When heavy syllables are present, stress falls on the heavy syllable nearest the same edge. As examples, consider Murik (Abbott Reference Abbott1985) and Aguacatec (McArthur & McArthur Reference McArthur and McArthur1956). Both exhibit two-way contrasts, where heavy syllables are syllables with long vowels:

1. (11)

   1. a. Murik

      

   2. b. Aguacatec

      

As (11a) illustrates, Murik stresses the leftmost heavy syllable, when one is available. Otherwise, it stresses the leftmost light syllable. Aguacatec, as illustrated in (11b), has the opposite directional specification. It stresses the rightmost heavy syllable, when one is available. Otherwise, it stresses the rightmost light syllable.Footnote ⁶

Two components are necessary in the analysis of default-to-same-side systems: one to establish directional orientation and one to introduce weight-sensitivity. The task of establishing directionality falls to the gridmark alignment constraints in (12). x_F-L aligns foot-level gridmarks with the prosodic word's left edge, and x_F-R aligns foot-level gridmarks with the prosodic word's right edge. By influencing the position of a gridmark column's foot-level gridmark, foot-gridmark alignment influences the position of the column as a whole and determines the default location for stress.

1. (12)

   1. a. x_F-L The left edge of every foot-level gridmark is aligned with the left edge of some prosodic word.

   2. b. x_F-R The right edge of every foot-level gridmark is aligned with the right edge of some prosodic word.

Non-fin(x_F, μ, σ) produces the appropriate weight-sensitivity. Because it bans stress from syllable-final moras, it requires that stressed syllables be bimoraic, regardless of their position.

To produce a default-to-same-side pattern, Non-fin(x_F, μ, σ) must dominate gridmark alignment, so that it is more important for stress to avoid a light syllable than it is for stress to occur at the default edge.Footnote ⁷ For a left-oriented system like Murik, the crucial ranking would be Non-fin(x_F, μ, σ)≫x_F-L. In forms with heavy syllables, Non-fin(x_F, μ, σ) would shift stress away from the left edge and onto a heavy syllable, with x_F-L ensuring that it occurred over the leftmost. In forms without heavy syllables, x_F-L would return stress to the light syllable at the left edge. Similarly, for a right-oriented system like Aguacatec, the crucial ranking would be Non-fin(x_F, μ, σ)≫x_F-R. In forms with heavy syllables, Non-fin(x_F, μ, σ) would shift stress from the right edge and onto a heavy syllable, with x_F-R ensuring that it occupied the rightmost. In forms without heavy syllables, x_F-R would return stress to the light syllable at the right edge. Since these interactions are fairly straightforward, and similar to those involved in analyses based on peak prominence or stress-to-weight, I omit the example tableaux. For a more detailed presentation, see Hyde (Reference Hyde, Baković, Ito and McCarthy2006).

Though Murik and Aguacatec represent the simplest types of default-to-same-side systems, their rankings can easily be modified to produce the slightly more complicated patterns that avoid stress on prosodic word-final syllables:

1. (13) Non-fin(x_F, σ, ω) (adapted from Prince & Smolensky Reference Prince and Smolensky1993) No foot-level gridmark occurs over the final syllable of a prosodic word.

When we add Non-fin(x_F, σ, ω) to the simple default-to-same-side rankings discussed above, the result is the typology summarised in (14).

1. (14)

   1. a. Left-oriented

      1. i. Non-fin(x_F, σ, ω) Non-fin(x_F, μ, σ) x_F-L Description: Leftmost heavy, else leftmost light; no stress on final syllable Example: Kashmiri (Bhatt Reference Bhatt1989, Kenstowicz Reference Kenstowicz1993)

      2. ii. Non-fin(x_F, μ, σ) Non-fin(x_F, σ, ω) x_F-L Description: Leftmost heavy, else leftmost light Example: Murik

      3. iii. Non-fin(x_F, μ, σ) x_F-L Non-fin(x_F, σ, ω) Same as (ii)

   1. b. Right-oriented

      1. i. Non-fin(x_F, σ, ω) Non-fin(x_F, μ, σ) x_F-R Description: Rightmost heavy, else rightmost light; no stress on final syllable Example: Western Cheremis (sonority-based) (Itkonen Reference Itkonen1955)

      2. ii. Non-fin(x_F, μ, σ) Non-fin(x_F, σ, ω) x_F-R Description: Rightmost heavy, else rightmost light; no stress on final syllable, unless it is the only heavy syllable Example: Sindhi

      3. iii. Non-fin(x_F, μ, σ) x_F-R Non-fin(x_F, σ, ω) Description: Rightmost heavy, else rightmost light Example: Aguacatec

For systems with two-way contrasts in syllable weight, non-finality's performance equals that of recent alternatives. The predictions in (14) match those produced by peak prominence in the Walker (Reference Walker1997) approach, for example, or those that might be produced by stress-to-weight in a similar framework.Footnote ⁸ Next, we turn to systems with three-way contrasts in syllable weight and consider the possibility of an even greater number of contrasts. This is an area where non-finality can be shown to have an important advantage, because it offers a principled account for the upper limit on significant weight distinctions.

2.2 Non-finality and three-way contrasts

An adequate analysis of weight-sensitivity must account for languages where stress is sensitive to a three-way contrast in syllable weight. For example, in Hindi (Kelkar Reference Kelkar1968, Hayes Reference Hayes1995) and Classical Arabic (Abul-Fadl Reference Abul-Fadl1961, Wright Reference Wright1971, McCarthy Reference McCarthy1979), stress prefers trimoraic superheavy syllables above bimoraic heavy syllables and bimoraic heavy syllables above monomoraic light syllables. Examples from Hindi are provided below.

1. (15)

   

As (15) illustrates, Hindi is a default-to-penult language, where stress prefers trimoraic CVVC and CVCC syllables to bimoraic CVV and CVC syllables and bimoraic CVV and CVC syllables to monomoraic CV syllables. When there is a tie for heaviest syllable, as in (15b), stress occupies the rightmost non-final of the tied syllables. When a form has a single heaviest syllable, as in (15a), stress occupies the single heaviest syllable, even if it means occupying the final syllable.

At first glance, it might seem impossible for non-finality to account for three-way contrasts in syllable weight. Since non-finality only distinguishes between final and non-final, it can only distinguish between one and more-than-one. It cannot distinguish between two and more-than-two. We saw in §2.1, for example, that Non-fin(x_F, μ, σ) prefers that stress fall on a multimoraic syllable, where it can avoid the syllable-final mora, rather than a monomoraic syllable, where it cannot:

1. (16)

   

As (16) demonstrates, however, the constraint does not recognise additional contrasts. Since all stressed multimoraic syllables perform equally well on Non-fin(x_F, μ, σ), it cannot require that stress occupy the trimoraic syllable in (a) rather than the bimoraic syllable in (b).

Fortunately, the problem has a simple solution. Non-finality cannot distinguish directly between two and more-than-two, but it can make the distinction indirectly when the two/more-than-two contrast is translated into a one/more-than-one contrast. The proposal accomplishes this translation through differences in the ways that multimoraic syllables map to the metrical grid. In §1.2, we saw that a high-ranked Non-fin(x_μ, μ, σ), ‘no mora-level gridmarks over syllable-final moras’, produces a monopositional mapping for bimoraic syllables. As (17) demonstrates, when it dominates MapGM(μ), ‘every mora has a mora-level gridmark within its domain’, it strips the final gridmark from bimoraic syllables, leaving them with only a single mora-level entry:

1. (17)

   

Applying the same ranking to trimoraic syllables, however, produces a bipositional mapping. As (18) indicates, Non-fin(x_μ, μ, σ) still strips the mora-level gridmark from the final mora, but MapGM(μ) ensures that the two remaining moras both map to the grid:

1. (18)

   

The result is a difference in gridmark mapping that distinguishes heavy syllables from superheavy syllables. Heavy syllables must map monopositionally, just like light syllables, but superheavy syllables can still map multipositionally.Footnote ⁹ Since the mapping distinction is a one/more-than-one distinction – heavy syllables have one mora-level gridmark where superheavy syllables have more than one – it is a distinction that non-finality constraints can detect.

To capture a three-way contrast like that found in Hindi, we can take advantage of the optimal mappings in (17) and (18) by distinguishing final from non-final twice, once with respect to moras and once with respect to mora-level gridmarks. Non-fin(x_F, μ, σ) still distinguishes heavy syllables from light syllables by prohibiting stress over syllable-final moras, but an additional constraint, Non-fin(x_F, x_μ, σ), given in (19), distinguishes superheavy syllables from heavy syllables, by prohibiting stress over syllable-final mora-level gridmarks.

1. (19) Non-fin(x_F, x_μ, σ) No foot-level gridmark occurs over the final mora-level gridmark of a syllable.

When the effects of the two constraints combine, the desired three-way contrast emerges:

1. (20)

   

In (20), the best option is for stress to occupy a superheavy syllable, as in candidate (a). Because they are multimoraic and multipositionally mapped, superheavy syllables allow stress to avoid both a syllable-final mora and a syllable-final mora-level gridmark. The next best option is for stress to occupy a heavy syllable, as in candidate (b). Since heavy syllables are monopositionally mapped but multimoraic, stress fails to avoid the syllable-final mora-level gridmark, but it can still avoid the syllable-final mora. The worst option is for stress to occupy a light syllable, as in candidate (c). Because light syllables are neither multimoraic nor multipositionally mapped, stress can avoid neither the syllable-final mora nor the syllable-final mora-level gridmark.

To flesh out the analysis for the weight-sensitive, default-to-penult system in Hindi, consider the ranking in (21).

1. (21)

   

First, a penultimate default is established by ranking Non-fin(x_F, σ, ω), ‘no stress on prosodic word-final syllables’, above x_F-R. Such a ranking draws stress as far to the right as possible while still avoiding the final syllable. Next, we establish the appropriate weight-sensitivity by ranking Non-fin(x_F, μ, σ), ‘no stress on syllable-final moras’, and Non-fin(x_F, x_μ, σ), ‘no stress on syllable-final mora-level gridmarks’, above the constraints that establish the penultimate default. This ensures that weight-sensitivity has priority over directional orientation. If the penult is not the heaviest syllable, stress can shift from the penult in an effort to seek out the heaviest syllable. Since the interactions are fairly straightforward, I omit the example tableaux.

Although non-finality can establish both two-way and three-way contrasts in syllable weight, it is important to understand that it does not have the ability to count moras. Instead, it uses a final/non-final distinction to indirectly detect a one/more-than-one distinction. It distinguishes monomoraic syllables from multimoraic syllables by distinguishing syllable-final moras from non-final moras, and it distinguishes bimoraic syllables from trimoraic and larger syllables by distinguishing syllable-final mora-level gridmarks from non-final mora-level gridmarks. For non-finality to detect additional weight distinctions, there would have to be additional one/more-than-one contrasts with a sufficiently intimate connection to mora count that they could be used as measures of syllable weight.Footnote ¹⁰ Since moras and mora-level gridmarks exhaust the elements that might qualify to create the appropriate contrasts, however, there can be no non-finality constraints capable of detecting additional weight distinctions, and the contrasts already discussed must constitute the full range of the approach.

To more clearly demonstrate the range of distinctions that non-finality can detect, consider the tableau in (22).Footnote ¹¹

1. (22)

   

Combined, Non-fin(x_F, μ, σ), ‘no stress on syllable-final moras’, and Non-fin(x_F, x_μ, σ), ‘no stress on syllable-final mora-level gridmarks’, allow the approach to distinguish between syllables with one mora, as in (e), syllables with two moras, as in (d), and syllables with three or more moras, as in (a–c). Because syllables with three or more moras always satisfy both constraints, however, the constraints cannot distinguish between them. They cannot distinguish syllables with three moras from syllables with four, for example, or syllables with four moras from syllables with five, and there are no other constraints in the proposal that could make these distinctions.

Non-finality's limited ability to detect weight contrasts is exactly the desired situation. Among the world's languages, the upper limit on significant weight contrasts seems to be the distinction between syllables with two moras and syllables with more than two. There appear to be no languages requiring the grammar to distinguish syllables with three moras from syllables with four, for example, or to distinguish syllables with four moras from syllables with five. In this context, then, non-finality's limitations constitute an important advantage: they offer a principled account for the upper limit on significant weight contrasts.

2.3 Peak prominence and stress-to-weight

In previous OT accounts, Stress-to-Weight and PkProm are the primary options for producing the kind of weight-sensitivity where stress avoids light syllables. The stress-to-weight approach is fairly straightforward. Hammond & Dupoux's (Reference Hammond, Emmanuel, Durand and Laks1996) formulation, for example, given in (23), prohibits stress over light syllables simply by requiring that stressed syllables be heavy:

1. (23) Stress-to-Weight (from Hammond & Dupoux Reference Hammond, Emmanuel, Durand and Laks1996) Stressed syllables are bimoraic.

Although its effects are similar, Prince & Smolensky's (Reference Prince and Smolensky1993) peak prominence approach is more complex. The general formulation in (24a) essentially states that a stress peak over an element with greater prominence is better than a stress peak over an element with lesser prominence. In conjunction with the scale in (24b), its effect is to position stress on heavier syllables at the expense of lighter syllables.

1. (24)

   

One way to implement the peak prominence approach is to say that the general formulation, in combination with the mora scale, generates the set of constraints in (25a) with the universal ranking in (25b).Footnote ¹²

1. (25)

   1. a. *Peak/σ_μ Stress does not occur on a monomoraic syllable. *Peak/σ_μμ Stress does not occur on a bimoraic syllable. *Peak/σ_μμμ Stress does not occur on a trimoraic syllable.

   2. b. Universal ranking *Peak/σ_μ *Peak/σ_μμ *Peak/σ_μμμ

Under the ranking in (25b), stress prefers syllables with two moras above syllables with one (due to *Peak/σ_μ), syllables with three moras above syllables with two (due to *Peak/σ_μμ) and syllables with four or more moras above syllables with three (due to *Peak/σ_μμμ).

Although the peak prominence and stress-to-weight formulations differ considerably from the non-finality formulation, they all have the same ability to capture two-way contrasts in syllable weight. This is why Non-fin, PkProm and Stress-to-Weight all predict the same typology for unbounded systems with two-way weight distinctions (see §2.1). When we consider the possibility of additional distinctions, however, differences begin to emerge.

PkProm's ability to produce three-way contrasts is clear and has been previously demonstrated by Prince & Smolensky (Reference Prince and Smolensky1993) for cases like Hindi. *Peak/σ_μ requires stress to avoid light syllables in favour of heavy syllables, and *Peak/σ_μμ requires stress to avoid heavy syllables in favour of superheavy syllables. The existence of *Peak/σ_μμμ is problematic, however, because it requires stress to avoid syllables with three moras in favour of syllables with four. Such a contrast is unattested among the world's languages, and this situation points to peak prominence's most serious shortcoming. Unlike non-finality, peak prominence cannot offer a principled account for the upper limit on significant weight distinctions. When combined with the mora scale, peak prominence is essentially a mora-counting device, and there is nothing in its formulation to limit how high it can count. While it is true that the scale cuts off after three moras, the cut-off point appears to be completely arbitrary. To avoid the unattested distinction made by *Peak/σ_μμμ, for example, the scale should cut off at two moras, but there seems to be no principle to prevent it from being extended instead, so that it includes four moras, five moras, six moras and so on. This, of course, would allow the approach to make an infinite number of distinctions that no language actually requires.

The situation with Stress-to-Weight is a bit different. Since Stress-to-Weight only has the ability to distinguish between heavy syllables and light syllables, being essentially equivalent to *Peak/σ_μ, it is clear that it cannot capture a three-way contrast in its current form. It is possible, however, that Stress-to-Weight might be reformulated as two separate constraints, as in (26).

1. (26)

   1. a. Stress-to-Heavy Stressed syllables are bimoraic.

   2. b. Stress-to-Superheavy Stressed syllables are trimoraic.

Stress-to-Heavy would have essentially the same effect as *Peak/σ_μ, and Stress-to-Superheavy would have essentially the same effect as *Peak/σ_μμ. Stress-to-weight is also similar to peak prominence, however, in that it is essentially a mora-counting approach, especially if we are free to formulate additional constraints referring to different numbers of moras. If we can add a constraint like (26b) that requires stressed syllables to have three moras, there seems to be no reason why we could not add constraints that require stressed syllables to have four moras, five moras and so on. Like peak prominence, then, stress-to-weight cannot offer a principled account for the upper limit on significant weight distinctions.

2.4 Summary

We have seen that non-finality matches the successes of stress-to-weight and peak prominence when it comes to producing weight-sensitivity in unbounded systems. For languages with two-way contrasts, non-finality predicts the same typology as stress-to-weight and peak prominence. This is expected, since Non-fin(x_F, μ, σ), ‘no stress on syllable-final moras’, has the same effect in prohibiting stressed light syllables as *Peak/σ_μ and Stress-to-Weight. For languages with three-way contrasts, the non-finality approach uses differences in gridmark mapping and an additional constraint, Non-fin(x_F, x_μ, σ), ‘no stress on syllable-final mora-level gridmarks’, to distinguish superheavy syllables from heavy syllables. While stress-to-weight and peak prominence can distinguish superheavy from heavy as well, only non-finality offers a principled account for the observation that the heavy–superheavy contrast marks the upper limit on attested weight distinctions. This indicates that it is both possible and desirable to eliminate stress-to-weight and peak prominence from the theory, transferring their workload to non-finality.Footnote ¹³

Before we move on, there is one other prediction that should be noted in this context. An anonymous reviewer points out that the possibility of ranking Non-fin(x_F, μ, σ), ‘no stress over syllable-final moras’, above a constraint like Dep(μ), given in (27), is problematic in unbounded systems, because it would result in lengthening of the stressed syllable for inputs containing only light syllables.

1. (27) Dep(μ) Every mora present in the output is also present in the input.

While this is true, the prediction is not unique to non-finality. Ranking either Stress-to-Weight or *Peak/σ_μ above Dep(μ) would produce exactly the same result.Footnote ¹⁴ Any framework with a constraint prohibiting stressed light syllables will contain the prediction that stressed syllables can be lengthened. As we shall see in §4, however, the prediction does have advantages in other contexts.

3.1 Non-finality and final syllables

One of non-finality's fundamental characteristics is its asymmetry. Non-finality constraints prevent stress from occupying the final element of a domain, but they do not prevent it from occupying initial or medial elements. In the context of weight-sensitivity, this asymmetry can sometimes go unnoticed. For example, as we saw in §2, when the domain of Non-fin is the syllable itself, stress is sensitive to the weight of all syllables, regardless of their position. The effects of the asymmetry become apparent, however, when the domain of Non-fin is larger. When applied to a larger domain, Non-fin makes stress sensitive to the weight of the domain's final syllable but not to the weight of its initial or medial syllables. The constraint relevant in the context of generalised trochee systems in Non-fin(x_F, μ, ω), repeated in (29), which bans foot-level gridmarks from prosodic word-final moras and, therefore, from light prosodic word-final syllables.

1. (29) Non-fin(x_F, μ, ω) No foot-level gridmark occurs over the final mora of a prosodic word.

Because it refers to prosodic word-final moras, and not to initial or medial moras, it limits its effects to the final syllable of the prosodic word.

Adopting the framework of Hyde (Reference Hyde2001, Reference Hyde2002), we can derive a Weṛgaia-type pattern from a more basic weight-insensitive pattern that positions stress on every odd-numbered syllable counting from the left. The adopted framework produces this more basic pattern, using the constraints in (30a) and the ranking in (30b).

1. (30)

   1. a. PrWd-L The left edge of every prosodic word is aligned with the left edge of some foot-head. Hds-R The right edge of every foot-head is aligned with the right edge of some prosodic word. MapGM(F) A foot-level gridmark occurs within the domain of every foot.

   2. b. Weight-insensitive ranking PrWd-L Hds-R MapGM(F)

Omitting the example tableaux, the ranking in (30b) produces the type of configuration in (31a) for even-parity forms and that in (31b) for odd-parity forms.

1. (31)

   1. a. Even-parity

      

   2. b. Odd-parity

      

PrWd-L anchors a single foot-head at the prosodic word's left edge, and Hds-R draws the remaining foot-heads towards the prosodic word's right edge (foot-heads are indicated using vertical association lines). Since Hds-R is weight-insensitive, preferring disyllabic footing to monosyllabic footing, the weight of the individual syllables does not affect the resulting stress pattern. MapGM(F) ensures that each foot-head coincides with a foot-level gridmark.

To establish the weight-sensitivity appropriate for Weṛgaia-type patterns, we would add Non-fin(x_F, μ, ω) to the ranking in (30b), as in (32), so that it dominates MapGM(F). This ensures that it is more important to avoid stress on a light final syllable than it is to stress the final foot.

1. (32) Weṛgaia ranking PrWd-L Hds-R, Non-fin(x_F, μ, ω) MapGM(F)

Consider the ranking's results for an odd-parity form whose final syllable is light. The light final syllable must remain stressless, but the ability of light initial syllables and light medial syllables to carry a stress is unaffected:

1. (33)

   

In (33), Non-fin(x_F, μ, ω) excludes candidate (b). Since (b) stresses its light final syllable, it positions a foot-level gridmark over the prosodic word-final mora. Although the optimal candidate (a) has a stressless final foot in violation of MapGM(F), leaving the final foot stressless leaves the light final syllable stressless. Notice that no violations of Non-fin(x_F, μ, ω) are incurred by either candidate in connection with stresses that occupy light initial or medial syllables.

Consider now the results for an odd-parity form whose final syllable is heavy. Stress is free to occupy the heavy final syllable, since an additional mora is available to support the gridmark column, and the column need not occur over the prosodic word-final mora:

1. (34)

   

In (34), the optimal candidate (b) stresses its heavy final syllable. Since every foot in (b) is stressed, it satisfies MapGM(F). Since stressing the heavy final syllable does not mean stressing the final mora, it also satisfies the higher-ranked Non-fin(x_F, μ, ω). Notice once again that Non-fin(x_F, μ, ω) ignores the weight of initial and medial syllables.

We have seen, then, that non-finality easily produces a Weṛgaia-type pattern. It makes stress sensitive to the weight of final syllables in generalised trochee systems, and it does so without also making it sensitive to the weight of initial or medial syllables. The basic typology predicted by the interaction of Non-fin(x_F, μ, ω) and MapGM(F) is summarised in (35).Footnote ¹⁶

1. (35) Typology for generalised trochee systems

   1. a. Non-fin(x_F, μ, ω) MapGM(F)  No stress on light final syllables

   2. b. MapGM(F) Non-fin(x_F, μ, ω)  Weight-insensitive system

The success of the non-finality approach in this context, coupled with its success in the context of unbounded stress systems, justifies a unified account of the two phenomena and supports non-finality's central role in the theory. The case is further strengthened in §3.2, where we compare non-finality's predictions to those of foot-minimality approaches.

3.2 Foot-minimality

In requiring that a foot contain at least two moras, foot-minimality (Prince Reference Prince1980, McCarthy & Prince Reference McCarthy and Prince1986, Hayes Reference Hayes1995) often has the effect of making stress sensitive to syllable weight. Since a heavy syllable has two moras, it can always be footed, even if it has to form a foot on its own. This means that heavy syllables are always potentially stressable. In contrast, a light syllable has only one mora, so it cannot form a foot on its own. In cases where additional syllables are unavailable to help support a minimal foot, a light syllable must remain unfooted and unstressed. Below, we examine the potential for foot-minimality to account for weight-sensitivity in generalised trochee languages. We will examine foot-minimality in both rule-based frameworks and constraint-based frameworks, and find that it causes substantial problems of overgeneration in both, but especially in the letter.

3.3 Summary

Non-fin(x_F, μ, ω), ‘no stress on prosodic word-final moras’, accounts for the weight-sensitivity found in generalised trochee languages. Since the constraint is asymmetric, like other non-finality constraints, it can affect the final syllable in a prosodic word without affecting initial or medial syllables. In contrast, foot-minimality approaches suffer from significant overgeneration problems. In a rule-based approach, foot-minimality makes stress sensitive both to final syllables and to initial syllables. In a constraint-based approach, foot-minimality makes stress sensitive to final, initial and medial syllables. This being the case, the non-finality approach clearly makes more accurate predictions, and the foot-minimality analysis should be abandoned. In fact, the pervasiveness of defective weight-sensitivity in the traditional OT approach strongly suggests that FtBin should be abandoned completely, not just in this particular context.Footnote ²³ (See Hyde Reference Hyde2002 for additional typological arguments against the FtBin/Parse-σ approach.)

Thus far, then, we have seen that non-finality makes more accurate typological predictions than the alternatives, both in the context of unbounded stress systems and in the context of generalised trochee systems. This presents a strong case that the two should receive a uniform analysis under a non-finality formulation. It also strengthens the case that non-finality is more than a superficial descriptive generalisation, having produced the desired results in two seemingly unrelated contexts.

4.1 Non-finality in the syllable and non-finality in the foot

Under a non-finality approach, rhythmic lengthening is just a special case of the weight-sensitivity that we have examined throughout the article. To avoid stressing a light syllable – which would mean stressing a domain-final mora – the syllable's vowel is lengthened to make it heavy. The proposal follows Kager (Reference Kager1995) in applying non-finality to the foot domain to promote iambic lengthening, but it goes a bit further in applying it to the syllable domain as well. Applying non-finality to the syllable domain gives the proposal a second mechanism to promote iambic lengthening, as well as a mechanism to promote trochaic lengthening. The relevant constraints are Non-fin(x_F, μ, σ) and Non-Fin(x_F, μ, F).

As we saw in §2, Non-fin(x_F, μ, σ) bans stress from syllable-final moras, making it sensitive to the weight of syllables generally. In contrast, Non-fin(x_F, μ, F) bans stress from foot-final moras, making it sensitive to the weight of foot-final syllables only. Where Non-fin(x_F, μ, σ) prohibits stress over light syllables in general, Non-fin(x_F, μ, F) prohibits stress over foot-final light syllables in particular.

To produce lengthening, one of these non-finality constraints must dominate the faithfulness constraint Dep(μ) (27). Under such rankings, when stress would occupy a light syllable, in violation of Non-Fin, Non-Fin can require that a mora be added, in violation of Dep(μ), to make the syllable heavy. Given their different formulations, however, the non-finality constraints do not have an equal ability to promote lengthening in every type of foot. Since Non-fin(x_F, μ, σ) prohibits stress over light syllables generally, it can produce lengthening when the stressed syllable occurs in an iamb or a trochee. Since Non-fin(x_F, μ, F) prohibits stress over foot-final light syllables in particular, it can produce lengthening when the stressed syllable occurs in an iamb but not when it occurs in a trochee.

To illustrate, first consider the situation where the stressed syllables occur in iambic feet. If the syllables are light, stress will occupy both a syllable-final mora and a foot-final mora. This being the case, ranking either non-finality constraint above Dep(μ) produces lengthening.

1. (50)

   

In (50a), where Non-fin(x_F, μ, σ) dominates Dep(μ), a second mora is added to the underlyingly light syllables to avoid stress on syllable-final moras. In (50b), where Non-fin(x_F, μ, F) dominates Dep(μ), a second mora is added to the underlyingly light syllables to avoid stress on foot-final moras.

Next, consider the situation where the stressed syllables occur in trochaic feet. If the syllables are light, stress will occupy a syllable-final mora but not a foot-final mora. This being the case, ranking Non-fin(x_F, μ, σ) above Dep(μ) produces lengthening, but ranking Non-fin(x_F, μ, F) above Dep(μ) does not:

1. (51)

   

In (51a), Non-fin(x_F, μ, σ) dominates Dep(μ), and the stressed syllables become heavy to allow stress to avoid syllable-final moras. In (51b), Non-fin(x_F, μ, F) dominates Dep(μ). Since stress does not occupy the foot-final syllables in either candidate, and there is no danger that it will occupy the foot-final moras, Non-fin(x_F, μ, F) fails to distinguish between the lengthening option and the faithful option, and Dep(μ) settles on the latter.

Given these results, the non-finality approach clearly meets its obligation to produce both types of lengthening. Two constraints, Non-fin(x_F, μ, σ) and Non-fin(x_F, μ, F), produce lengthening in iambs, and one, Non-fin(x_F, μ, σ), produces lengthening in trochees. As we shall see next, the difference in the number of constraints that can produce the two types accounts for the difference in frequency with which they occur.

4.2 Peak prominence and stress-to-weight

As discussed in §2.3, PkProm and Stress-to-Weight prohibit stress on light syllables generally. This being the case, they would produce lengthening in both iambs and trochees when ranked above Dep(μ), apparently presenting viable alternatives to non-finality for producing rhythmic lengthening. Since PkProm and Stress-to-Weight cannot limit weight-sensitivity to foot-final syllables, however, they fail to make the correct predictions in two areas.

First, consider the predictions of peak prominence and stress-to-weight with respect to the relative frequency of iambic and trochaic lengthening. Neither approach offers a principled means to restrict the effects of its constraints to foot-final syllables, so constraints that prohibit stress on light syllables generally would have to be used to promote lengthening in both trochees and iambs. Every ranking that produces lengthening in iambs would also produce lengthening in trochees, and every ranking that produces lengthening in trochees would also produce lengthening in iambs. Since the percentage of possible rankings that produce trochaic lengthening would be the same as the percentage of possible rankings that produce iambic lengthening, we would expect them to occur with equal frequency.

Second, consider the predictions of peak prominence and stress-to-weight concerning the typology of minimal words that accompany regular lengthening. Since lengthening must always result from constraints that prohibit stress on light syllables generally, the minimal words established by these constraints must always contain a heavy syllable. This means that peak prominence and stress-to-weight correctly predict the existence of H and HL minimal words, but it also means that they incorrectly predict the absence of LL minimal words.

Despite their ability to produce both iambic and trochaic lengthening, then, peak prominence and stress-to-weight fail to present viable alternatives to non-finality. Since they cannot restrict their effects to foot-final syllables, they cannot predict the relative frequency of iambic lengthening and trochaic lengthening, and they cannot predict the typology of minimal words associated with regular lengthening.

4.3 The Iambic-Trochaic Law

Since it has played such a significant role in the development of metrical stress theory, particularly in the context of rhythmic lengthening, it is important to examine the predictions of the Iambic-Trochaic Law (Hayes Reference Hayes1985, Reference Hayes1995) with respect to the issues outlined above:

1. (56) Iambic-Trochaic Law

   1. a. Elements contrasting in intensity naturally form groupings with initial prominence.

   2. b. Elements contrasting in duration naturally form groupings with final prominence.

First, consider the predictions of the Law with respect to the existence of both iambic lengthening and trochaic lengthening. Since one of the Law's fundamental requirements is that the constituents of iambic feet have a durational contrast and that the constituents of trochaic feet do not, any approach that might reasonably be said to be based on the Law will predict the existence of iambic lengthening and the non-existence of trochaic lengthening. The reason is simply that both types of lengthening create durational contrasts. An LL iamb becomes an LH iamb, and an LL trochee becomes an HL trochee. While the result for iambs is sanctioned by the Law, the result for trochees is not.

Approaches based on the Iambic-Trochaic Law, then, fail to meet the first of the obligations discussed above – that an account of rhythmic lengthening be able to produce both iambic lengthening and trochaic lengthening. Since they fail to produce trochaic lengthening at all, it can hardly be argued that they meet the second obligation either – the obligation to capture the relative frequency between the two types. Lengthening in trochaic feet occurs less frequently than lengthening in iambic feet, but it does not occur with a frequency of zero.

Next consider the predictions of the Law with respect to the typology of minimal words associated with regular lengthening. One of the most significant features of the Iambic-Trochaic Law is that it does nothing to enforce word- or foot-minimality requirements. It does nothing to ensure that a word or foot is disyllabic, or even bimoraic, because it only applies to feet that are already disyllabic. The Law can force an iamb's stressed syllable to be bimoraic, because it requires a durational contrast between the two syllables of an iambic foot. Since monosyllabic feet have only one syllable, however, they cannot contain a durational contrast, and the Law cannot force monosyllables to be heavy. Given this situation, approaches based on the Law must also include a separate stipulation concerning word- or foot-minimality. Since the two are not necessarily connected, there is no reason that their effects should coincide, and the approach incorrectly predicts that regular lengthening can be accompanied by an L minimal word. The Law also fails, then, in the third of the obligations mentioned above – the obligation to predict the correct typology of minimal words accompanying regular lengthening.

4.4 Harmonic Parsing

The Harmonic Parsing approach of Prince (Reference Prince1990), the last approach examined here, incorrectly predicts that regular lengthening languages allow LH minimal words. The approach might be implemented in an OT framework with the two universal rankings in (57).

1. (57)

   

As (57) indicates, there is a set of constraints that prohibit various configurations for each foot-type, and these constraints receive a universal ranking according to the relative unacceptability of the prohibited configurations. For an iambic foot-type, in particular, (57a) indicates that L feet are less acceptable than LL and H feet, and LL and H feet are less acceptable than LH feet.

To produce iambic lengthening, we would rank Dep(μ) below *L and *LL, allowing moras to be inserted to avoid these unacceptable iambic configurations. The result would be canonical LH feet in longer forms and H feet in monosyllabic forms. This is the desired result. However, if we were also to consider faithfulness constraints that prevent the insertion of segments – ranking them below *L, *LL and *H – underlying L forms would become LH forms on the surface. The high-ranking *L, *LL and *H constraints would ensure that enough segmental material could be added to an underlyingly monomoraic form to make it a canonical iamb: /CV/→[CV.CVː]. The result is the incorrect prediction mentioned above, that regular lengthening languages can have LH minimal words.

On the positive side for Harmonic Parsing, an anonymous reviewer rightly points out that the universal ranking in (57a) does not predict that iambic lengthening can be accompanied by L minimal words. Since Dep(μ) must rank below *LL to produce iambic lengthening in longer forms, it must also rank below *L, allowing for lengthening in monosyllabic forms as well. There are some additional negative points, however, beyond the prediction of LH minimal words already mentioned. First, the Harmonic Parsing approach, like the Iambic-Trochaic Law approach, fails to produce trochaic lengthening. Second, as an anonymous associate editor points out, the approach is unappealing, because the prohibition against L feet must be included in the grammar three times: in the iambic ranking, in the trochaic ranking and in FtBin. Prohibitions against LL and H feet are also included in both the iambic and trochaic rankings.

4.5 Summary

In this part of the discussion, I have outlined three issues that an adequate analysis of rhythmic lengthening must address. The first is the existence of two types of lengthening – iambic and trochaic – and the second is the difference in frequency with which they occur. The third is the typology of minimal words that can accompany regular lengthening.

First, we saw that non-finality meets the obligation to produce both types of lengthening. Non-finality in the foot can produce iambic lengthening, and non-finality in the syllable can produce both iambic lengthening and trochaic lengthening. Second, because there are more ways to produce iambic lengthening than trochaic lengthening, the approach correctly predicts that lengthening should occur less frequently among trochaic systems than iambic systems. The peak prominence and stress-to weight approaches, which would use a single constraint to produce both types of lengthening, fail to predict this asymmetry. The Iambic-Trochaic Law and Harmonic Parsing approaches fail to produce trochaic lengthening at all.

Third, we saw that non-finality correctly predicts the typology of minimal words that can accompany regular lengthening. It can limit regular lengthening languages to H, LL and HL minimal words, because the same constraints that promote lengthening also establish the appropriate minimal word restrictions. In contrast, the Iambic-Trochaic Law approach fails to predict the correct typology, because it produces regular lengthening with L minimal words. The Harmonic Parsing approach fails to predict the typology because it produces regular lengthening with LH minimal words.

Non-finality, then, makes more accurate typological predictions than the alternatives in the context of rhythmic lengthening, just as it does in the contexts of unbounded stress systems and generalised trochee systems. Its success in each of these areas allows the proposal to approach them with a unified analysis, and it indicates that non-finality's role in the grammar is much more significant then previously supposed.