2.1 Harmonic Serialism

HS shares with parallel OT several trademark features, including the characterisation of a grammar as a ranking of some presumed-to-be-universal set of constraints, but it departs from parallel OT in its assumptions about how an input is mapped onto an output.Footnote ² In parallel OT, any and all mutations of an input are performed in parallel, and the resulting candidates are evaluated once, with a single winner chosen relative to the ranking of the constraints. In contrast, an input to an HS grammar is gradually altered to reach an output, with each step in the derivation chosen by optimisation over a set of alternatives derived by ‘do[ing] any one thing’ to the previous iteration's output (Prince & Smolensky Reference Prince and Smolensky2004: 6). The same ranking is used at each iteration, and the derivation converges when the input to a particular iteration is returned as the optimal candidate at that iteration, as this indicates that no additional changes result in a more harmonic output relative to the constraint hierarchy.

In terms of the formal architecture, Con and Eval work the same in HS and parallel OT, while Gen and the relationship between Gen and Eval are different. The Gen of HS does not have the ‘freedom of analysis’ which characterises the Gen component of parallel OT (McCarthy & Prince Reference McCarthy and Prince1993b). Instead, it only provides candidates differing in at most one respect from the input at each iteration. The Gen–Eval relationship is also different in HS, in that Gen and Eval are in a loop until convergence: Gen produces a set of single-change candidates, Eval selects the optimal one relative to the constraint hierarchy of the language and this intermediate output is passed back to Gen for another iteration in which all single-change candidates from this intermediate form are computed and then compared.

Because of the nature of optimisation, it is true in HS as well as in parallel OT that any form that wins over a faithful candidate is less marked with respect to the constraint hierarchy (Moreton Reference Moreton and McCarthy2004). This is because a form which violates a faithfulness constraint can only win when it better satisfies a higher-ranked markedness constraint. The result is that derivations are always harmonically improving. Each form is more harmonic than the previous form and less harmonic than any subsequent form (until convergence); this is guaranteed by the architecture of the system.

Finally, a winner at any iteration is a locally optimal candidate; it wins when compared to the members of a limited candidate set, which includes only the input to that iteration and forms that are one change away from the input. Thus, every form in an HS derivation is a local optimum. At each iteration both the best kind of change is chosen (whether to delete a segment or to build a metrical foot, for example), and also the best instance of the best change (e.g. the best way to delete one segment or the best way to build one foot). Parallel OT, in contrast, always finds the global optimum relative to that input and constraint ranking. The global optimum is the best possible candidate, relative to a given constraint ranking, among the infinite set of candidates produced by the unrestricted Gen of parallel OT. Sometimes an HS derivation terminates at a local optimum that also happens to be the global optimum, but sometimes it does not. In the latter case, the typological predictions of parallel OT and HS can differ even when the same constraint ranking is employed. Failure to converge on the hypothetical global optimum in an HS derivation occurs when it is not possible to reach it in a series of gradual, locally optimal, harmonically improving steps, however one step has been defined. This paper will argue (along with other recent work, e.g. McCarthy Reference McCarthy, Baković, Ito and McCarthy2006, Reference McCarthy2010a, Reference McCarthyb) that parallel OT's global optimum is not always the typologically correct output. In other words, HS's failure to reach such a candidate is not a failure at all.

2.2 Gradualness in IFO

2.3 Illustration

This section presents a stress derivation in HS/IFO for the language Pintupi (Pama-Nyungan; Northern Territory, Australia; Hansen & Hansen Reference Hansen and Hansen1969, Reference Hansen and Hansen1978), which has been analysed as having a quantity-insensitive trochaic stress system (Hayes Reference Hayes1995). Main stress is initial, with secondary stresses falling on odd-numbered non-final syllables. The data in (4) demonstrate the pattern. Vowel length in Pintupi is only contrastive in the initial syllable, which always receives main stress, and syllable codas are assumed to be non-moraic, since stress is indifferent to them.

1. (4)

   

I analyse Pintupi with left-aligning (that is, left-to-right) syllabic trochees, adapting the standard analysis from Hayes (Reference Hayes1995), using constraints developed in McCarthy & Prince (Reference McCarthy and Prince1993a) and Prince & Smolensky (Reference Prince and Smolensky2004).Footnote ⁶ The constraints that will be used inherit their definitions from parallel OT analyses, but they will ultimately result in different predictions in IFO (as the next sections will show) because of the difference between parallel and serial evaluation.

The constraint Parse-σ, defined in (5a), provides the impetus for foot-building (Prince & Smolensky Reference Prince and Smolensky2004), while generalised alignment constraints AllFt-L and AllFt-R, defined in (5b, c), account for directionality by preferring feet to be aligned as far as possible to the edge of the word (McCarthy & Prince Reference McCarthy and Prince1993a).

1. (5)

   

In order to enforce left-headed feet (i.e. trochees) over right-headed feet (i.e. iambs), the two constraints in (6) are necessary. These are equivalent to the RhType (‘rhythmic type’) constraints of Prince & Smolensky (Reference Prince and Smolensky2004: 63). Monosyllabic feet are assumed to satisfy both constraints.

1. (6)

   

Feet in Pintupi are strictly disyllabic, so a constraint preferring binary feet is needed. I adopt Prince & Smolensky's (Reference Prince and Smolensky2004: 56) foot-binarity constraint, FtBin, defined in (7), which they adapt from Prince (Reference Prince1980).

1. (7)

   

In principle, this constraint assigns violations to a foot with fewer than two moras, (ˈL), and feet with more than two syllables, (σσσ), etc., but it does not rule out (ˈH), since a heavy syllable is binary at the moraic level. Thus, FtBin can force disyllabic feet just when a language makes no quantity distinctions. Pintupi contrasts vowel length only in initial position, so if we make the reasonable assumption that the grammar will account for the limited distribution of long vowels, the definition of FtBin in (7) will be sufficient. It will prevent words in Pintupi from having monosyllabic feet, ruling out parses like (ˈσσ)(ˈσσ)(ˈσ) when it is ranked above Parse-σ, which successfully accounts for the absence of stress on final syllables in this language.Footnote ⁷ This will be evident in the tableaux below.

For a syllabic trochee stress pattern, these constraints must be ranked so that a five-syllable input /σσσσσ/ is ultimately parsed as (ˈσσ)(ˈσσ)σ, in a series of harmonically improving foot-building steps. The derivation will follow the trajectory shown in (8), with a five-syllable word from Pintupi. The following paragraphs provide ranking arguments for the derivation of this form in IFO.

1. (8)

   

In the first step, a left-aligned disyllabic trochee beats every other candidate (see (2) for an exhaustive list). The tableau in (9) shows the first step of the derivation. This and subsequent tableaux in this paper are presented in a modified version of the comparative format of Prince (Reference Prince, Carpenter, Coetzee and de Lacy2002). Each row displays the number of violation marks that the candidate receives on each constraint as a series of positive integers (replacing the familiar *'s). Rows with losing candidates are also annotated with Ws and Ls to indicate how each losing candidate compares to the winner with respect to each constraint. When a losing candidate receives more violations than the winning candidate on a given constraint, a W accompanies the loser's violations, to indicate that the constraint favours the winner. When a losing candidate receives fewer violations than the winning candidate on a given constraint, an L appears instead, to show that the constraint favours the loser. If a losing candidate has the same number of marks for a constraint as the winning candidate, neither a W nor an L is present. This tableau format allows ranking arguments to be displayed clearly. For the intended winner to win, any loser-favouring constraint must be dominated by a winner-favouring constraint, and thus any L in the tableau must be dominated by a W in the same row. For the left-aligned disyllabic trochee to be optimal in the first step of the derivation, the tableau in (9) shows that AllFt-L must dominate AllFt-R (according to row (c)), and Trochee must dominate Iamb (row (d)). Parse-σ must also be high enough ranked to compel building this foot, even though doing so causes violations of Iamb and AllFt-R, as indicated by the location of Ws and Ls in row (a).

1. (9)

   

For a full analysis, it is necessary to continue through the derivation and confirm that the rankings that are needed at the first iteration are consistent with those required at subsequent iterations. Additional ranking arguments can also be made as the derivation proceeds. At the second iteration, (ˈpu.ɭ iŋ)(ˈka.la)u wins over its competitors. As row (a) of the tableau in (10) shows, this requires that one additional ranking be assumed: Parse-σ≫AllFt-L. McCarthy & Prince (Reference McCarthy and Prince1993a) show that this ranking must hold to account for rhythmic stress in parallel OT; otherwise, a single foot remains at the left edge and additional feet are not built. The same holds in IFO.

1. (10)

   

The third iteration requires that (ˈpu.ɭ iŋ)(ˈka.la)u again be returned as the best output, indicating that additional foot-building is not harmonically improving and signalling convergence. Because the input to this iteration, (ˈpu.ɭ iŋ)(ˈka.la)u, contains only one free syllable, there is only one other candidate for adding foot structure, (ˈpu.ɭ iŋ)(ˈka.la)(ˈu). This candidate loses on the grounds that it contains a monomoraic foot, even though it satisfies Parse-σ perfectly. The ranking FtBin≫Parse-σ accounts for this, as shown in (11).

1. (11)

   

The summary tableau in (12) shows the full derivation of this form with this ranking in place.Footnote ⁸ To recap, candidate (b) wins in the first iteration because it satisfies Trochee and FtBin, and is left-aligned to the edge of the word in accordance with AllFt-L. This form is passed to the second iteration, where it appears in (e) as the locally faithful candidate. At this step, candidate (f) is chosen as optimal because it adds a foot of the proper form (disyllabic trochee) and satisfies Parse-σ better than not adding a foot. This form is then passed to the third iteration, at which point the new locally faithful candidate in (g) is compared to the only remaining stress candidate, which has added a monomoraic foot on its final syllable. The fully parsed candidate fatally violates FtBin, which outranks Parse-σ, and the derivation converges by choosing candidate (g).

1. (12)

   

This example shows how standard stress constraints in OT combined with the architecture of HS and the assumptions of IFO are capable of modelling the common directional stress pattern of Pintupi.

2.4 Summary

IFO proposes that stress patterns emerge from a series of optimisations which successively choose the best foot. Gen produces candidates with one additional foot at each iteration, and the constraint ranking determines which foot is chosen as optimal and passed to the next iteration. The assumption of strict inheritance dictates that which syllables constitute a foot's membership and which syllable is designated as head of that foot are not alterable in the course of deriving word stress.

In the next three sections I compare the predictions of IFO and parallel OT using the standard stress constraints and metrical representations that were employed in the preceding analysis. There are two reasons for adopting this method of comparison. First, some assumptions about Gen and Con have to be made in order for HS and parallel OT to make typological predictions, and holding these assumptions constant highlights the role of serialism vs. parallelism for the resulting typologies. And secondly, the stress constraints of McCarthy & Prince (Reference McCarthy and Prince1993a) and Prince & Smolensky (Reference Prince and Smolensky2004) are widely used in parallel OT, as are the representational assumptions on which they are based. It is reasonable to say that this set of assumptions represents the standard theory of stress in parallel OT. Throughout the discussion I will continue to refer to this as ‘the standard theory of stress in parallel OT’ (or occasionally just ‘the standard theory’), in order to emphasise that the specifics of the discussion depend, as always, on one's assumptions about Gen and Con.

3.1 Local weight-sensitivity in Weɽ gaia

Weɽ gaia (Pama-Nyungan; Southeastern Australia (extinct); Hercus Reference Hercus1969, Reference Hercus1986) has a stress pattern that is similar to that of Pintupi, which was discussed in the previous section. Main stress is initial, with secondary stresses on remaining odd-numbered syllables. But while stress never falls on the final syllable in Pintupi, in Weɽ gaia a final odd-numbered syllable is stressed if (and only if) it is heavy, making it a canonical generalised trochee stress pattern. Vowel length in Weɽ gaia is limited to initial position (Hercus Reference Hercus1986: 81), and thus only closed syllables are able to induce final stress in odd-parity words.Footnote ⁹ (14a) shows words with an even number of syllables, (b) odd-parity words with a final light syllable and (c) odd-parity words with a final heavy syllable.

1. (14)

   

3.2 Non-local weight-sensitivity (unattested)

It is clear that a relatively straightforward analysis of Weɽ gaia is possible in both IFO and in the standard theory of stress in parallel OT, with the addition of a commonly used rhythm constraint. But the constraints needed for the standard analysis in §3.1.2 predict other partially quantity-sensitive stress patterns which are non-local and are not attested, revealing an overgeneration problem for the standard theory of stress in parallel OT. The discussion in this section follows Hyde (Reference Hyde2007), though very similar problems for the standard theory are discussed by Karttunen (Reference Karttunen, Butt, Dalrymple and King2006) and Frampton (Reference Frampton2007).

When rhythm constraints like *Clash are ranked low enough to allow the standard parsing constraints to dictate stress patterns, Hyde demonstrates that a class of languages that have ‘a very peculiar type of weight-sensitivity’ (2007: 312) is predicted to exist. With the ranking FtBin≫Parse-σ≫AllFt-L≫*Clash for example, parallel OT generates a language with the stress system illustrated in the following tableaux.

When no heavy syllables are present in a word with an odd number of syllables, the parsing appears to be unambiguously left-to-right, as shown in (21).

1. (21)

   

However, as shown in (22), an initial heavy syllable is parsed into a monosyllabic foot, as permitted by FtBin, in order to better satisfy Parse-σ.

1. (22)

   

Similarly, a medial heavy syllable with an even number of light syllables to its left and to its right is parsed as a monosyllabic foot in (23). *Clash will not be respected, because it is low-ranked, unlike in generalised trochee languages.

1. (23)

   

The tableau in (24) shows that this language is indeed only partially quantity-sensitive. The input /HLHLH/ has three heavy syllables, and only one (the leftmost) is stressed and footed as a monosyllable, while the other two heavy syllables are parsed into the weak branch of a foot. Thus heavy syllables are not preferred to be stressed generally under this ranking, and in fact are only parsed as monosyllabic feet when doing so improves the word's overall performance on Parse-σ. When several heavy syllables can serve this purpose, the choice between them is made by AllFt-L, as comparing candidate (a) with (b) and (c) in tableau (24) reveals.Footnote ¹¹

1. (24)

   

The tableaux in (25) show furthermore that heavy syllables in even-parity words are not parsed into monosyllabic feet, even when Parse-σ can be equally satisfied by doing so (e.g. (25b.ii)).

1. (25)

   

The result of this ranking is a stress system described in terms of weight-sensitivity in the following way, paraphrasing Hyde (Reference Hyde2007: 312): parsing is insensitive to the weight of a heavy syllable when it occurs in an even-numbered syllable of an odd-parity word, or any syllable of a word with even parity; parsing is sensitive to the weight of a heavy syllable when it occurs in an odd-numbered syllable of an odd-parity word, and is the closest heavy syllable to the left edge of the word among those heavy syllables with these properties. The description of this stress pattern is necessarily somewhat convoluted. A schematic illustration is given in (26), where σ=any weight (H or L).

1. (26)

   

For Hyde, this prediction is one of several stress patterns produced by the standard theory that show an odd pattern of weight-sensitivity. In the rest of this subsection I offer a different way of viewing this problematic prediction, in terms of (non-)locality (see also Frampton Reference Frampton2007).

Although an input with an odd number of light syllables suggests that the language uses left-to-right parsing, as was shown in (21), the other forms in the language fail to show a consistent direction of metrification. For an input like /HLLLL/ the outcome is (ˈH)(ˈLL)(ˈLL), with the heavy syllable parsed as a monosyllabic foot, as was shown in (22), while for /HLLL/ it is (ˈHL)(ˈLL), with the heavy syllable parsed into a disyllabic foot with the immediately following syllable, as in (25a). The strangeness of this stress system derives from the fact that the parity count of the syllables in the word must be known in order to know how to parse an initial heavy syllable despite the fact that it otherwise appears to be a left-to-right stress system. If the total number of syllables in the word is odd, as in /HLLLL/, then an initial heavy is parsed as a monosyllabic foot, but if the total number is even, as in /HLLL/, an initial heavy is parsed into a disyllabic foot with the syllable that follows, whether heavy or light.

Providing a generalisation for how a given word-medial heavy syllable will be parsed in this language reveals the pattern to be very much like the non-local truncation process discussed in the introduction. For a given word-medial heavy syllable, it is parsed into a monosyllabic foot if and only if there are no heavy syllables in odd-numbered syllables to its left and there are an even number of syllables to its right; otherwise, it will be parsed into a disyllabic foot (this can be confirmed by consulting (26)). In stress systems it is common for the metrification of a particular syllable to depend on information at an unbounded distance preceding or following a syllable, though not both – a word-medial syllable in a language with rightward alternating trochaic stress like Pintupi (§2.3) will be stressed if an even number of syllables precede (unbounded) and if it is not adjacent to the right edge of the word (bounded), otherwise the syllable does not receive stress. This kind of dependency is naturally explained by the directional iteration of foot-building. But the unattested language predicted by the standard theory in parallel OT effectively relies on information at unbounded distances in both directions in order to know how to treat an individual syllable. In this sense, the prediction is nearly identical in character to the non-local truncation example.Footnote ¹²

This prediction is problematic, because a language with non-local weight-sensitivity of this kind has not been attested. Attested stress systems with weight distinctions overwhelmingly demonstrate them to be local. In Weɽ gaia, it is only at the end of the metrical parse that parsing is sensitive to the weight of a final stray syllable; in other quantity-sensitive trochaic languages heavy syllables are treated uniformly throughout the word or are only affected only by their local context. Given the strange character of the non-local pattern just described, it is not plausibly an accidental gap in the typology of stress, but instead appears to be an example of undesirable overgeneration for the standard theory of stress in parallel OT.

What can be done to eliminate this prediction from the standard theory? Positing new constraints is not a successful strategy, because expanding Con can only ever add languages to the predicted typology of a given set of constraints. Although there are rankings in which this prediction does not surface, there will always be a ranking in which constraints that prevent it (*Clash, for example) are ranked too low to matter. Removing or modifying the responsible constraints would be a more promising step towards preventing this prediction, but it is difficult to do this and still preserve the ability to analyse Weɽ gaia and similar languages without venturing well beyond the standard theory. The burden of responsibility for this prediction lies with Parse-σ and FtBin when implemented with parallelism.Footnote ¹³ But a constraint like Parse-σ is required to motivate footing under standard representational assumptions, and the definition of FtBin used here reflects the need for a constraint that bans (ˈL) while allowing other foot types, which was argued for in §3.1. Some of the characteristics of this strange language appear to be due to gradient alignment constraints (AllFt-L/R). Nonetheless, theories that abandon gradient alignment in favour of other constraints to model directionality (e.g. Kager Reference Kager2001, McCarthy Reference McCarthy2003) will still predict non-local partially quantity-sensitive stress patterns if Parse-σ and FtBin are retained; when high-ranked, these constraints conspire to place monosyllabic feet wherever necessary to maximise the parsing of the whole word, despite the preferences of lower-ranking constraints.

It seems the standard theory of stress in parallel OT requires a more radical revision. Hyde's (Reference Hyde2007) analysis solves the problem for parallel OT by altering the standard representational assumptions to force exhaustive parsing and by changing Con to eliminate many of the standard constraints, including Parse-σ and FtBin, in favour of constraints from the Non-Finality family. In the next section I show that HS allows a different solution, even when no changes to Con or the standard representational assumptions are made. IFO uses a serial derivation that lacks foresight, and as a result, its concomitant local decision-making cannot produce the unattested non-local stress system under any ranking of the standard constraints. A comparison between the solution advocated here and the one presented by Hyde is delayed until §6.

3.3 Why HS is local

The previous section showed that parallel OT predicts an unattested language with the ranking FtBin≫Parse-σ≫AllFt-L≫*Clash. In IFO, on the other hand, the attested generalised trochee pattern is produced under this ranking, as was evidenced in §3.1.Footnote ¹⁴ Showing a different outcome in parallel vs. serial OT for a given ranking is not, by itself, particularly informative. Instead, we are interested in a typological claim – that the non-local stress system predicted by the standard theory of stress in parallel OT is not predicted by IFO at all, given reasonable assumptions about Con. Showing that a language cannot be produced in HS requires demonstrating that there is no combination of harmonically improving derivations that produces the relevant set of optima under a single ranking (McCarthy Reference McCarthy2010a, Reference McCarthyb). This section shows that HS/IFO indeed does not produce the unattested language discussed in the previous section under any ranking of standardly assumed stress constraints.

The hypothetical language discussed in the previous section had the strange property of appearing to base parsing decisions on word parity. To show that the same language cannot be produced with IFO, we must demonstrate that the theory will not allow an input like /HLLL/ to become (ˈHL)(ˈLL) and input like /HLL/ to become (ˈH)(ˈLL), while also generating a pattern that looks left-to-right in a word comprising an odd number of light syllables, /LLLLL/→(ˈLL)(ˈLL)L. These input–output pairs would require derivations like those in (27).

1. (27)

   

There is no ranking of the standard constraints that will produce the derivations in (27) with IFO. At the first iterations, a ranking that would prefer /HLLL/→(ˈHL)LL, as required for (a), would also prefer /HLL/→(ˈHL)L, contrary to what is found in (b). The tableaux in (Reference Jesney28) show this result. These inputs are treated the same at the first iteration. The grammar does not have the foresight to know that (ˈH)(ˈLL) is the global optimum for input /HLL/, so it will not take this into account at the first iteration and choose (ˈH)LL instead. Furthermore, the assumption of strict inheritance prevents the actual first iteration's optimum, (ˈHL)L, from becoming (ˈH)(ˈLL) at a subsequent step.Footnote ¹⁵

1. (28)

   

In a similar way, a ranking that would produce /HLL/→(ˈH)LL as is needed for (27b), would also prefer /HLLL/→(ˈH)LLL, contrary to (27a). This is shown in (29). These tableaux show that when a constraint favouring (ˈH) over (ˈHL), which I abbreviate *(ˈHL), outranks Parse-σ, it favours (ˈH) in both derivations, not just (29a).Footnote ¹⁶

1. (29)

   

Thus the combination of outputs in the unattested language from §3.2, though all optimal under the same ranking in parallel OT, cannot be modelled as outputs in the same language in HS/IFO with these constraints.

Like all typological claims in OT, this claim relies on an assumption about Con. Specifically, Con must not include constraints with definitions like ‘a foot should be followed by an even number of syllables’ or ‘there should be an even number of unparsed syllables at all times’. If such constraints were admitted into the theory this prediction would not hold, as it would then be possible to assess the consequences of each foot choice for the potential metrical parses of the remaining syllables. A constraint of this kind could only set up the derivation for subsequent exhaustive footing indirectly, by referencing parity, but the constraint itself has no metrical characteristics. Instead, it would enforce an output preference that happens to be important for leading the way to the global optimum in this example. The exclusion of such constraints from Con does not seem unreasonable.

The theory of IFO proposed here lacks any source of derivational foresight by design. Although it can ‘see’ the whole word in each of its local evaluations, it does not envision the possible paths that each local optimum might lead to, and does not know that some local optima may lead to a global optimum, while others do not. Instead, it chooses only on the basis of the relative harmony of the candidates at each iteration. As I have shown in this section, this is a desirable property of HS/IFO when compared with the standard theory of stress parallel OT, since it more accurately reflects typology. Global parsing maximisation is par for the course in the standard theory, but since no language seems to stress words in this way, the standard theory is too permissive. In the next two sections I show that this is not an isolated case, and that the standard theory in parallel OT predicts other non-local interactions that are not attested. In each case, HS with IFO correctly predicts they should not occur.

4.1 Local trochaic shortening in Fijian

Trochaic shortening is a quantity-adjustment process wherein a stressed heavy syllable becomes light, usually by a process of vowel shortening, before an unstressed light syllable. This process is attested, according to Hayes (Reference Hayes1995: 148), in Fijian, Hawaiian, Tongan, (Middle) English and some Italian dialects, and it is usually argued to be motivated by a preference for trochaic feet to group elements of equal weight (e.g. McCarthy & Prince Reference McCarthy and Prince1986, Prince Reference Prince1990, Hayes Reference Hayes1995; cf. Kager Reference Kager1993). Shortening of the heavy syllable in an HL sequence allows it to be parsed into a balanced (ˈLL) trochaic foot, avoiding the unbalanced (ˈHL) trochee and underparsed (ˈH)L. Fijian (Austronesian; Fijian Islands; Schütz Reference Schütz1985, Dixon Reference Dixon1988) will be used to exemplify trochaic shortening.

The stress system of Fijian is quantity-sensitive, and is analysed by Hayes (Reference Hayes1995: 142ff) with right-to-left moraic trochees, that is, with foot shapes (ˈH) and (ˈLL). Main stress falls on the final syllable if heavy, otherwise it surfaces on the penult; syllables with long vowels or diphthongs are counted as heavy. In general, secondary stresses fall on non-final heavy syllables, and sequences of light syllables are grouped into disyllabic trochees. The data in (30) illustrate the basic patterns; the forms in (a) show stress in words ending with light syllables, and those in (b) show words with final heavy syllables.

1. (30)

   

There are no words in Fijian which end in a sequence of a heavy syllable followed by a light syllable (Schütz Reference Schütz1985: 528–529, Dixon Reference Dixon1988: 15, 26, Hayes Reference Hayes1995: 145). Alternations confirm that this is an active prohibition, as the examples in (31) demonstrate.

1. (31)

   

The roots in (a) consist of a single heavy syllable whose vowel is shortened when a monosyllabic light syllable affix is added. Dixon (Reference Dixon1988) provides arguments from reduplication that the long vowel of these roots should be taken as underlying. The form in (b) shows an underlyingly HL root that undergoes shortening of the heavy syllable when unaffixed, but which surfaces faithfully when an affix displaces the heavy syllable out of penultimate position. Fijian trochaic shortening is obligatory when the HL sequence is word-final, but is optional when a heavy syllable precedes an unparsed light syllable elsewhere in the word. For reasons of space I concentrate here on deriving the variant in which trochaic shortening applies word-finally but not word-medially.

4.2 Non-local trochaic shortening (unattested)

IFO and parallel OT are equally able to account for Fijian trochaic shortening in penultimate syllables, but we can evaluate the analyses based on their predictions about other languages. The crucial ingredients in the parallel OT analysis of Fijian are essentially the same as those in the IFO analysis – the ranking of Max-μ below AlignWd-R, BalTroch and FtBin prevents word-final (ˈH)L, (ˈHL) and H(ˈL) from being optimal, favouring instead (ˈLL). But the ranking and behaviour of Parse-σ and Max-μ is a crucial difference between the theories. Unlike IFO, the parallel OT analysis requires that Max-μ dominate Parse-σ in order to limit shortening to only word-final HL sequences. In IFO the constraints were unrankable because they did not conflict. If this ranking is reversed to Parse-σ≫Max-μ, an unattested language with non-local shortening is predicted to exist by the parallel theory, but not the serial one. The following paragraphs demonstrate why this prediction is undesirable.

Under a ranking such as BalTroch, Parse-σ≫Max-μ, the high ranking of Parse-σ and BalTroch will conspire to produce non-local shortening patterns. For this illustration we can otherwise keep the ranking the same as in the Fijian analysis: Parse-σ≫AllFt-R≫AllFt-L for iterative right-to-left parsing, and undominated Trochee and FtBin for minimally bimoraic trochees. (The ranking of AlignWd-R is not crucial in this language, so it is omitted from the discussion.) With this grammar, inputs with heavy syllables in final position will undergo shortening if (and only if) the global harmony of the metrical parse is improved by doing so.

A word with a final heavy syllable that is preceded by an even number of light syllables will not exhibit shortening of the heavy syllable, as shown in (40), because an (ˈH) is a licit balanced trochee, and maximal parsing into feet while satisfying foot form is possible by parsing the even-parity string of light syllables into disyllabic trochees of the form (ˈLL).

1. (40)

   

However, a word with a final heavy syllable preceded by an odd number of light syllables will show shortening of the heavy syllable, as shown in (41). In this case, best satisfaction of Parse-σ and constraints on foot form (BalTroch and FtBin) is achieved only in a candidate that shortens the heavy to achieve an even number of light syllables, which can be fully parsed into disyllabic units.Footnote ²²

1. (41)

   

What makes this combination of optima problematic from a typological standpoint is that the language shows right-to-left parsing in odd-parity sequence of light syllables, as shown in (42). A simple directional description of this stress system is not easily formulated, because the parsing of syllables at the right edge of the word depends not only on the local environment, but also on the total parity count of the preceding syllables.

1. (42)

   

These inputs show a language with right-to-left parsing that must consider the parity count of the syllables preceding a final heavy syllable in order to know whether to parse it as a monosyllabic foot or to shorten it and parse it with the preceding syllable as a disyllabic foot. The prediction is in fact slightly more complicated than the tableaux in (40)–(42) suggest, since inputs with heavy syllables in other positions in the word must be considered. The result is a stress system that parses a heavy syllable as a monosyllabic foot if it occurs in an odd-numbered syllable of an odd-parity word and is the closest to the right edge of all heavy syllables satisfying this requirement,Footnote ²³ and shortens all other heavy syllables in the word to create (ˈLL) feet. Such a stress system has not been attested.

Variations on this non-local prediction, all unattested, are predicted with other permutations of these constraints in parallel OT. This class of languages clearly demonstrates non-local interactions between stress and quantity adjustments, because the number and position of light and heavy syllables throughout the word have to be taken into account in order to know whether to shorten a given heavy syllable, yet parallel OT predicts these languages using the same constraints required for an analysis of Fijian in the standard theory. It is difficult to imagine how a minimal change to the constraint set could rule out this prediction while continuing to admit local trochaic shortening. As argued in §3.2, a more radical change to the standard theory is required.

Non-local interactions of this sort are not something we would expect to see in a natural language stress system, and IFO predicts they should not occur. In the parallel OT analysis of Fijian's local shortening process, the ranking of Parse-σ and Max-μ is crucial – under one ranking the attested shortening pattern of Fijian emerges, but under the other we get the unattested language just described. In the IFO analysis, on the other hand, Parse-σ and Max-μ are unrankable, because they do not conflict. It follows that both rankings of these constraints are consistent with local shortening in IFO, in contrast to parallel OT. Furthermore, no other ranking of the standard constraints produces this pattern in IFO either. Reproducing the non-local shortening language would require inputs /LLLLH/ and /LLLH/ to be treated differently at the first step, as shown in (43), with the final heavy syllable in (43a) parsed as a monosyllabic foot and the final heavy syllable in (43b) parsed as the dependent in a disyllabic foot. These steps cannot be made simultaneously optimal in IFO, by extension of the reasoning in §3.3, without spurious constraints that refer directly to word parity. Thus IFO predicts that metrically conditioned quantity adjustments should be local.

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   Footnote ²⁴

The same constraints that were necessary for an analysis of Fijian in the standard theory of parallel OT predict unattested languages with non-local variants of the process as well. The similarity between the unattested language from §3 and the one discussed in this section should be obvious. Parallel evaluation permits non-local interactions because it considers all possible metrical parses and quantity adjustments at one time. IFO, on the other hand, accounts for Fijian trochaic shortening using the same constraints and representations, but gradualness prevents the prediction of the non-local variants. The next section turns to a final non-local prediction of the standard theory, the interaction of stress with restrictions at the edges of prosodic domains.

5.1 Local rhythmic reversal in Axininca

Stress in the Apurucayali dialect of Axininca (Payne et al. Reference Payne, Payne and Santos1982, McCarthy & Prince Reference McCarthy and Prince1993b) is generally quantity-sensitive, and in sequences of light syllables the stress pattern is straightforwardly left-to-right iambic – every other syllable beginning with the second is stressed, as shown in (44a). However, stress nearly always avoids the final syllable (words with diphthongs in the final syllable are the exception). As a result, disyllabic words have initial stress, as in (44b), while polysyllables ending in an even number of light syllables vary between shifting the last stress to the penult and omitting the stress altogether, (44c).Footnote ²⁶ In the analysis below I focus on deriving the variant with rhythmic reversal (i.e. penult stress), following an analysis in the standard theory by McCarthy & Prince (Reference McCarthy and Prince1993b).

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McCarthy & Prince (Reference McCarthy and Prince1993b) analyse rhythmic reversal in Axininca with a trochaic foot in final position that emerges as optimal in an otherwise iambic language in order to satisfy a constraint against stress on the final syllable. Their analysis can be straightforwardly adapted into HS using the same constraints in the same ranking. The HS analysis involves a derivation that builds left-aligned iambs until doing so would stress the final syllable, in which case iambic foot form is sacrificed in order to avoid the final stress. The proposed foot structures are (i.ˈʧ ʰ i)(ka.ˈki)na ‘he has cut me’, (ˈsa.ri) ‘macaw’ and (ki.ˈmi)(ˈta.ka) ‘perhaps’. The constraint militating against final stress is Non-finality, defined in (45), which must outrank Iamb because it can compel a trochee to be built.

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We must also assume the ranking Parse-σ≫AllFt-L≫AllFt-R in order to enforce iterative left-to-right parsing, Iamb≫Trochee in order to have a default preference for right-headed feet and FtBin≫Parse-σ because feet surfacing in Axininca never contain fewer than two moras. The final ranking that must be assumed is Parse-σ≫Iamb, which accounts for the fact that a trochaic foot surfaces word-finally even though leaving the syllables unfooted would allow vacuous satisfaction of Iamb. The ranking is exemplified in the tableaux that follow.

The derivation of the regular iambic stress pattern in an odd-parity word will proceed as shown in (46). Non-finality is omitted from this tableau because it does not crucially decide any winners when regular parsing avoids the final syllable. At each of the first two steps, an iambic foot is chosen as optimal. The third step shows convergence, because the only remaining stress candidate fatally violates FtBin, and (e) emerges as the winner.

1. (46)

   

A derivation of a word with an even number of light syllables in Axininca is shown in (47). The derivation builds iambs from the left until there are two syllables remaining, at which point it will choose to build a trochee on the two remaining syllables. Candidate (b) wins in the first iteration because regular iambic parsing is preferred. Then candidate (f), which is the eventual winner, wins in the second iteration because high-ranked Non-finality prevents regular iambic parsing at the right word edge, and the ranking of Parse-σ over Iamb means that it is more important to parse words into feet than it is for the feet to be iambic, so candidate (d) also loses. The third iteration shows convergence, because no more parsing is possible.

1. (47)

   

As this analysis shows, it is straightforward to account for Axininca's rhythmic reversal in HS/IFO using the stress constraints of the standard theory. The constraint against final stressed syllables becomes relevant when parsing the final syllables of a word, and it enforces its preference then.Footnote ²⁷

5.2 Non-local rhythmic reversal (unattested)

McCarthy & Prince's (Reference McCarthy and Prince1993b) analysis of Axininca rhythmic reversal in parallel OT, which derives the correct optima with the same ranking, is equally straightforward on the surface. However, the standard constraints in parallel OT also predict a language with global rhythmic reversal, in which the effect of Non-finality is to change foot structure throughout the entire word. The winning candidate for input /hotitana/ is (ho.ˈti) (ˈta.na), which has a stress clash. If we assume that Con contains the constraint *Clash, which was in fact shown to be necessary for a standard theory analysis of Weɽ gaia in §3, it must be low-ranked for the analysis of Axininca. But factorial typology includes a ranking that is just like that in Axininca, but with *Clash high-ranked, and in such a language (ho.ˈti)(ˈta.na) will lose to a candidate with reversal in both feet, (ˈho.ti)(ˈta.na). This is shown in (48). The winning candidate in (48) is parsed into trochees despite the ranking Iamb≫Trochee, because it is the only candidate with iterative footing which neither stresses the final syllable nor shows a violation of *Clash. This same ranking will still produce iambs in a word ending with an odd number of light syllables, because in such words iambic rhythm can be preserved without the potential for stressing the final syllable, thereby avoiding the potential clash configuration altogether.

1. (48)

   

By itself, this prediction is non-problematic. The language predicted under this ranking is one in which odd-parity words have stress on even-numbered syllables, while even-parity words have stress on odd-numbered syllables. This predicts a stress system with alternating rhythm akin to a simple right-to-left syllabic trochee stress pattern, and since languages with this stress system are attested (e.g. Cavineɲ a, Key Reference Key1968), there is at this point no evidence that this prediction is problematic. But problematic predictions do arise from this ranking when foot-form constraints that differentially treat iambs and trochees are also high-ranked, because in this case global rhythmic reversal will have visible consequences, causing odd and even parity words to obey different stress generalisations.

For example, according to the asymmetric foot typologies of McCarthy & Prince (Reference McCarthy and Prince1986), Hayes (Reference Hayes1995) and others, trochees ideally group elements of equal weight (see also §4), while iambs prefer quantitative imbalance. Shortening of stressed syllables is attested in trochaic languages, such as Fijian, but quantity-adjustment processes in iambic languages usually involve the opposite, lengthening of a stressed syllable to achieve the ideal foot form (LˈH) (examples can be found in Hayes Reference Hayes1995: 83). This entails the existence of constraints that prefer evenness in trochees and unevenness in iambs. As a consequence, one prediction of the global reversal in (48) is a language in which stressed syllables in even-parity words are shortened, to obey constraints that want trochees to be balanced, while stressed syllables in odd-parity words are lengthened, to satisfy constraints that want iambs to be unbalanced. Stressed syllables in this language will lengthen or shorten depending on the parity count of the syllables in the word, ostensibly to obey Non-finality in combination with *Clash and constraints on foot form. This is illustrated schematically in (49) and (50). In these tableaux I/TL (for Iambic/Trochaic Law; Hayes Reference Hayes1995) stands for the constraint or constraints that enforce quantitative asymmetry in iambs and trochees.

1. (49)

   

2. (50)

   

As before, adding constraints to Con cannot get rid of this prediction, but eliminating the responsible constraints is not a tenable strategy for the standard theory either: *Clash is required to analyse Weɽ gaia in parallel OT, Non-finality is crucial in the analysis of Axininca and many other languages, and languages with iambic lengthening and trochaic shortening require an asymmetric set of foot-form constraints that can compel the insertion or deletion of a mora according to their ranking with respect to Dep-μ and Max-μ. Clearly, a more radical change from the standard theory is required, since we would not expect to find a stress system in natural language that requires length on stressed syllables in words of one parity while prohibiting length in stressed syllables in words of the opposite parity.

This prediction is not reproducible in IFO. In this language, a constraint referencing the right edge of the word (Non-finality) has conspired with *Clash to effect parsing all the way back to the left edge of the word, in opposition to the ostensible direction of parsing in the language. The left-to-right directionality of parsing under this ranking in IFO prohibits Non-finality from changing the preferred foot type throughout the word. Furthermore, if the ranking instead favoured right-to-left directionality, then words of both parity counts would be affected in the same way by Non-finality; it would not be possible to anticipate iambs in one and trochees in the other. The ability of *Clash to create non-local stress systems by interacting with Non-finality is quite limited in HS/IFO. This is in clear contrast to the behaviour of these constraints in the standard theory of parallel OT, in which optimisation is performed over all possible metrical parses, and which predicts languages that show non-local constraint trade-offs as a result.

5.3 An apparent counterexample

The stress pattern described in the previous section and illustrated in (49) and (50) displays an improbable pattern of stressed syllable shortening and lengthening and is clearly unattested. However, there is one language, Yidiɲ , that is claimed to have a stress system similar enough in some ways to this unattested language to warrant additional discussion. This section describes Yidiɲ stress and briefly discusses why it is a challenge for both HS/IFO and parallel OT. Although Yidiɲ has been used as an argument for parallelism in some previous work (e.g. McCarthy Reference McCarthy2002: 149–152), the conclusion of this section will be that the stress pattern of Yidiɲ is not currently well enough understood to constitute an argument for or against any theory of stress.

Dixon (Reference Dixon1977a, Reference Dixonb) provides a detailed description of the stress system of Yidiɲ , a language of Australia. Stress in Yidiɲ is characterised by both strict alternation of stress by syllables and quantity-sensitivity. Long vowels count as heavy and may occur in any syllable except the first. For words with an odd number of syllables only the stress pattern in (51a) is found, while for words with an even number of syllables the patterns in (b) and (c) are both permitted. The choice between (b) and (c) for an even-parity word is made on the basis of the distribution of quantity, with stress aligning to syllables with long vowels, though words with no long vowels always have the pattern in (b). Words with an odd number of syllables always have a long vowel in the penult, with the option for a long vowel in other even-numbered syllables as well. This stress system is unusual in being both quantity-sensitive and strictly alternating (cf. Hayes Reference Hayes1995),Footnote ²⁸ as well as in the interdependence of stress and vowel length in odd-parity words.

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On the basis of these facts, most previous analyses of Yidiɲ stressFootnote ²⁹ have assumed that words with an odd number of syllables employ iambic feet, while even-parity words are parsed into trochees or iambs depending on the distribution of syllable weight. Hung (Reference Hung1993, Reference Hung1994), for example, argues that Yidiɲ is an essentially iambic language and that the preference for trochees in even-parity words is driven by Non-finality (though trochees are blocked when a long vowel appears in an even-numbered syllable). This description makes Yidiɲ stress look very similar to the unattested language described in the previous section, and Hung's analysis cannot be reproduced in IFO for the same reason that IFO does not reproduce the unwanted prediction in that section. IFO can produce a language that avoids final stress by alternating away from the penult, though it cannot produce this stress system by anticipating iambs in words of one parity and trochees in words of another parity.Footnote ³⁰ The other difficulty facing an IFO implementation of Hung's analysis is that the constraint against final stress is overridden by a long vowel in any even-numbered syllable of an even-parity word (see (51c)).

On the surface, a consideration of Yidiɲ 's stress system appears to highlight a dichotomy between a theory that undergenerates and a theory that overgenerates. The IFO prediction that stress systems should be local makes it difficult to adapt a traditional analysis of Yidiɲ , but parallel OT's global parsing with the standard constraints predicts in addition to Yidiɲ many non-local stress patterns that are unattested, as evidenced by the minimally different problematic prediction in §5.2 and the predictions discussed in §§3 and 4.

However, there are significant reasons to doubt whether any parallel OT analysis actually can account for Yidiɲ 's stress system when its additional complexities are taken into account. The central difficulty for an analysis in parallel OT is that stress and vowel length have a necessary interdependence, but vowel length in Yidiɲ can arise as the opaque result of two processes that target odd-parity words: penultimate vowel lengthening and final syllable deletion. For example, a trisyllabic stem /gindanu/ ‘moon’ surfaces as [gin.ˈdaːn] in the absolutive (bare) form, but as faithful [gin.da.nu-] in the remainder of its paradigm (Dixon Reference Dixon1977b: 13). The vowel length and, crucially, the concomitant stress on the second syllable in the bare form derive exclusively from the underlying parity of the stem, no longer visible on the surface. This opacity makes a full analysis of Yidiɲ stress in parallel OT almost impossible if the predictable vowel length in forms like [gin.daːn] is to be derived by the grammar. Parallel OT's problem with opacity is well known and is not limited to a particular constraint set. It is thus difficult to see how Yidiɲ 's stress system could possibly constitute an argument against serialism, despite its apparently non-local character.

It is clear that something more will have to be said for a satisfactory analysis of Yidiɲ . In IFO it is possible to analyse Yidiɲ 's stress system without resorting to a mix of iambs and trochees if vowel length can be taken as given. Hayes (Reference Hayes1997, Reference Hayes, Hermans and van Oostendorp1999) provides some justification for treating predictable vowel length as underlying, based partly on the fact that length is a central player in Yidiɲ 's morphophonology. With vowel length prespecified, an IFO analysis could treat Yidiɲ as a right-aligning trochaic system that requires heavy syllables to be stressed and every word to end in a foot.Footnote ³¹ Alternative analyses not relying on the assumption that vowel length is given may be possible if non-standard representational and/or operational assumptions that have been argued for in previous serial analyses of Yidiɲ are adopted (e.g. Crowhurst & Hewitt Reference Crowhurst and Hewitt1995b), though such solutions would have to be pursued with care to ensure that the genuinely problematic predictions discussed in the previous section are not reintroduced as well.

Yidiɲ is sometimes put forward as an argument for parallelism in stress, and the preceding discussion makes it clear why. But closer inspection of its stress system suggests that it cannot in fact be taken as unequivocal evidence in favour of that conclusion. Despite the difficulty for HS/IFO posed by current characterisations of this language, it is quite possible that future work sensitive to the role of morphology in Yidiɲ 's stress system could yield new insights that allow it to fall in line with the overwhelming majority of attested stress systems which demonstrate locality.

6.1 Non-finality-based parallel OT

The comparison between IFO and parallel OT in §3 began with a discussion of the problem with the standard theory that was also presented by Hyde (Reference Hyde2007). On the basis of the standard theory's inadequacy, Hyde concludes that a thorough revision of the theory of stress constraints and representations is needed, a conclusion that he also pursues in other work (e.g. Hyde Reference Hyde2002). Thus, rather than assuming ranked and violable Parse-σ, he assumes that exhaustive parsing is a property of Gen, and rather than assuming that feet necessarily represent stress, he assumes that the relationship between metrical constituency and prominence is violable. Constraints from the Non-finality family are argued to govern the alignment of grid marks with respect to the right edges of all levels of prosodic representation (mora, syllable, foot, word), and this combination of assumptions correctly derives the conditional weight-sensitivity of generalised trochee languages and extends to many other areas of stress typology as well.Footnote ³² Throughout, I have identified the problematic predictions discussed in this paper as evidence that the standard theory of stress constraints and representations functions non-locally in parallel OT and have therefore proposed that HS/IFO offers a different kind of solution. The typological advantages of IFO for the stress interactions discussed in this paper are less impressive when compared to the quite different theory of Hyde, but IFO nonetheless retains an advantage. Hyde's solution fails to generalise to very similar locality problems in non-metrical domains. IFO, on the other hand, is couched in Harmonic Serialism, which provides a general solution to the locality problems faced by parallel OT.

The introduction provided an example of a non-metrical locality problem that arises in parallel OT but not in HS (see the references cited in the introduction for additional examples). High-ranked constraints prohibiting syllable-final obstruents and requiring word-final codas can conspire to predict a language with truncation in every word after the rightmost sonorant consonant or not at all in words with no sonorant consonants (McCarthy Reference McCarthy, Baković, Ito and McCarthy2006, Reference McCarthy2010b). For any given segment in a word of this unattested language, knowing whether deletion will occur depends not just on its local context nor just on information to one side of it, but on information at unbounded distances to both its left and its right simultaneously. This is precisely the sense of non-locality that the standard theory of parallel OT predicts for stress, but which HS (with IFO) again solves, as §§3–5 showed in detail. These non-local predictions can only be described in terms of an omniscient view of the word, with dependencies that extend infinitely in both directions. Processes of this kind are not generally found in the phonological systems of natural languages. If such predictions only arose in parallel OT as a result of the standard view of stress, a stress-specific solution such as the one proposed by Hyde would be preferred as an alternative. But since such problems for parallel OT are pervasive and domain-general, HS has the advantage of being a general solution and solving a wider range of such problems.

Furthermore, other recent work demonstrates that analysing stress in HS provides solutions to problems beyond those that have been the focus of this paper, for which Hyde's theory can offer no comparable advantage. McCarthy (Reference McCarthy2008b) argues that metrically conditioned syncope cannot be coherently analysed in a non-derivational theory. Syncope is motivated by the avoidance of unstressed vowels, but without an intermediate step in which foot structure has been assigned, it is nearly impossible to correctly identify the vowels targeted for deletion. HS provides the framework for ordering stress before syncope, and with some additional assumptions about Con it predicts the desired intrinsic ordering of these processes.

Elfner (Reference Elfner2009) shows that opaque interactions between stress and epenthesis receive a natural analysis in HS, where derivational steps permit differential treatment of epenthetic and non-epenthetic segments for the purposes of syllabification and stress assignment. Elfner cites Kiparsky (forthcoming) for arguments against extant parallel OT approaches, which typically analyse the attested cases with a positional faithfulness constraint requiring the head of a prosodic constituent to have an input correspondent, on the basis that they make the incorrect prediction that vowels epenthesised into extrametrical positions cannot opaquely affect stress assignment when in fact such cases are attested.

Kimper (forthcoming) shows that serial prosodic structure building in HS can be combined with a theory of variable constraint ranking to analyse attested cases of prosodic local optionality that are not analysable in parallel OT. Theories of variation in parallel OT have difficulty with local optionality, because they predict that all loci of potential application of a process will be treated the same, other things being equal, but the successive evaluations in an HS derivation allow individual loci to be treated differently, successfully accounting for the observed cases. Kimper's proposal accounts for variation in the construction of Minor Phrases in Bengali and the metrically conditioned but variable process of schwa deletion in French.

Finally, Jesney (forthcoming) shows that HS solves pathologies arising from positional faithfulness constraints in parallel OT. Positional faithfulness constraints are meant to preferentially preserve contrasts in prominent positions, but parallel OT predicts that a possible way to satisfy a faithfulness constraint referring to a metrically prominent syllable is to move stress to a different syllable (where being faithful does not conflict with high-ranked markedness constraints). Many of the stress patterns that result from the presence of such candidates are unattested and non-local. Jesney shows that HS provides a solution to this problem by allowing privileged positions to be defined on the basis of the previous iteration's output. This prevents candidates from manipulating prosodic structure to avoid positional faithfulness violations and allows these constraints to function as intended.

The evidence presented in this paper and other recent work suggests that HS consistently solves locality problems which are not limited to stress, and that analysing stress in a framework with serial optimisation provides benefits beyond the locality effects discussed in this paper. Hyde's proposal greatly improves the typological predictions of a parallel OT theory of stress, but in doing so it fails to connect the pathologies of the standard theory with parallel OT's non-local predictions in domains outside of metrical theory. And since Hyde's solution is not derivational, it does not offer solutions to other problems for a parallel OT theory of stress such as metrically conditioned syncope, opaque stress–epenthesis interactions, local optionality of prosodic structure and positional faithfulness pathologies. While perfectly matching the observed typology of stress in HS will require continued work, the elimination of parallel OT's locality problems and the other benefits of serial optimisation in metrical structure nonetheless suggest that the breadth of problems solved by HS make iterative foot optimisation worthy of further consideration.

6.2 Derivational rule-and-constraint-based theories

The locality results described in this paper derive primarily from the fact that IFO, unlike parallel OT, builds feet incrementally. In this way IFO is similar in many respects to rule-based, or rule-and-constraint-based, models of stress, such as Hayes (Reference Hayes1995), which is also implemented with incremental foot-building and generally makes the same or similar representational assumptions as those adopted here.Footnote ³³ But while IFO and these rule- and constraint-based theories share serialism and representations, a crucial difference is that IFO assumes ranked and violable constraints to determine the descriptive dimensions of a stress pattern, while most other derivational models determine directionality, foot-headedness, iterativity, etc., for each language parametrically, with constraints that are inviolable.

For IFO and other OT-based models, violable constraints predict that the constraints’ preferences can be overturned when conflicting constraints are higher ranked. This matches observed typology, which finds that perturbations in foot headedness and alignment can be motivated in contexts where the default option would degrade harmony rather than improve it (Prince & Smolensky Reference Prince and Smolensky2004: ch. 4). In the analysis of Fijian, for example, HS/IFO permits an (ˈHL) foot to be built at the word edge only, because satisfaction of high-ranked AlignWd-R requires the preference for balanced trochees to be (temporarily) overridden. Similarly, Axininca prefers iambic feet, but will tolerate a trochaic foot to avoid stressing the final syllable. Non-uniformity of this kind is well attested both in stress and in other domains (see e.g. McCarthy Reference McCarthy2002: §3.2), and the ability of OT's ranked and violable constraints to account for this behaviour carries over to HS as well.