2.1.1. Neoštokavian

In NS, lexical highs determine stress position. Stress falls on the syllable immediately preceding the word’s only high, as in (8), or on the high-toned syllable if no syllable precedes, as in (9). In underlyingly toneless inputs, NS displays initial stress with high tone insertion, as in (10).

Forms in (9) and (10) are indistinguishable in isolation; the tonal patterning of prefixes indicates whether the initial syllable is underlyingly high-toned (as in (9)) or has an inserted high (as in (10)). Forms with an initial lexical high retain their tone with a prefix, as in (11), while underlyingly toneless forms have a high inserted on the prefix, as in (12).

Bethin (Reference Bethin1994, Reference Bethin1998) analyses NS as a syllabic trochee system.Footnote ¹ This analysis sheds light on the stress–tone adjacency in NS seen in (8): the stressed and high-toned syllable must be contained within a disyllabic trochee, as shown in (13).

Thus, NS stress assignment is quantity-insensitive: stress falls on the syllable preceding a lexical H regardless of syllable weight, as in (8).

2.1.2. Old Štokavian

As a general tendency, stress in OS typically falls on the high-toned syllable (Zec & Zsiga Reference Zec, Zsiga, Kubozono, Itô and Mester2022), as shown in (14).

The preference for stress on high-toned syllables arises from the Head-H constraint (Yip Reference Yip2001), defined in (15).

Despite the general preference for stressed high-toned syllables in OS, stress does not invariably fall on the high-toned syllable in all prosodic environments in all OS dialects (Zec & Zsiga Reference Zec, Zsiga, Kubozono, Itô and Mester2022). There are two cases in which some OS dialects avoid stressing the high-toned syllable. The first point of variation across individual OS dialects stems from the prosodic patterning of final light syllables. When a lexical H is attached to a final light syllable, stress falls on the final light in only a handful of OS dialects, as in (16), and on the toneless penult in most OS dialects, as in (17):

In OS dialects that prohibit final stress, as in (17), only light final syllables are barred from bearing stress, as in (18), while final heavies regularly receive stress if high-toned underlyingly, as in (19).Footnote ² Recall that a H tone must be attached to the first mora of a heavy syllable.

Word-final high-toned lights regularly receive stress in enclisis, which results in productive stress alternations, as in (20).

The illicitness of stressed final lights but not of stressed final heavies in OS falls out from the moraic version of Nonfinality.Footnote ³ Mora-oriented Nonfinality penalises word-level prominence on the rightmost mora of the prosodic word (ω) (Hyde Reference Hyde2007). Stressed final heavies do not violate the moraic version of Nonfinality because they form a bimoraic foot headed by the syllable’s first mora, which is the penultimate mora of a word. Thus, when stress is on a final heavy, the prominence peak does not coincide with the word’s rightmost mora.

The second point of variation in OS concerns the metrical treatment of toneless heavy syllables. Individual OS dialects differ with respect to whether they prefer stressing high-toned lights over toneless heavies, as in (22), or vice versa, as in (23).

The pattern in (23) arises in response to the Weight-to-Stress Principle (WSP; Prince Reference Prince1990), defined in (24). For (23) to arise, WSP must dominate Head-H.

The combinations of the metrification strategies in (16)–(17) and (22)–(23) give rise to four basic prosodic types in OS. In Type 1 (East Montenegro; Stevanović Reference Stevanović1933), stress invariably falls on the high-toned syllable, as in (25a). In Type 2 (Southwest, Central and East Serbia, parts of Montenegro and Kosovo; Jović Reference Jović1968; Simić Reference Simić1972), stress generally falls on the high-toned syllable, except when the high-toned syllable is light and final, as in (25b). In Type 3 (Lepetane in the Kotor Bay, Montenegro; Tomanović Reference Tomanović1935) high-toned syllables are stressed unless the immediately preceding syllable is heavy, in which case stress falls on the toneless heavy, as in (25c). Type 4 (Smederevo–Vršac dialect cluster; Ivić Reference Ivić1958) avoids stressing final high-toned lights and prefers stressing toneless heavies over high-toned lights, as in (25d). In all environments not listed in (25), stress invariably falls on the high-toned syllable in all four types of OS dialects.

The prosodic variation observed across individual OS dialects can be attributed to the interplay of three constraints in OS: Head-H, Nonfinality and WSP. In Type 1 dialects, Head-H dominates both Nonfinality and WSP. In Type 2 dialects, Head-H takes precedence over WSP, but ranks below Nonfinality. Type 3 is the mirror image of Type 2: Head-H outranks Nonfinality, but ranks below WSP. In Type 4, Head-H is dominated by both Nonfinality and WSP. The present study is primarily concerned with Type 2 and 4 OS dialects.

Putting the pieces together, OS stress is tone-driven and quantity-sensitive. The sensitivity to tone is evident from the preference for stressing syllables with a lexical H. Quantity-sensitivity manifests itself in several interactions. In Type 3 and 4 OS dialects, toneless heavy syllables attract stress over high-toned lights. The ban on final prominence in OS likewise makes reference to weight. There is an asymmetry between final high-toned lights, which are unstressable in Type 2 and 4 OS dialects, and final high-toned heavies, which regularly receive stress in all OS dialects. All descriptive facts presented in this section can be unified by assuming that OS forms the moraic trochee defined in (26), the head mora of which is preferably high-toned.

This footing preference explains the weight–stress and tone–stress interactions, along with nonfinality effects in OS, in a unified fashion. The moraic trochee analysis sheds light on another central property of OS word prosody: the ban on rising contours. In OS, highs must be attached to the first mora of a heavy syllable. Assuming the metrical structure in (26) for OS, stressed heavy syllables form a bimoraic trochee in this dialect group. Accordingly, the second mora of a stressed heavy constitutes the non-head position of a bimoraic trochee. Thus, in rising contours, a H tone would be linked to the non-head mora. Cross-linguistically, there is a dispreference for high-toned foot non-heads. This is formally captured by the constraint *Nonhead-H (de Lacy Reference de Lacy2002):

In OS, *Nonhead-H penalises stressed heavies with a rising contour tone because they feature a H tone on the non-head mora of a bimoraic trochee (see §3.2.2 for further discussion).

2.1.3. Interim summary

OS and NS have virtually identical underlying representations. The key distinction between the two dialect groups is that OS preferably stresses the high-toned syllable, while NS stresses the immediately preceding syllable:

OS is a moraic trochee dialect, while NS exhibits the syllabic trochee. The footing differences between the two dialect groups are outlined in (29).

OS stress pattern is quantity-sensitive, with feet containing at most two moras. NS stress pattern is quantity-insensitive: feet comprise two syllables regardless of their weight.

3.2.1. Monosyllabic lengthening through local constraint conjunction

BCMS tolerates feet with a toneless head mora, as in (33) and (39). In bimoraic feet, toneless head moras cannot acquire a high by tone insertion or TF. The faithful realisation of toneless foot heads in this context suggests that Head-H is individually overridden by the relevant faithfulness constraints, including Dep-H, which prohibits the insertion of a H tone, and NoFlop-tone (Alderete Reference Alderete2001), which militates against TF. The rankings are shown in the tableaux in (43) and (44).

BCMS likewise permits monomoraic feet, as in (32). This fact suggests that FtBin is dominated by the anti-lengthening faithfulness constraint Dep-µ, as demonstrated in (45).

When violated simultaneously, Head-H and FtBin gang up and override a higher-ranking faithfulness constraint: Dep-µ in the case of ML and PL, and NoFlop-H in the case of TF. Classical OT is incapable of deriving gang effects without nonstandard devices (Pater Reference Pater2009a, Reference Paterb, Reference Pater, McCarthy and Pater2016). The failed OT derivation of ML is provided in (46).

OT accommodates ganging-up cumulativity using LCC (see §1), which incurs a violation whenever all conjuncts are violated within a designated local domain (syllable, foot or the like). To capture the observed gang effect in BCMS, I introduce the local conjunction of Head-H and FtBin at the foot level. The LCC analysis of vowel lengthening in toneless monosyllables is outlined in (47).

The candidate that obeys Dep-µ wins out when FtBin is violated on its own. This is the case in (45), where the faithful candidate (45a) [ brát] violates FtBin but obeys Head-H. Faithful realisation is preferred because there is no simultaneous violation of Head-H and FtBin. However, when Head-H and FtBin are jointly violated, they gang up against Dep-µ as in (47). There are two ways to avoid the coincident violation of Head-H and FtBin: vowel lengthening (candidate (47d)) or high insertion (candidate (47b)). Vowel lengthening is chosen over tone insertion because Dep-H outranks Dep-µ (see also Zec Reference Zec1999: 245, especially tableau (57)). The constraint grammar that derives ML is diagrammed in (48).

Head-H alone cannot decide between the winner (47d) [] and the faithful loser (47a) *[], since both candidates violate it. However, the conjoined constraint Head-H & FtBin favours unfaithful mapping over faithful realisation. The winning candidate repairs only one of the two markedness violations incurred by its faithful competitor. Nevertheless, the partial repair offered by the lengthened form is sufficient to satisfy Head-H & FtBin. This renders vowel lengthening optimal for toneless monomoraic inputs. Thus, the ML process is driven jointly by Head-H and FtBin. In strict-ranking OT, this cumulative constraint interaction is captured by LCC, as (47) demonstrates.

3.2.2. Tonal flop and penultimate lengthening: constraint-based analysis

The analysis proposed in §3.2.1 readily extends to the processes of TF and PL observed in some OS dialects of BCMS. These are argued in §2.5 to have the same purpose as ML: the elimination of toneless degenerate feet.

TF targets stressed toneless lights as in (37), but not stressed toneless heavies (35). The absence of TF in cases like // → [] (not *[]) ‘arm.nom.sg’ in (35a) indicates that Head-H cannot be the sole driving force behind TF, else it would apply across the board. Judging from the absence of TF in (35), Head-H must be individually overridden by NoFlop-tone, as in (49).

The constraint grammar in (49) predicts that TF will be inhibited in all environments in OS. This is problematic because stressed toneless lights attract tone from a final light syllable in some OS dialects, as (37) shows.

In (50), I outline a failed attempt to derive the TF pattern in (37) under the constraint rankings from (49). This grammar erroneously favours the faithful candidate with penultimate stress over the intended winner that undergoes TF. Note that I ignore the issue of foot structure in the candidate forms in (50).

Consequently, the mappings in (49) and (50) appear to be inconsistent with each other. Example (49) points to NoFlop $\gg $ Head-H. However, this ranking fails to derive the correct winner in (50).

Looping back to the form [] in (50), there are two structural analyses consistent with it. One possibility is outlined in (51a): the form displays a bimoraic trochee with a toneless head mora and a high-toned non-head mora. Alternatively, in (51b), the final high-toned light is unfooted and the penult forms a toneless degenerate foot.

The structure in (51a) satisfies FtBin at the expense of *Nonhead-H, which requires that the non-head mora of a foot not be high-toned. As argued in §2.1.2, high-toned foot non-heads are prohibited in OS. This prohibition manifests itself in the dialect’s ban on rising contours, but also in the illicitness of (51a). Accordingly, it is better for high-toned moras in OS to be left unfooted than to be included in the non-head position of a foot.Footnote ¹¹ This preference in OS is consistent with de Lacy’s (Reference de Lacy2002) theory of tone–stress interaction, where *Nonhead-H penalises high-toned foot non-heads and no constraint punishes unfooted high-toned moras or syllables.

In (51b), adherence to *Nonhead-H results in a toneless monomoraic foot. This structure is penalised by the conjoined constraint Head-H&FtBin. Therefore, both faithful candidates that exhibit penultimate stress violate some top-ranking constraint in OS. The bimoraic foot in (51a) is ruled out by *Nonhead-H. The form in (51b) fatally violates Head-H & FtBin. TF offers a way to satisfy both of these constraints. This process makes the stressed penult high-toned, satisfying Head-H, and renders the final light syllable toneless. This enables the inclusion of the final syllable in the non-head position of a bimoraic trochee, which benefits FtBin without offending *Nonhead-H. By so doing, the TF candidate [] outperforms all faithful competitors, as shown in (52). TF is preferred over vowel lengthening because Dep-µ outranks NoFlop-tone.

In sum, NoFlop cannot be violated in OS to comply with Head-H alone, as seen in (49). However, this constraint gives way to the local conjunction of Head-H and FtBin in (52).

OS dialects that exhibit TF likewise display vowel lengthening in toneless monomoraic words, as in // → [] ‘ice.nom.sg’. The full constraint hierarchy for the subgroup of OS dialects that display TF is diagrammed in (53).

The constraint hierarchy in (53) correctly derives both ML and TF. Since Dep-µ dominates NoFlop, TF is preferred to vowel lengthening in polysyllabic forms, as in (52). Vowel lengthening is the optimal strategy to eliminate toneless degenerate feet in monomoraic forms because Dep-H outranks Dep-µ. Importantly, all crucial rankings relevant for ML in (48) are included in (53).

The LCC analysis devised in (52) carries over to PL. This lengthening process makes the foot bimoraic, satisfying FtBin. However, FtBin cannot be the sole PL-inducing constraint. OS dialects tolerate monomoraic feet, as long as they are high-toned, as in (54). This indicates that in OS, FtBin ranks below Dep-µ.

Thus, PL targets toneless, but not high-toned, stressed lights. The process does not militate against all monomoraic feet, but rather toneless monomoraic feet.

Importantly, all OS dialects display the metrical requirement that no foot be toneless and monomoraic simultaneously. All OS dialects employ ML in toneless monomoraic forms to avoid this doubly marked structure. However, individual OS dialects employ different strategies to achieve this goal in disyllabic and polysyllabic forms. In some OS dialects, this is done by means of TF. These dialects rank Dep-µ above NoFlop, as shown in (52). Conversely, PL arises in those OS dialects that rank NoFlop above Dep-µ. The analysis is provided in (55).

As in (52), final stress (candidate (55a)) is ruled out by Nonfinality. Candidate (55b) is knocked out by *Nonhead-H. Candidate (55c) fatally violates Head-H & FtBin. The TF candidate, (55d), violates NoFlop, which is undominated in this subgroup of OS dialects. The winning candidate, (55e), satisfies all top-ranking constraints at the expense of Dep-µ.

The sole difference between OS dialects that display PL and those that display TF lies in the ranking of Dep-µ relative to NoFlop. The constraint hierarchy for the OS dialects that exhibit PL is given in (56).

In (56), NoFlop $\gg $ Dep-µ ensures that PL is preferred to TF in polysyllables. Similarly, Dep-H $\gg $ Dep-µ ensures that ML is preferred to tone insertion in toneless monomoraic words. The constraint grammar in (56) retains all the constraint relations from (48) needed to derive ML.

Taking stock, I identified two subgroups of OS dialects. In one subgroup, which has the grammar in (52), there are two competing strategies to avoid toneless degenerate feet. In monosyllables, vowel lengthening is the optimal strategy to do away with a toneless degenerate foot. In polysyllables, TF takes precedence over vowel lengthening, ensured by the constraint hierarchy in (53). The other subgroup, exemplified by (55), consistently employs vowel lengthening to eliminate toneless degenerate feet, both in monosyllables and in polysyllabic forms. This preference falls out from the constraint hierarchy in (56).

I also provided a unified account of three superficially distinct metrical processes in BCMS: ML, TF and PL. These have not been considered functionally related in previous work. These processes take part in a conspiracy against toneless degenerate feet in the language. To capture the prohibition on toneless degenerate feet in BCMS, I introduced the local conjunction of Head-H and FtBin.

3.3.1. Prosodic minimality in BCMS in standard HG

In the cases of cumulative markedness interaction typically discussed in the HG literature (Pater Reference Pater2009b, Reference Pater, McCarthy and Pater2016), the repair strategy employed to remove coincident marked configurations eliminates all marked structures that are barred from cooccurring within a single domain. At the level of HG analysis, such cumulativity effects are modelled by asymmetric (i.e., one-to-many) trade-offs between constraint weights (Pater Reference Pater2009b, Reference Pater, McCarthy and Pater2016; Smith Reference Smith2022). Asymmetric trade-off between faithfulness ( $\mathbb {F}$ ) and markedness constraints $\mathbb {M}_1$ and $\mathbb {M}_2$ arises when the candidate that satisfies either $\mathbb {M}_1$ or $\mathbb {M}_2$ at the expense of $\mathbb {F}$ loses out to the faithful competitor, while the candidate that satisfies both $\mathbb {M}_1$ and $\mathbb {M}_2$ at the expense of $\mathbb {F}$ prevails against the faithful competitor.

This is how standard HG models the restrictions on voiced obstruents in Japanese loanword phonology, an oft-quoted example of ganging-up cumulativity (Nishimura Reference Nishimura2003; Kawahara Reference Kawahara2006; Pater Reference Pater2009b, Reference Pater, McCarthy and Pater2016). In Japanese, multiple voiced obstruents are tolerated within a morpheme in loanwords like those in (57), unlike in the native vocabulary (Lyman Reference Lyman1894). Likewise permitted in loanword phonology are otherwise intolerable voiced geminates, as in (58). However, when a voiced geminate co-occurs with a voiced singleton within a morpheme, the geminate optionally devoices, as in (59).

Since multiple voiced singletons are allowed within a morpheme (as in (57)), Ident-voice, which protects the underlying voicing of an obstruent, outweighs OCP-voice, which bars multiple voiced obstruents within a morpheme. Similarly, Ident-voice outweighs NoVoicedGeminate, which discriminates against voiced geminates, as evident from (58). Geminate devoicing in (59) is possible because OCP-voice and NoVoicedGeminate gang up to overcome higher-weighted Ident-voice.

Crucially, the repair employed to eliminate coincident marked structures in (59) removes both relevant marked structures. This explains why it is the voiced geminate rather than the voiced singleton that undergoes devoicing. Singleton devoicing, as in *[toggu], satisfies only OCP-voice, but not NoVoicedGeminate. Thus, *[toggu] shares a NoVoicedGeminate violation with the faithful contender [doggu] and violates the individually strongest constraint (Ident-voi), as shown in (60).

Notably, in geminate devoicing in Japanese, a single unfaithful mapping satisfies both markedness constraints at the expense of a higher-weighted faithfulness constraint. This contrasts with the cumulativity effect in toneless monomoraic feet in BCMS, where no single repair strategy removes both marked structures. Both available repairs (vowel lengthening and tone insertion) remove only one of the coincident marked structures, while the other one persists.

Tone insertion (// → []) makes the foot-heading mora high-toned, thereby satisfying Head-H. However, the foot remains monomoraic, incurring a FtBin penalty. Vowel lengthening (// → []) makes the foot bimoraic in response to FtBin. The head mora remains toneless, violating Head-H. The only way to remove both of the coincident marked structures and satisfy both ganging constraints is to subject a toneless monomoraic foot to both vowel lengthening and tone insertion: []. This option violates two higher-weighted faithfulness constraints: Dep-H and Dep-µ.

Contrary to the Japanese geminate devoicing in (60), there is a symmetric (i.e., one-to-one) trade-off between constraint weights in the HG analysis of ML in BCMS (61). For the intended winner [] to prevail against the faithful contender [], a higher-weighted Dep-µ penalty must be traded against a single lower-weighted penalty (FtBin) in Head-H-violating contexts. An HG grammar with no means to amplify the severity of coincident constraint violations erroneously selects as optimal the faithful candidate for toneless monomoraic inputs. Due to the shared violation of Head-H, faithful realisation is favoured over lengthening regardless of the weight assigned to Head-H, as (61) shows.

In (61), the intended winner (candidate (61b)) satisfies only one of the markedness constraints, namely, FtBin, and still violates Head-H. Since the intended winner and the faithful candidate (61a) share a Head-H violation, vowel lengthening incurs a greater cumulative penalty than no lengthening. Having no means to add weight to the coincident violation of Head-H and FtBin, the standard HG analysis cannot generate a gang effect under the weighting conditions in (61). These weighting conditions are independently motivated by the lack of lengthening in high-toned monosyllables in BCMS (as seen in (32)).

A similar result is observed in the PL process in OS. Under the weighting conditions independently established for OS, vowel lengthening in stressed toneless lights incurs a greater cumulative penalty than a doubly marked toneless monomoraic foot. Because Dep-µ is individually stronger than FtBin, the weight incurred by coincident violation of Dep-µ and Head-H is greater than that incurred by simultaneously violating FtBin and Head-H. Under the standard HG analysis of PL, shown in (62), the intended winner (62e) loses to the faithful candidate (62c), which exhibits a toneless degenerate foot.

Unlike the lengthening processes in (61) and (62), standard HG is capable of deriving TF. The HG analysis of TF is outlined in the tableau in (63).

The weighting conditions in (63) are similar to those in (62), the main difference being the fact that Dep-µ outweighs NoFlop in (63). As a result, the TF candidate (63e) emerges as optimal. TF satisfies both Head-H and FtBin in one go, producing an asymmetric trade-off between NoFlop and two lower-weighted markedness constraints: Head-H and FtBin. The HG analysis of TF accounts for this gang effect without any supplementary devices.

To recapitulate: standard HG is incapable of deriving tone-sensitive vowel lengthening in BCMS, wherein toneless monomoraic feet, but not their high-toned counterparts, become bimoraic to comply with the language’s foot minimality condition. Under the independently motivated weighting conditions in BCMS, the HG analysis of the relevant lengthening processes fails to replicate the effect of constraint conjunction in OT; see (47), (52) and (55). This suggests that HG’s built-in additive cumulativity of constraint violations does not supplant all effects of conjoined constraints, which calls for the enrichment of standard HG’s apparatus.

3.3.2. Weighted constraint conjunction in HG

The effect of violating Dep-µ in BCMS is more severe than the effect of violating FtBin individually. This is apparent from cases like (32), where high-toned monomoraic feet are unable to undergo vowel lengthening. The effect of coincident violation of Dep-µ and Head-H is expected to exceed the effect of violating FtBin and Head-H simultaneously, as the HG analysis in (61) and (62) encapsulates. The reasoning behind this expectation is schematised in (64).

However, what transpires in BCMS is inverse to (64b): the joint violation of Head-H and FtBin has a more detrimental effect on metrical well-formedness than the coincident violation of Dep-µ and Head-H, as (65) shows:

For (64a) and (65) both to be true, it must be the case that in doubly violating contexts, Head-H and FtBin add up to more than the combination of their independent contributions. In other words, the effect of the joint violation of Head-H and FtBin is greater than the combination of the effects of these constraints’ independent violations. Thus, the cumulative effect of Head-H and FtBin violations in BCMS is superadditive rather than additive, based on the criteria defined in (3):

Following Green & Davis (Reference Green, Davis, Farris-Trimble and Barlow2014) and Shih (Reference Shih2017), the HG analysis of prosodic minimality in BCMS must adopt the weighted local conjunction of Head-H and FtBin to accommodate the exacerbated severity of their joint violation, as in (66). The presence of this conjoined constraint in the HG grammar of BCMS adds weight to the coincident violation of Head-H and FtBin. The HG account of ML is provided in (67). The extra weight attributed to the doubly marked candidate (67a) enables the lengthening candidate (67b) to prevail against the faithful competitor.Footnote ¹²

The weighted LCC analysis in (67) readily extends to PL in OS dialects of BCMS, shown in (62) to pose a challenge to standard HG. With the added weight incurred by the joint violation of Head-H and FtBin (candidate (68c)), subjecting the toneless light penult to vowel lengthening (candidate (68e)) emerges as the least costly metrical strategy under the weighting conditions shown:

While HG can derive TF in isolation without the need for LCC (as shown in (63)), this does not imply that OS dialects displaying TF do not require LCC for other relevant processes. Notably, all OS dialects with TF also exhibit ML in toneless monomoraic forms. Given that standard HG fails to account for ML (see (61)), the local conjunction of Head-H and FtBin is necessary even in OS dialects with TF to capture the full range of foot minimality effects.

Therefore, the formal account of TF is fully compatible with that of ML: both processes can be captured under a single constraint grammar enriched with Head-H&FtBin, under the weighting conditions presented in (69). This is shown for TF in (69a). The same grammar generates ML in toneless monomoraic forms, as in (69b), and no lengthening in their high-toned counterparts, as in (69c).

In conclusion, the prosodic minimality effects in BCMS arise as a result of the interaction of Head-H and FtBin. The cumulative effect of Head-H and FtBin violations was shown to be superadditive. That being the case, the HG analysis of the processes that conspire against toneless degenerate feet necessitates the local conjunction of Head-H and FtBin – just like the equivalent OT analysis advanced in §3.2.

OT and HG thus end up requiring the same machinery to model the interaction of Head-H and FtBin in BCMS. This demonstration contributes to the OT–HG debate by providing further evidence for conjoined constraints in weighted constraint grammar (Albright Reference Albright2009; Hayes et al. Reference Hayes, Wilson and Shisko2012; Green & Davis Reference Green, Davis, Farris-Trimble and Barlow2014; Shih Reference Shih2017), contrary to the widespread assumption that HG obviates the need for conjoined constraints (Farris-Trimble Reference Farris-Trimble2008; Pater Reference Pater2009a, Reference Paterb, Reference Pater, McCarthy and Pater2016; Potts et al. Reference Potts, Pater, Jesney, Bhatt and Becker2010).

However, this study, considered in isolation, is indeterminate between OT and HG as a theory of ganging-up cumulativity, though other work has provided more conclusive evidence relevant to the OT–HG debate (see Zuraw & Hayes Reference Zuraw and Hayes2017; Breiss Reference Breiss2020; Smith & Pater Reference Smith and Pater2020, among others, for the current state of this debate). Importantly, the two frameworks invoke conjoined constraints for different purposes. OT avails itself of conjoined constraints to model all cases of ganging-up cumulativity, treating additive and superadditive ganging as equally complex in terms of the formal machinery they necessitate. By contrast, HG needs this supplementary device only for modelling superadditive ganging-up. HG thus treats superadditive ganging as more complex than additive ganging-up.

4.2.1. TrochaicQuantity and pitch-based rhythmic grouping

Central to Zec’s (Reference Zec1999) explanation of why ML fails to apply in high-toned monosyllables in BCMS is the preference for equal grouping in trochaic systems, ensuring that the foot-heading position is not heavier than the weak position (McCarthy & Prince Reference McCarthy and Prince1986; Prince Reference Prince1990; Hayes Reference Hayes1995). Zec (Reference Zec1999) extends this requirement to pitch-based grouping. The TrochQuant constraint penalises the strong–weak contrast based on relative pitch, ensuring that the strong syllable/mora of a trochee must not be higher-pitched than the weak syllable/mora.

It has been observed that rhythmic groupings with varying intensity are preferably perceived as left-headed, while groupings with a contrast in duration are perceived as right-headed. The rationale behind the TrochQuant constraint is that grouping preferences based on pitch parallel those based on duration. There has been plentiful experimental work on rhythmic grouping effects (see Crowhurst Reference Crowhurst2020 for an overview). Many experimental studies on pitch-based grouping effects report a trochaic bias in alternating sequences with varying pitch (Bion et al. Reference Bion, Benavides-Varela and Nespor2011; Bhatara et al. Reference Bhatara, Boll-Avetisyan, Unger, Nazzi and Höhle2013; de la Mora et al. Reference de la Mora, Nespor and Toro2013). These results suggest that pitch-based grouping effects differ from duration-based grouping effects, given that higher-pitched elements are preferably associated with group onsets.

Therefore, pitch patterns with intensity rather than duration with respect to rhythmic grouping. The reported trochaic bias in pitch-based grouping poses a challenge for Zec’s (Reference Zec1999) account of BCMS ML, which holds that trochees with a higher-pitched first element are disfavoured in much the same way as those with a contrast in duration. Thus, one of the central theoretical underpinnings of Zec’s account – the parallelism between quantity-based and tone-based grouping preferences – is contradicted by available experimental evidence. This challenges Zec’s assertion that pitch behaves like duration in rhythmic grouping.

4.2.2. TrochaicQuantity penalises doubly unmarked structure

TrochQuant treats bimoraic trochees headed by a high-toned mora as marked. This contradicts two prevalent cross-linguistic tendencies, one being the attraction of high tone to prosodically prominent positions (Goldsmith Reference Goldsmith1987; Hayes Reference Hayes1995; Yip Reference Yip2001; de Lacy Reference de Lacy2002; Gordon Reference Gordon and Weijer2023), and the other being the affinity between stress and heavy syllables (Prince Reference Prince1990; Hayes Reference Hayes1995; Gordon Reference Gordon2006; Ryan Reference Ryan2016). This constraint implies that the combination of two unmarked structures results in a marked configuration: both high-toned foot heads and bimoraic trochees are unmarked individually, but their combination incurs a markedness penalty.

As a result, TrochQuant produces a number of pathological effects. First, consider the constraint grammar in which TrochQuant outranks Max-µ. In this hypothetical language, heavy syllables with a high-toned first mora become light when stressed, as in (76). However, their toneless counterparts surface faithfully, as in (77). In other words, a bimoraic trochee becomes degenerate because its head mora is high-toned.

Second, TrochQuant’s dominance over Max-H gives rise to a pathological tone deletion pattern whereby high tone deletes in the head position of a bimoraic trochee (as in (78)), but not in the head position of a monomoraic foot (as in (79)), nor in an unstressed syllable (as in (80)):

Another adverse effect of TrochQuant is illustrated in (81). A H tone is lured away from the foot-heading mora to an unfooted mora to comply with TrochQuant. The pattern is counterintuitive because documented cases of tone shift observe the opposite tendency: highs shift from metrically weak positions to prominent positions (Downing Reference Downing1990; Bickmore Reference Bickmore1995; de Lacy Reference de Lacy2002; Breteler Reference Breteler2018).

Finally, even when TrochQuant ranks below faithfulness and thus fails to induce any unfaithful mappings, it is still capable of producing pathological effects. Suppose there is a language with lexical tone that preferably stresses the leftmost heavy syllable, else defaulting to the leftmost syllable, as in (82). Suppose further that this hypothetical language ranks TrochQuant over WSP. This ranking gives rise to the pathological mapping in (82c): the leftmost heavy, the first mora of which is high-toned, repels stress to the light peninitial syllable for no reason other than having a high-toned first mora.

This repulsion effect runs afoul of the propensity of high tone to attract stress (Goldsmith Reference Goldsmith1987; Gordon Reference Gordon and Weijer2023).

4.2.3. Undergeneration

Zec (Reference Zec1999) discusses ML without addressing the other processes that conspire against toneless degenerate feet: TF and PL. This section explores whether Zec’s account extends to these other functionally related processes in BCMS.

To accomplish this, I conducted a learning simulation using the OT-Help software. The constraint set used in this simulation mirrors the one used in §3.4, the only difference being the inclusion of Zec’s TrochQuant in place of the Head-H & FtBin conjunction from §3.4.

The simulation found that Zec’s account captures only a subset of the relevant processes in BCMS. Specifically, TrochQuant struggles to model a subgroup of the OS dialects that display TF (as in (37)). The grammar that Zec’s constraint set fails to derive is given in (83). These data match the stress pattern of the Kosovo–Resava dialect of BCMS (Ivić Reference Ivić1958; Simić Reference Simić1972).

The attentive reader will notice that the surface forms in (83c), (83e) and (83f) show monomoraic rather than bimoraic feet (e.g., [] rather than [] in (83c)). This adjustment was necessary in order for Zec’s (Reference Zec1999) TrochQuant-based account to be made to work, given that TrochQuant penalises bimoraic trochees with a high-toned head mora. On the present account, monomoraic feet posited in (83c), (83e) and (83f) would violate FtBin for no obvious reason since Head-H&FtBin does not favour monomoraic over bimoraic feet. However, for Zec’s account, it is crucial to assume that these OS forms have monomoraic rather than bimoraic feet.

Even when this adjustment in favour of TrochQuant is made, the algorithm finds no OT grammar that derives all mappings in (83). The RCD algorithm stalled without reaching the target grammar. Six out of nine constraints were left unranked: Head-H, FtBin-µ, WSP, NoFlop-H, Dep-µ and TrochQuant.

No totally ranked hierarchy was established for the above six constraints because of a ranking inconsistency involving TrochQuant. The RCD algorithm demotes Dep-µ below FtBin on the basis of vowel lengthening in toneless monosyllables (as in (83a)). Since there is no lengthening in high-toned monomoraic forms (see (83b)), the algorithm demotes FtBin below TrochQuant. The subranking TrochQuant $\gg $ FtBin $\gg $ Dep-µ is precisely how Zec (Reference Zec1999: 244–245) accounts for vowel lengthening in toneless monosyllables in BCMS, as discussed in §4.1.

The TF mapping in (83c) provides a rationale for demoting NoFlop below Head-H. This is illustrated in the combination tableau in (84). The only way to justify the absence of TF in (83d) is by demoting Head-H below TrochQuant (as in (85)). Finally, WSP gets demoted below Head-H to accommodate the preference for stressed high-toned lights over stressed toneless heavies in the Kosovo–Resava dialect (as in (83e)), illustrated in the tableau in (86).

After these five iterations of constraint demotion, the learner posits the following constraint grammar:

The grammar in (87) is inconsistent with the mapping // → [] in (83g). Taken in isolation, (83g) requires Head-H to dominate TrochQuant. However, this ranking contradicts the ranking established in (85):

Thus, the RCD algorithm cannot find a totally ranked hierarchy for the six constraints in (87). Employing TrochQuant to model prosodic minimality in the OS dialects that display TF creates a ranking paradox. The mapping in (88), needed for (83g), cannot be made consistent with the rest of the dialect’s phonological grammar in (83).

This undesirable effect of Zec’s (Reference Zec1999) TrochQuant is limited to strict-ranking OT. The inconsistency encountered in (88) does not carry over to HG, where Head-H and WSP can gang up to jointly override TrochQuant. This gang effect enables the intended winner [] to prevail against the problematic competitor *[] in (88).