Consonant harmony in Nilotic: contrastive specifications and Stratal OT

Through analyses of dental harmony in four Nilotic languages, this paper argues both for contrastive representations and for a stratal version of Optimality Theory. Dholuo, Päri, Shilluk and Anywa all have dental harmony patterns which bar the co-occurrence of dental and alveolar segments. Details of the dental harmony patterning vary between languages and are tied to contrasts in the inventory. In Anywa, harmony is non-structure-preserving and an allophonic dental nasal surfaces in harmonic forms. This pattern can be analyzed in a stratal model of OT but leads to a ranking paradox if only a single level of evaluation is used. Further support for a stratal analysis can be found in the interaction between harmony and consonant mutation processes in the four languages. In Dholuo, harmony applies at the stem level and consonant mutation results in disharmonic surface forms in morphologically complex words. In Anywa, harmony applies later, at the word level, and words formed through consonant mutation must obey the dental harmony restrictions.


Introduction
This paper argues for the integration of contrastive specifications with a stratal version of Optimality Theory through analyses of dental harmony in Nilotic languages. The proposal that features needed to contrast members of a phonemic inventory are also those features which are active in phonological processes has played a central role in a variety of theoretical frameworks (e.g. Steriade 1987;Archangeli 1988;Avery & Rice 1989;Dresher 2009). While some notion of contrast remains central in a range of phonological literature, interest in modeling contrast through feature specification and underspecification has declined since Optimality Theory (Prince & Smolensky 1993) has become the dominant model of phonological formalisms. The OT principle of Richness of the Base excludes language-specific restrictions on input representations, a traditional method of representing contrastive specifications in pre-OT theories. Previous work (e.g. Mackenzie & Dresher 2004;Dresher 2009) has demonstrated that contrastive specifications can be achieved as outputs of OT grammars using markedness and faithfulness constraints. While these works have shown that contrastive specifications consistent with a principled definition of contrast can be achieved in OT without compromising Richness of the Base, they have generally failed to show how constraint rankings which determine contrastive specifications should be integrated with constraint rankings which motivate phonological processes. This paper demonstrates that contrastive representations as outputs of OT grammars can be integrated into a stratal model of OT in which serial evaluation is limited to three levels (e.g. Kiparsky 2000;Bermúdez-Otero 2003).
The Nilotic languages Dholuo, Päri, Shilluk, and Anywa all have dental harmony in the form of morpheme structure constraints which bar the co-occurrence of dental and alveolar stops. The details of the harmony vary between languages as does the size and shape of the consonant inventory. Previous analyses (Mackenzie 2009; have argued that the connection between inventory shape and the patterning of dental harmony in Nilotic languages provides evidence for a theory of contrast in which features are hierarchically ordered with some features taking scope over others (Dresher 2003;2009). The theory of the contrastive hierarchy ties contrastive specifications to inventory shape while allowing variation between languages with similar inventories. I follow the contrastive hierarchy analysis of Nilotic dental harmony here and show that the necessary contrastive specifications can be obtained through constraint ranking in a stratal model of OT. While evidence for the contrastive hierarchy is found in the connection between inventory shape and the patterning of dental harmony, evidence for a stratal analysis comes from a ranking paradox that arises in the analysis of Anywa harmony if only a single level of evaluation is used.
Two claims follow from this analysis. First, accounting for the differences in the patterning of dental harmony in Dholuo, Anywa, and Päri requires a serial, stratal version of OT. That is, while contrastive specifications can be achieved in OT, explanatory use of such representations is not consistent with the single level evaluation model of classic OT. Secondly, contrastive representations can be integrated with independently motivated levels of stratal OT. For contrastive specifications to play an explanatory role in accounting for phonological processes, it is not necessary to achieve contrastive representations prior to all other phonological generalizations. Rather, these representations can be achieved as outputs of the stem level and constraints achieving contrastive representations can be integrated with constraints which motivate stem-level processes. This analysis makes predictions about the interaction of harmony and morphological processes. Specifically, non-structure-preserving harmony, as in Anywa, is predicted not to occur at the stem level.
The paper is organized as follows. Section 2 provides an introduction to the theory of the contrastive hierarchy and a method for converting contrastive feature hierarchies to OT constraint rankings. Section 3 provides a brief introduction to Stratal OT. Section 4 gives analyses of Dholuo and Päri, demonstrating the crucial role of contrast in accounting for differences in the patterning of dental harmony in the two languages. This section also provides an analysis of Shilluk dental harmony and its interaction with consonant mutation processes. The analyses of Dholuo, Päri, and Shilluk show that the constraints which motivate harmony can be integrated with the constraints necessary for determining contrastive specifications. Section 5 provides an analysis of dental harmony in Anywa. While the harmony process in Anywa is highly similar to that found in the other languages, harmony in Anywa is non-structure-preserving and leads to a ranking paradox in a classic OT account. The analysis presented here shows that this problem can be resolved in a multi-stratal version of OT with dental harmony in Anywa occurring at the word level and contrastive specifications determined at an earlier, stem-level evaluation. Taken together, these analyses demonstrate that differences in harmony patterning between languages can depend both on differences in contrastive specifications and differences in the level at which harmony applies. Section 6 concludes.

The contrastive hierarchy and Optimality Theory
The analyses of dental harmony presented in the following sections provide evidence for the theory of the contrastive hierarchy (Dresher 2003;2009). The theory of the contrastive hierarchy provides an explicit definition of contrast in which features are hierarchically ordered with some features taking scope over others. The order of features in the hierarchy can vary between languages, allowing for crosslinguistic variation in feature specifications, even between languages with similar inventories. Empirical consequences of the contrastive hierarchy are necessarily dependent on the notion that feature activity in phonological processes is tied to contrasts in the inventory. This "contrastivist hypothesis" is defined as follows in Hall (2007: 20): "The phonological component of a language L operates only on those features which are necessary to distinguish the phonemes of L from one another." As Hall (2007) discusses, this formulation is open to interpretation, given the ambiguity of what it means for a feature to distinguish phonemes from one another and the range of proposals concerning the nature and definition of contrast. Taken together with the theory of the contrastive hierarchy, however, the contrastivist hypothesis predicts that only features that are formally deemed contrastive by the theory will be active in phonological processes.
According to the theory of the contrastive hierarchy, contrastive specifications are determined by a series of binary divisions of the inventory. This is formalized as the Successive Division Algorithm (SDA).
(1) Successive Division Algorithm (Dresher 2009: 16) a. Begin with no feature specifications: assume all sounds are allophones of a single undifferentiated phoneme. b. If the set is found to consist of more than one contrasting member, select a feature and divide the set into as many subsets as the feature allows for. c. Repeat step (b) in each subset: keep dividing up the inventory into sets, applying successive features in turn, until every set has only one member.
The feature selected first will be contrastive for the entire inventory whereas lower ordered features will be contrastively specified only for those subsets of the inventory which require the feature in question in order to be uniquely specified. The contrastive hierarchy is a theory of phonological representations. As such, it is, in principle, orthogonal to computational questions such as whether phonological patterns arise from parallel evaluation and constraint ranking as in OT, or from the application of sequentially ordered rules, as in SPE. Although the emphasis on representations and inventory structure, which is central to the theory of the contrastive hierarchy, is generally associated with derivational theories, previous work has demonstrated that contrastively specified representations can be achieved as outputs of OT grammars. Mackenzie and Dresher (2004) provide an algorithm capable of converting any contrastive hierarchy to an OT constraint ranking. This algorithm was revised in Dresher (2009)  In step (a), a contrastive feature hierarchy is converted into a corresponding ranking of feature-specific faithfulness constraints. Faithfulness constraints are of the form Max [F] and are violated if a feature specification, either [+] or [-], present in the input is absent from the output.
Step (b) provides a ranking of feature co-occurrence constraints which ensures that each feature will only be specified for those subsets of the inventory in which the feature is contrastive. Constraints of the form *[aF i , F] Segment exclude the specification of any value of the feature F i for a segment which has the specification, or set of specifications, F where F consists of higher ordered feature specifications. These markedness constraints have the effect of limiting the scope of a feature by restricting the set of segments which will be specified for that feature. Steps (a) and (b) are repeated until faithfulness constraints referring to all features in the contrastive hierarchy have been ranked along with the markedness constraints which limit the scope of those features. In the final step, the constraint *[F] is ranked below the constraints ranked in steps (a) and (b). *[F] assigns a violation mark for each feature specification in a representation and reflects a preference for representations to be minimal. Although all feature specifications incur a violation of *[F], contrastive specifications will surface faithfully due to the high-ranking of faithfulness constraints referring to contrastive features determined by step (a). Faithfulness constraints referring to non-contrastive features will be ranked below *[F]. This algorithm is capable of converting any contrastive hierarchy into an OT constraint ranking.
The theory of the contrastive hierarchy is a theory of phonological representations. The contrastive hierarchy provides an explicit definition of contrast, which, in concert with the contrastivist hypothesis, makes predictions about the relation between inventory shape and feature activity and the range of variation we expect to find in this relation across languages. The algorithm in (2) will take any contrastive hierarchy and convert it to an OT constraint ranking. The theory of the contrastive hierarchy proposes that only constraint rankings consistent with (2) will be found crosslinguistically and thus imposes restrictions on the set of possible OT grammars. 1 The following example illustrates how the contrastive hierarchy and the algorithm for converting a contrastive hierarchy to a constraint ranking work. Consider a simplified inventory of coronal segments consisting of /t, d, n/. This inventory contains three segments and two contrastive features will be needed for each member of the inventory to be uniquely specified. Assuming the relevant features are [voice] and [nasal], we have two possible contrastive hierarchies, illustrated below. 1 The theory of the contrastive hierarchy has implications for theories acquisition and learnability but is not itself a theory of language acquisition. The algorithm in (2) converts contrastive hierarchies to constraint rankings and the theory of the contrastive hierarchy predicts that all (stem-level) grammars will be consistent with such rankings. Theories of learnability and acquisition are needed to address the issue of how such rankings are acquired. See Mackenzie (2013) for additional discussion of this point. Although the hierarchies illustrated in Figure 1 (a) and (b) have the same set of segments in the surface inventory, they have different feature specifications which result from different orderings of features in the contrastive hierarchy. We might expect these systems to pattern differently in the phonology. In the system in (a), we may expect /d/ and /t/ to pattern as similar to one another and to interact in processes to the exclusion of /n/. Examples of this type of patterning are common, as in cases where obstruents, such as /d/ and /t/, interact in voicing assimilation and sonorants, such as /n/, are neutral (e.g. Russian). In the system illustrated in (b), on the other hand, we may expect /d/ and /n/ to interact in processes to the exclusion of /t/. Such patterns are also attested, as in cases of long-distance nasal harmony in Bantu where /d/ and /n/ interact and /t/ is neutral (e.g. Hyman 1995).
Any contrastive hierarchy can be converted to an OT constraint ranking using the algorithm in (2). To take the hierarchy illustrated in Figure 1 (a) for example, step (a) of the algorithm requires us to select the faithfulness constraint referring to the highest ordered feature in the hierarchy, in this case Max [nasal], and rank this constraint above any featural faithfulness constraints that have not yet been ranked. Step (b) requires a markedness constraint of the form *[aF i , F] where F consists of features ordered higher than [F i ] to be ranked above Max [nasal]. However, since [nasal] is the highest ordered feature this step cannot apply and we return to step (a), ranking the faithfulness constraint referring to the next ordered feature, Max[voice], below Max [nasal]. Again, we turn to step (b) and this time this requires us to rank the constraint *[avoice, +nasal] above Max[voice]. This markedness constraint will be violated by any [+nasal] segment which is specified for any value of the feature [voice]. At this point, faithfulness constraints referring to all contrastive features have been ranked and we proceed to step (d), ranking the general markedness constraint *[F] below all the constraints ranked by application of previous steps of the algorithm. The ranking produced by applying the algorithm for converting a contrastive hierarchy to a constraint ranking to the contrastive hierarchy in Figure 1 (a) is shown in (3) With this ranking, any fully specified input will map to a contrastively specified output consistent with the proposed contrastive hierarchy. For example, the tableau below considers an input containing a nasal specified as [+voice, +nasal]. . Candidate (b) is optimal. This is the contrastively specified candidate, according to the feature hierarchy in Figure 1 (a As illustrated above, rankings produced by the algorithm for converting a contrastive hierarchy to a constraint ranking produce contrastively specified representations from fully-specified inputs. One additional mechanism is needed, however, in order to ensure that contrastively specified representations are achieved in a manner that is truly compatible with Richness of the Base. The faithfulness constraints used in the algorithm are Max[F] constraints. Max is used, rather than Ident, in order to penalize outputs which lack feature specifications which are present in the input. That is, Max[F] militates against underspecification relative to the input. The Max[F] constraints also penalize feature value mismatches between input and output. If a [+F] input specification maps to a [-F] value in the output, this violates Max[F] because a positive feature value in the input is absent from the output. 2 Max[F] constraints, however, only penalize the absence of feature specifications which are present in the input. If underspecified inputs are considered, Max[F] constraints will do nothing to ensure that outputs are sufficiently specified to be consistent with the theory of the contrastive hierarchy. As discussed in previous work on the contrastive hierarchy and Optimality Theory (Dresher 2009;Mackenzie 2013), additional constraints requiring feature specification in output forms are necessary in order to ensure contrastive representations and to be consistent with the premise of Richness of the Base which allows input representations to be free. Dresher (2009) proposes the use of constraints of the form Spec[F] which require features to be present in output forms, regardless of their presence or absence in input forms. With respect to the algorithm for converting a contrastive hierarchy to a constraint ranking, Spec[F] constraints referring to contrastive features must be ranked above the general constraint against feature specification,*[F], and below any contextual markedness constraints of the form *[aF i , F] Segment which refer to the feature in question and prevent specification of non-contrastive features. 3 Use of such constraints in conjunction with the other constraints needed to convert a contrastive hierarchy to a constraint ranking will ensure, not only that input features deemed redundant by the contrastive hierarchy will be eliminated from output representations, but also that features which are deemed contrastive by the feature hierarchy will be present in output representations, even if they are absent from inputs. Although the use of Spec[F] constraints adds additional complexity to the mapping of contrastive hierarchies to constraint-rankings, the need for Spec[F] constraints is not a result of the theory of the contrastive hierarchy but is a consequence of the principle of Richness of the Base. If inputs are truly free, any model of OT will require constraints which demand feature specifications in outputs even in cases where such features are absent from input representations. 4 Ranking of Spec[F] constraints will not be illustrated here but these constraints will play a role in the analysis of dental harmony in Anywa in later sections.
The theory of the contrastive hierarchy is motivated in part by theoretical considerations about what it means to be contrastive and what constitutes a logical theory of contrast (see e.g. Dresher 2009). A large part of the motivation for the theory of the contrastive hierarchy is, however, empirical. Crosslinguistic data provide evidence that features which are active in phonological processes are those features which are contrastive as defined by the theory of the contrastive hierarchy. Empirical arguments for the contrastive hierarchy are necessarily tied to the contrastivist hypothesis (Hall 2007) which holds that the phonological computation operates only on contrastive features.
If contrastive representations are achieved from a rich base via constraint interaction, and the constraints which determine contrastive representations are integrated with other constraints in the phonological grammar, it is unclear how it can be assured that only contrastive features are referred to in phonological processes. Some previous works using the theory of the contrastive hierarchy within the framework of OT have avoided this problem by assuming that the evaluation which results in contrastive specifications operates at a level prior to evaluations leading to phonological processes in a multi-level version of OT (e.g. Dresher 2009). These works have remained vague with respect to what the level that determines contrastive specifications is and what independent theoretical motivation it may have. These works have thus not truly integrated the theory of the contrastive hierarchy into a theory of constraint interaction. Data presented here will show that a single-level of OT evaluation is not sufficient to account for phonological patterning and that contrastive specifications must be determined prior to phonological processes, in 3 Dresher (2009) states that all Spec[F] constraints can be ranked as a block above *[F] and below all contextual markedness constraints limiting the scope of feature specifications. Such ranking will, indeed, ensure that underspecified inputs map to contrastively specified outputs. Nothing prevents individual Spec[F] constraints from being ranked higher, however. The analysis of the interaction of dental harmony and consonant mutation in Shilluk in Section 4 proposes that each Spec[F] constraint is ranked above the corresponding Max[F] constraint. 4 As pointed out by an anonymous reviewer, restricting inputs to fully specified forms is consistent with ROTB as long as there is no variation in inputs across languages. Although this is a potentially attractive alternative to considering underspecified inputs, I will not pursue the possibility here due to the range of works making use of input underspecification in OT (e.g. Inkelas 1994;Harrison & Kaun 2001;Colina 2013). some cases. The goal of this paper is to provide an integrated theory of contrastive specifications and constraint interaction and to address the question, what is the level at which contrastive specifications are determined?

Stratal Optimality Theory
In Stratal Optimality Theory (Kiparsky 2000;Bermúdez-Otero 2003;Rubach 2003 among others), the phonological grammar consists of an ordered series of OT evaluations. Stratal OT limits the set of distinct parallel evaluations to three, the stem, word, and phrase levels. In accordance with Richness of the Base, inputs are free at the initial level of evaluation. This is the stem level and constraint ranking here determines the segmental inventory as well as morpheme structure constraints. The output of the stem level serves as the input to the word level evaluation. The output of the word level, in turn, serves as the input to the phrase level.
Considered in light of the theory of the contrastive hierarchy, Stratal OT requires that contrastive specifications be determined at the stem level along with other aspects of inventory structure. The accounts of dental harmony argued for here attribute differences between languages both to differences in their respective hierarchies of contrastive features and to differences in the level at which harmony applies. Crucial reference to differences in constraint ranking between levels is needed specifically to account for nonstructure-preserving harmony in Anywa. The arguments made here are similar to those in Bermúdez-Otero's (2007) analysis of voicing assimilation in Catalan where he shows that non-structure-preserving neutralization processes can result in ranking paradoxes in classic, single-level OT. The principle of structure preservation prohibits processes in the lexical phonology from creating structures that are not part of the phonemic inventory (Kiparsky 1982;1985). Structure preservation played an important role within the theory of Lexical Phonology, imposing limitations on rule ordering and aiding in the learnability of rules. While structure preservation has no direct analogue in Optimality Theory (see e.g. McCarthy 2007: 43), the analysis that follows demonstrates that the absence of certain non-structure-preserving processes from stem-level phonology follows from the basic architecture of a Stratal OT grammar in combination with the principle of Richness of the Base and the theory of the contrastive hierarchy.

Dental harmony in Nilotic
Western Nilotic languages have a system of dental consonant harmony (Hansson 2001;2010;Rose & Walker 2004). These languages have a phonemic contrast between stops at the dental and alveolar places of articulation. Harmony bars the co-occurrence of dentals and alveolars, requiring all coronals to agree in dentality.
Many cases of consonant harmony are discernable only as morpheme structure constraints that hold within roots and not as active alternations (Hansson 2001;2010;Rose & Walker 2004) and some of the Nilotic dental harmony cases fall within this description. In a stratal OT analysis, morpheme structure constraints are determined at the stem level. Incorporating stratal OT with a theory of contrastive specifications thus requires the constraints that motivate harmony which is discernible only as restrictions on the form of roots to be integrated with the constraints that determine contrastive specifications.
The following analyses of Dholuo, Päri, and Shilluk show that constraint rankings responsible for determining contrastive specifications can be integrated with constraint rankings which motivate harmony. Differences between the patterning of harmony across languages provide evidence in support of a theory in which the contrastive status of features is influenced by the size and shape of the phonemic inventory.

Dholuo
Dholuo (Western Nilotic) has a contrast between dental and alveolar stops. This contrast is present among voiceless, voiced, and prenasalized stops but absent among nasals.
(5) Dholuo coronal stops (Tucker 1994: 30) Voiceless Stops Voiced Stops Prenasal Stops Nasals As illustrated in (6) below, voiced and voiceless stops participate in dental harmony in Dholuo (a) but the nasal is neutral (b) and alveolar nasals appear with both dental and alveolar stops (Yip 1989;Tucker 1994;Hansson 2001;2010  The tree diagram in Figure 2 illustrates the operation of the contrastive hierarchy. We begin by considering the coronal inventory as a whole. The contrastive hierarchy proposed for Dholuo results in specifications in which voiced, voiceless, and prenasalized stops are contrastively specified for [distributed] but the nasal is not. With these specifications, dental harmony in Dholuo can be motivated by a constraint that bars segments with distinct specifications for [distributed] from co-occurring within a form. The constraint in (7) will be violated by forms that contain both alveolar and dental oral or prenasalized stops but will not be violated by nasals occurring with either [+distributed] or [-distributed] segments. This is a basic feature co-occurrence restriction, akin to the OCP constraints in Suzuki (1998) but penalizing distinct feature specifications as opposed to identical ones. As in other consonant harmony systems, segments which interact in Dholuo dental harmony need not be adjacent to one another. The issue of locality in harmony systems has received significant attention in the literature (Gafos 1996;Rose & Walker 2004; Kimper 2011 among many others) and the relation between contrast and locality has been explored in previous work (e.g. Avery & Rice 1989;Shaw 1991;Hansson 2001;2010). The analysis of dental harmony advocated here relies on contrastively specified outputs. In such an approach, certain aspects of locality will be captured using the simple feature co-occurrence constraint in (7). Only segments with contrastive specification in the harmonic feature have the potential to violate the harmony-driving constraint.
Other segments are irrelevant, regardless of their location relative to segments interacting in the harmony process. Segments which interact in consonant harmony patterns tend to be highly similar and a requirement for interacting segments to share certain feature specifications is built into various proposals regarding the mechanisms of consonant harmony (e.g. Hansson 2001;2010;Rose & Walker 2004). Although no explicit reference to similarity is present in the analysis proposed here, some of the similarity effects observed in previous work arise from contrastively specified outputs consistent with the theory of the contrastive hierarchy. Segments are contrastively specified for a specific feature only if that feature serves to differentiate members of an inventory not already distinguished by a higher ordered feature. If major place features are ordered above a feature like [distributed], this feature can only be contrastive within the set of [+coronal] segments. Even within the set of segments which share a major place class, some members of the set may not be contrastively specified for [distributed], depending on the structure of the inventory and the hierarchy of features. Similarity between segments is thus expected in a contrastive hierarchy analysis, even without any reference to similarity or shared features in the formulation of the harmony-driving constraint. As the feature hierarchy may vary between languages, this approach predicts variation between languages in terms of which segments will interact in harmony processes.
The contrastive specifications proposed for Dholuo can be achieved as output representations with the constraint ranking shown in the Hasse diagram in figure 3.  The ranking above is determined in accordance with the algorithm for converting a contrastive hierarchy to a constraint ranking given in (2). The faithfulness constraint referring to [sonorant], the feature ordered highest in the contrastive hierarchy, is ranked first.
[nasal] is the next highest ordered feature and the faithfulness constraint Max[nasal] is ranked next. Above this faithfulness constraint, is ranked the contextual markedness constraint *[anasal, -sonorant]. This constraint is violated by any specification for the feature nasal for a segment that is specified as [-sonorant]. Since it is ranked above Max[nasal], it will eliminate outputs containing obstruents which are specified as [-nasal]. Max[distributed] is the next ranked faithfulness constraint but above this constraint is ranked the markedness constraint * [adistributed, +nasal]. This markedness constraint will eliminate nasals specified for any value of the feature [distributed] from surfacing. The constraint *[avoice, +sonorant] will eliminate sonorants from surfacing with a voicing specification. And, finally, below Max[voice], the constraint *[F] will eliminate any specifications for features that are not part of the proposed contrastive hierarchy.
With this ranking, any fully specified input will map to a contrastively specified output. The tableau below illustrates an evaluation of a fully specified nasal. In addition to ruling out representations that are inconsistent with the contrastive hierarchy, this ranking will also eliminate dental nasals from surfacing, thus restricting outputs to members of the inventory. The evaluation of an input dental nasal is illustrated in (9) . This is consistent with the contrastive representations proposed for the Dholuo inventory. Tableaux (8) and (9) demonstrate that inputs consisting of either a fully specified alveolar nasal or a fully specified dental nasal will map to outputs consisting of a nasal that is not specified for any value of the feature [distributed]. The harmony-driving constraint in (7) can be integrated with the Dholuo constraint ranking which ensures that output representations are contrastively specified. If the harmony-driving constraint is ranked above Max[distributed], input forms containing oral stops with distinct specifications for [distributed] will map to harmonic output forms.
(10) Dholuo: dental harmony among oral stops In tableau (10) What is crucial here is that a disharmonic input will map to a harmonic output. Unlike inputs with multiple oral stops, a disharmonic input with a nasal and an oral stop will surface faithfully. Regardless of whether or not the input nasal is specified as [−distributed], the optimal output will contain a nasal that is unspecified for that feature and thus satisfies the harmony-driving markedness constraint.  [-αdistributed] drives harmony and is violated by forms containing multiple oral stops that differ in the dental/alveolar distinction. Forms containing a dental oral stop and an alveolar nasal, however, do not violate the constraint because the nasal is unspecified for the harmonic feature. Representations consistent with this analysis can be achieved using the algorithm for converting a contrastive hierarchy to a constraint-ranking. The harmony-driving constraint *[αdistributed][-αdistributed] can be integrated with this ranking. The resulting constraint hierarchy can account for contrastive representations and dental harmony in a single level of evaluation.
The proposed constraint ranking for Dholuo is summarized in figure 4, below.

Päri
Päri is another Nilotic language with a dental/alveolar contrast among coronals and with consonant harmony barring dentals and alveolars from co-occurring (Andersen 1988;Hansson 2001;2010;Rose & Walker 2004). Unlike Dholuo, the Päri inventory is symmetrical with the dental/alveolar contrast present among voiced, voiceless, and nasal stops.

Dental t ̪ d̪ n̪
Päri also differs from Dholuo in that nasals participate in dental harmony.
(13) Päri harmony (Andersen 1988) n̪ ɔt ̪ 'sucking' *nɔt ̪ d̪ á:n̪ -ɛ 'person (ergative)' *d̪ á:n àtwá:t'adult male elephant' Because there is a minimal contrast between dentals and alveolars for each set of coronal stops, any ranking of features in a contrastive hierarchy will result in contrastive specifications for the harmonic feature within the set of nasals. A possible contrastive hierarchy for Päri using the same hierarchy of features used in the analysis of Dholuo is illustrated in figure 5, below. 8 Although the proposed order of features in the contrastive hierarchy is the same in the two languages, the OT constraint ranking must differ in order to derive the differences in the inventory. The constraint ranking resulting from applying the algorithm in (2) to the hierarchy of features proposed for Päri is illustrated in figure 6. Because the Päri inventory does contain a dental nasal, the constraint *[αdistributed, +nasal], which played a role in Dholuo, is not highly ranked in Päri. The only relevant contextual markedness constraint is *[avoice, +nasal] which prevents specification for the feature [voice] in [+nasal] segments.
If the harmony-driving constraint is integrated into the Päri constraint ranking, nasals, like all other coronal stops, will be subject to harmony. At this point, determining which of the candidates which satisfy dental harmony is selected as optimal is not crucial. What is important is that a disharmonic form containing a dental nasal and an alveolar dental will map to a harmonic output form. Nonetheless, data showing the interaction of dental harmony and consonant mutation processes suggest that a disharmonic form containing a combination of dentals and alveolars will surface as a form containing only dental stops. The following data show the possessive marker which involves the addition of a final vowel as well as mutation in which final liquids are realized as nasal-stop clusters. The final consonants created through mutation are subject to harmony. 9 (15) Päri (Andersen 1988) dèːl 'skin' dèːnd-á 'my skin' t ̪ùol 'snake' t ̪ùon̪ d̪ -à 'my snake' In the analysis of Päri, the constraint driving dental harmony can be integrated into the constraint ranking which determines contrastive specifications. Because the inventory of Päri contains both a dental and an alveolar nasal, any hierarchy of features will result in contrastive specification for the feature [distributed] in the nasal set. The nasals thus specified for the harmonic feature also participate in harmony. The proposed constraint ranking for Päri is summarized in figure 7.

Shilluk 10
Like Päri, Shilluk has an inventory of coronal stops which is symmetric with respect to the dental/alveolar contrast. Dental and alveolar stops contrast among the voiced, voiceless, and nasal stops.
(16) Shilluk coronal stops (Gilley 1992 Also as in Päri, the dental nasal participates in harmony in Shilluk. 11 (17) (Gilley 1992: 142) t ̪i̠n̪ 'small' ti ̠n 'today' àd̪ út ̪ 'stinger' dút 'loin cloth' With respect to the structure of the inventory and the basic patterning of dental harmony, Päri and Shilluk are alike. Dental harmony in Shilluk can therefore be accounted for using the same contrastive feature hierarchy and constraint ranking proposed in the analysis of Päri. Discussion of Shilluk is nonetheless included here because of differences between Shilluk and Päri found in the interaction of dental harmony and consonant mutation processes. As mentioned in the preceding section, consonant mutation feeds harmony in Päri. If a root-final liquid is realized as a nasal-stop cluster as a result of mutation, the cluster must harmonize with coronal stops elsewhere in the word (e.g. [t ̪ùol] 'snake', [t ̪ùon̪ d̪ -à] 'my snake'). In Shilluk, mutation also feeds harmony but, unlike in Päri, it is the alveolar of the derived consonant that imposes harmony on coronal stops elsewhere in a form. Example (18) shows a verb ending in a labial stop where, in addition to the suffixation of a vowel, the instrumental is formed through the addition of mid tone, vowel length, the 10 Thanks to an anonymous reviewer for raising the issue of Shilluk consonant mutation and its interaction with harmony. 11 Shilluk dental harmony is discussed in Gilley (1992) and Hansson (2001;2010). No mention of harmony is made in Remijsen et al. (2011) and disharmonic forms are included in the data in this source. The following analysis relies on data from Gilley (1992) and assumes the description of dental harmony given there.
vocalic feature expanded pharynx (indicated with underlining), and voicing of the final stop. The data in (b) show that when a root ends in an /l/ and there is no other coronal in the form, the mutation process causes the lateral to be realized as an alveolar stop. In (c), we see that an alveolar stop derived from an /l/ via mutation causes a preceding dental to be realized as an alveolar, satisfying the dental harmony constraint. This pattern is illustrated with the instrumental and antipassive forms of the verb 'to cook'. What is of particular interest in the Shilluk data is the fact that the lateral /l/ is not itself contrastively specified for the harmonic feature. As the transitive form of 'cook' in (18) illustrates, alveolar /l/ freely occurs with dental stops in Shilluk. In this respect, Shilluk is like other Nilotic languages where the liquids /l/ and /r/ are neutral with respect to dental harmony. There is no alveolar/dental contrast among liquids and I assume that the manner feature distinguishing liquids from coronal stops is ordered above the feature [distributed] in the contrastive feature hierarchies of all languages considered here. This results in representations in which the liquids lack specification for the feature [distributed] and, as a result, fail to participate in harmony. A proposed hierarchy of features for Shilluk is illustrated in figure 8, below, with the entire inventory of coronals. The order of features is identical to that proposed in the analysis of Päri but with the addition of the feature [approximant], used to differentiate between liquids and stops. The constraint ranking resulting in outputs consistent with this hierarchy is shown in Figure 9, below. Again, this is identical to the ranking shown for Päri but with the  With this constraint ranking, voiced and voiceless stops will be contrastively specified for the feature [distributed] but liquids will not be. A fully specified input containing an alveolar liquid and a dental stop, as in the form [t ̪al], 'to cook', will map to a contrastively specified output with the feature [distributed] specified for the stop but not the /l/. This is illustrated in the tableau below. . Note that, although the constraint motivating harmony is not shown here, such a constraint will be vacuously satisfied by the winning candidate in (c) and will not affect the outcome of the evaluation. Now consider the formation of the instrumental. A full analysis of the mechanisms that drive mutation is beyond the scope of this paper and I will not address changes in tone, vowel length, or vocalic features. For our purposes, it is sufficient to accept that the instrumental morpheme requires the final consonant of the root to be realized as a voiced stop. What will be addressed in this analysis is the feature specifications of the stop which surfaces in the instrumental forms. Leaving aside the issue of dental harmony for the moment, let us consider the evaluation of the instrumental form of [kyel], 'fry', in tableaux (20). This form has no coronals other than the one affected by mutation and will thus not be subject to dental harmony. The input shown is contrastively specified with no [distributed] feature present on the lateral. While all output candidates shown end in a voiced coronal stop, they vary in the feature specifications of that final stop. The constraint ranking is the same as that given above with the inclusion of an additional constraint, Spec [distributed]. As discussed in section 2, constraints requiring specification in contrastive features must be included in the constraint set in order to deal with underspecified inputs. In all cases, achieving contrastive representations in output forms requires such constraints to be ranked above the constraint *[F] and below contextual markedness constraints limiting the scope of contrastive feature specifications. . The constraint ranking is determined by the contrastive hierarchy proposed for the language. This ranking ensures that only contrastively specified members of the Shilluk inventory will be selected as optimal. In this example, the input correspondent of the voiceless coronal stop is a lateral unspecified for the feature [distributed]. The constraint ranking, however, requires that this output be specified for [distributed], as all coronal voiceless stops are in the language. The use of Spec[F] constraints ensures that underspecified inputs map to contrastively specified outputs and requires a /d/ derived from an input /l/ to be specified for [distributed]. As noted in section 3, the principle of structure preservation as developed in the theory of lexical phonology (e.g. Kiparsky 1982;1985) has no direct analogue in OT grammars. The fact that there are no language specific restrictions on inputs, as required by the principle of Richness of the Base, undermines the notion of a basic inventory of structures for a given language. It is nonetheless worth noting that in the analysis proposed here, the requirement that output coronal stops be specified for distributed is both consistent with the principle of structure preservation and illustrates additional implications that structure preservation holds in combination with Richness of the Base. In a discussion of English voicing, Kiparsky (1985: 92) states that structure preservation 'not only blocks voiceless sonorants from appearing in underlying representations and lexical derivations but also blocks the redundant specification [+voice] from being assigned to sonorants in lexical derivations.' The Shilluk example shows that OT implementation of the contrastive hierarchy results in constraint rankings which not only prevent specification of redundant features, such as [−distributed] in [l], but also requires specification of contrastive features, such as [−distributed] in [d], even in cases where such features are absent from inputs.
Both dental and alveolar stops are part of the inventory of Shilluk and the ranking shown above requires all coronal stops to be specified for [distributed], even in the absence of input specification. This ranking is not, however, sufficient to determine which value of [distributed] will be specified on a coronal stop when the input lacks specification in this feature. In Shilluk, the coronal stops derived from liquids via consonant mutation are realized as [-distributed]  If the constraint motivating harmony is integrated into the ranking in Figure 9, derived alveolar stops in instrumental forms will trigger harmony, as illustrated in tableau (22) The analysis outlined here shows that dental harmony can be triggered by final coronal stops derived from liquids, even if the liquids themselves lack contrastive specification in the harmonic feature. The constraint ranking that ensures outputs are restricted to contrastively specified members of the Shilluk inventory requires output oral stops to be specified for [distributed] regardless of input specification. High-ranking Dep[+distributed] prevents [+distributed] dentals from surfacing in the absence of input [+distributed] specifications.
This proposal has implications for the analysis of dental harmony in Shilluk. Instrumental forms such as [ta̠ ːd-ā] 'cook', from [t ̪al], are discussed in Hansson (2001;2010) who interprets these data as evidence that dental harmony in Shilluk is right-to-left. The analysis proposed here does not rely on any mechanisms associated with directionality of harmony systems and suggests, instead, that Shilluk dental harmony is a dominant-recessive system with [-distributed] being the dominant feature value. Instrumental [ta̠ ːd-ā] is consistent with both analyses. The two proposals make distinct predictions if harmony occurs with prefixing mutation where an initial liquid is realized as a stop and a dental occurs later in the form. Under these circumstances, the right-to-left directionality account predicts that the [+distributed] value of the dental on the right will persist in cases where the form undergoes harmony whereas the analysis proposed here predicts that the [-distributed] value of the derived alveolar on the left will trigger a change to [-distributed] in a following stop. Alternatively, a dental stop created through word-final mutation would also be expected to pattern differently according to the two approaches, with the directional analysis predicting harmony to [+distributed] for all stops and the analysis given here predicting the dental created through mutation be realized as a [-distributed] alveolar if an alveolar stop occurs elsewhere in the form. To my knowledge, no mutation of initial segments is found in Shilluk. Although some plural forms include final dental stops created through mutation (e.g. [yoː] 'road', [ye̠ ːt ̪] 'roads'), none of the examples of this type in Gilley (1992: 86) have preceding alveolar stops. This leaves us without empirical evidence discriminating between the two interpretations of the data. The analysis proposed here requires all disharmonic inputs to surface as forms containing only [-distributed] segments. Forms with multiple dental stops surface only as outputs of input forms containing multiple dentals.
The complete constraint ranking proposed for the Shilluk inventory and dental harmony is summarized in the Hasse diagram in figure 10.

Dental harmony in Anywa: non-structure-preserving harmony
The analysis of dental harmony in Dholuo, Päri, and Shilluk illustrates the connection between inventory shape, contrastive specifications, and phonological activity. In Dholuo, the inventory is asymmetric, lacking a dental/alveolar contrast among nasals. In Päri and Shilluk, the inventory is symmetrical. Nasals contrast along the dental/ alveolar dimension, as do other coronal stops. If all of these languages have a feature hierarchy in which the feature [nasal] is ordered above [distributed], the nasal will be unspecified for [distributed] in Dholuo but will be specified for this feature in Päri and Shilluk. When the contrastive hierarchy is converted to a ranking of OT constraints in Dholuo, output forms with co-occurring dental oral stops and alveolar nasals fail to violate the constraint barring segments with distinct specifications of [distributed] and the nasal fails to participate in harmony. In Päri and Shilluk, on the other hand, the nasal is specified for [distributed] and the constraint ranking achieving this specification also requires the nasals to participate in harmony. In these cases, dental harmony, contrastive specifications, and the phonemic inventory can be achieved in a single OT evaluation.
Differences between Dholuo, Päri, and Shilluk result from differences in the inventory. The hierarchy of features is alike in these languages but Dholuo differs from Päri and Shilluk in that Dholuo has only a single alveolar nasal in the inventory and Päri and Shilluk have both a dental and alveolar nasal. The theory of the contrastive hierarchy, however, allows the hierarchy of features to vary, even between languages with similar inventories. This predicts the possibility of a language with an asymmetric inventory like Dholuo, but with the nasal contrastively specified for the feature [distributed]. In such a case, the nasal is expected to be subject to harmony, even though there is no dental nasal in the inventory. The following analysis proposes that Anywa is such a language.

Dental t ̪ d̪
Unlike in Dholuo, however, the nasal participates in harmony in Anywa and dental nasals surface allophonically in harmonic forms. Outside of forms showing evidence of dental harmony, such as those below, dental nasals do not appear in Anywa. 12 (24) Anywa: nasals participate in harmony (Reh 1996) n̪ ùd̪ ò 'to lick' ōd̪ óòn̪ 'mud' t ̪ùd̪ 'ropes' núudó 'to press something down' dīn 'to thrash something' tūud 'pus' The possibility of a pattern like that of Anywa is predicted by the theory of the contrastive hierarchy. If contrastive specifications depend, not only on the phonemic inventory, but also on the hierarchy of features, the scope of the harmonic feature may vary between languages resulting in different representations. In Anywa, the feature [distributed] is ordered high, resulting in contrastive specification for the nasal in the harmonic feature. Note that the dental nasal is not included in the phonemic inventory shown above. The process leading dental nasals to surface in harmonic forms is addressed later in this section, in the analysis of dental harmony. What is crucial here is that, with the feature [distributed] ordered high, the /n/ is contrastively specified for the harmonic feature even though there is no minimal contrast between dental and alveolar nasals in the phonemic inventory. This is illustrated in the contrastive hierarchy in figure 11. Using the algorithm in (2), the Anywa contrastive hierarchy above can be converted to the following constraint ranking: Figure 12: Anywa constraint ranking for contrastive specifications.

Anywa dental harmony: a ranking paradox
As in the analysis of Dholuo, Päri, and Shilluk, if the harmony-motivating constraint is integrated into the Anywa constraint ranking in Figure 12, the evaluation will rule out disharmonic forms as well as segments that contain non-contrastive feature specifications. However, the attested forms with allophonic dental nasals will not surface. The same ranking which eliminates dental nasals from the inventory results in disharmonic inputs containing nasals surfacing as harmonic forms containing dental obstruents.  (25), the input consists of a form that obeys the dental harmony process and contains a dental nasal. The faithful and attested candidate in (a) is eliminated due to a violation of the markedness constraint * [anasal, +dist]. This constraint rules out any specification for the feature [nasal] in segments that are specified as [+distributed] and is responsible for preventing dental nasals from surfacing in the inventory in general. The Anywa grammar must allow input dental nasals to surface as some other segment found in Anywa in order to account for the inventory. As illustrated in the tableau above, such an input-output mapping will also be available to satisfy the need for forms to obey dental harmony. The optimal candidate in (c) contains two dental oral stops. This candidate obeys dental harmony and also obeys the markedness constraint against dentals with specification for [nasal]. This candidate violates the constraint Max[nasal] but this faithfulness constraint must be ranked below the constraint *[anasal, +dist] in order to account for the Anywa inventory and the proposed contrastive specifications. The ranking paradox illustrated above is one example of a more general problem with modeling non-structure-preserving processes in OT. As discussed in the analysis of consonant mutation in Shilluk, the principle of structure-preservation (e.g. Kiparsky 1982;1985) loses coherence in a framework that rejects language-specific restrictions on input forms. The principle is largely rejected in OT works, even in those arguing for a stratal version of OT (e.g. Roca 2005;Bermúdez-Otero 2013). Working within the framework of the contrastive hierarchy, Hall (2007) addresses this issue in an analysis of Czech voicing assimilation and shows that contrastive specifications can be integrated with analyses of at least some non-structure-preserving neutralization processes if the markedness constraints which penalize non-contrastive feature specifications are reformulated as constraints which penalize the alignment of feature values. In the present case, such an approach would involve redefining markedness constraints such as *[anasal, +distributed] such that they do not penalize the co-occurrence of [nasal] specifications and [+distributed] specifications per se but only penalize the co-occurrence of these features if they are identically aligned. If we adopt a theory of assimilation which involves multiply-linked features, a form like [n̪ ùd̪ ò] would avoid violation of such a constraint if the form contains only a single [+distributed] feature linked to both consonants. In such an analysis, the features [+nasal] and [+distributed] co-occur on the segment [n̪ ] but they are not identically aligned. The [+nasal] feature occurs only on [n̪ ] whereas the [+distributed] feature is multiply-linked and is associated to both the [n̪ ] and the [d̪ ]. The harmonic form thus satisfies the constraint against identical alignment of [+nasal] and [+distributed] and the harmonic form with the allophonic dental nasal would be evaluated as optimal. A dental nasal occurring outside of a harmonic context would have [+nasal] and [+distributed] specifications which are identically aligned and would correctly be ruled out by the relevant markedness constraint.
The ranking paradoxes illustrated in the analysis of Anywa, above, and in Hall's (2007) analysis of Czech voicing assimilation directly follow from the proposed hierarchies of features and the algorithm for converting a contrastive hierarchy to a constraint ranking. The difficulty that non-structure-preserving neutralization poses for Classic OT, however, is more general. Bermúdez-Otero (2007) addresses the issue of non-structure-preserving neutralization in the context of voicing neutralization in Catalan. Without assuming any particular theory of contrastive specification, Bermúdez-Otero demonstrates that processes which affect both contrastive and redundant feature specifications can lead to a ranking paradox. In Catalan, processes of voicing neutralization can result in surface [v] as an allophone of /f/, although [v] is absent from the phonemic inventory. As is the case for the dental nasal in Anywa, in Catalan, the allophone [v] cannot be ruled out from the input due to the principle of Richness of the Base. Rankings which allow input [v] to surface as some actual member of the Catalan inventory in the general case will also be available in contexts of voicing neutralization. Evidence from loanword adaptation suggests that a mapping from input [v] to output [b] is available and that output [b] is also expected to be preferred in voicing assimilation contexts. Bermúdez-Otero (2007) points out that the ranking paradox that arises in this case is similar to problems that arise in the analysis of opacity. He argues for a solution within the framework of stratal OT in which markedness constraints against the allophone [v] are ranked high at the stem level but demoted at higher levels of evaluation.
The proposal that follows advocates an analogous solution to the analysis of Anywa dental harmony and provides independent evidence that multiple levels of evaluation are needed. The analysis put forward here does not, however, require all non-structurepreserving processes to be absent from stem-level evaluations. A number of arguments in favour of stem-level, non-structure-preserving processes have been put forward in the stratal OT literature (e.g. Ito & Mester 2001;Roca 2005;Bermúdez-Otero 2013). Only those processes which are both allophonic and neutralizing are precluded at the stem-level by rankings required by the contrastive hierarchy. In Anywa, dental harmony leads to allophonic variation in the nasals but among the other coronal stops, the dental/alveolar contrast neutralized by harmony is phonemic. In these cases, the contrastive hierarchy needed to ensure contrastive specification of the segments participating in harmony, specifically the nasal in Anywa, results in a ranking paradox if the neutralizing process takes place at the earliest level of evaluation.

Dental harmony at the word-level
The ranking paradox illustrated in the analysis of Anywa above arises if dental harmony, the phonemic inventory, and contrastive specifications are determined in a single level of evaluation. There is evidence, however, that dental harmony occurs at a later level of evaluation in Anywa than does dental harmony in Dholuo.
In Anywa, a variety of word-formation processes involve consonant mutation. In the examples below, a detransitivizing morpheme changes stem-final coronal sonorants to oral stops.
(26) Anywa: words formed by consonant mutation undergo harmony (Reh 1996: 59) Detransitived a. d̪ ɪ̄r 'to jostle sth.' d̪ ìd̪ ò t ̪ōor 'to finish sth.' t ̪òod̪ ò b. dɔl 'to fold sth.' dùdò tīir 'to adjust sth.' tíidó The transitive forms in (26) all end in the coronal sonorants /l/ or /r/. There is no dental/alveolar contrast among sonorants in Anywa and the sonorants do not participate in dental harmony. In the detransitivized forms, these sonorants become oral stops through the process of consonant mutation. The underived forms in (a) contain dental stops and mutation leads the stem-final coronal sonorants to become dental stops. The forms in (b) contain alveolar stops and mutation leads the sonorants to be realized as alveolar stops. In other words, Anywa consonant mutation feeds dental harmony.
This contrasts with the patterning of consonant mutation in Dholuo. Although Dholuo does not have exactly the same type of consonant mutation as Anywa, a relevant process is found in pluralized forms. One type of pluralization in Dholuo results in final coronal sonorants being realized as prenasalized stops.

(27)
Dholuo mutation creates exceptions to harmony (Tucker 1994: 557-603) Singular Plural t ̪ʊɔn 'brave man' t ̪uo n di t ̪uol 'snake' t ̪uo n de Recall that the Dholuo inventory has a dental/alveolar contrast among prenasalized stops and prenasalized stops participate in dental harmony. The disharmonic plural forms in (27) would be ungrammatical in monomorphemic forms. I propose that dental harmony in Anywa occurs at the word level along with, or subsequent to, word-formation processes which trigger mutation. In Dholuo, on the other hand, dental harmony occurs at the stem level and word-level consonant mutation results in exceptions to harmony.
In Anywa, harmony is not determined in the same evaluation as contrastive specifications. At the stem level, the inventory and contrastive representations are determined. The input to the word level consists of contrastively specified outputs of stem-level evaluations. 13 The stem-level ranking for Anywa is the ranking proposed in the previous section as determined by the algorithm for converting a contrastive hierarchy to a constraint ranking. Unlike proposed rankings for Dholuo, Päri, and Shilluk, however, the constraint that drives harmony, *[αdistributed] [-αdistributed], is ranked low, as illustrated in figure 13. This ranking will map any input segment to a contrastively specified member of the Anywa inventory. The fact that the harmony-driving constraint is ranked below faithfulness constraints referring to contrastive features means that this ranking does not enforce dental harmony and disharmonic forms are possible outputs of the stem level. The output of the stem-level evaluation will serve as the input to the word-level evaluation. At the word level, dental harmony is enforced by high-ranking *[αdistributed] [-αdistributed]. Both *[αdistributed] [-αdistributed] and Max[nasal] must outrank the constraint penalizing dental nasals in order to allow input-output mappings in which dental nasals surface in forms with dental harmony. The proposed word-level ranking is shown below. The contrastively specified, disharmonic output of the stem-level evaluation in (28) -adistributed]. The optimal candidate in (b) satisfies dental harmony and contains an allophonic dental nasal. This candidate violates the constraint against dentals specified for the feature nasal, * [anasal, +distributed]. At the stem level, this constraint played an important role in preventing dental nasals from surfacing as part of the inventory. At the word-level, this constraint is ranked below the constraint that enforces dental harmony and below the faithfulness constraint Max [nasal]. The candidate in (c) also satisfies dental harmony but the input alveolar nasal has mapped to a dental oral stop. Such a candidate was problematic in (25) where we attempted to derive dental harmony, contrastive specifications, and the surface inventory of Anywa in a single level of evaluation. Here the candidate is eliminated due to violation of the faithfulness constraint Max [nasal]. At the word level, faithfulness to nasality is ranked above faithfulness to [distributed] and the markedness constraint against dentals specified for the feature [nasal], allowing the dental nasal to surface.
There is a relevant candidate, not shown in (29), that requires consideration. A candidate which satisfies the dental-harmony driving constraint through underspecification would be optimal given the constraints shown, analogous to the winning candidate in the proposed analysis of Dholuo. The tableau in (29)  . If only these constraints are considered, the underspecified candidate will win regardless of constraint ranking. In order to address this issue, and to successfully model Anywa dental harmony, we need a markedness constraint which penalizes the absence of a feature. Constraints of this type were introduced in the discussion of converting a contrastive hierarchy to a constraint ranking in section (2). The markedness and faithfulness constraints included in the algorithm for converting a contrastive hierarchy to a constraint ranking successfully map fully-specified inputs to contrastively specified outputs. Constraints of the form Spec[F] are needed to ensure that underspecified inputs will also map to contrastively specified outputs. Use of Spec[F] constraints was also illustrated in the analysis of Shilluk consonant mutation. In the ranking determined by the algorithm for converting a contrastive hierarchy to a constraint ranking, Spec[F] constraints are ranked below markedness constraints, such as *[αnasal, +distributed], which limit the scope of contrastive features. This ranking, however, is only required to determine the inventory and ensure contrastive representations in the initial stage of evaluation, at the stem level. At later levels, constraint rerankings are necessary to model non-structure-preserving processes. The constraint Spec [distributed], independently needed to ensure contrastive representations at the stem level, can be added to the hierarchy shown in tableau (30) and prevent the underspecified candidate from winning. The use of Spec[F] provides the crucial distinction between mappings which change the value of a feature specification, which violate Max [F], and mappings which result in the absence of any specification at all for the relevant feature. In cases where the relevant feature is specified in the input, such mappings violate both Max[F] and Spec [F].
As illustrated in the following tableau, Spec[distributed] must be ranked above the markedness constraint * [αnasal, +distributed] at the word-level in Anywa in order to ensure that the need for dental harmony is not satisfied via underspecification of the harmonic feature.  (b), containing the allophonic dental nasal, to surface as optimal. The analysis of Anywa dental harmony requires the markedness constraint against dental nasals, *[αnasal, +distributed] to be ranked lower at the word level than at the stem level, relative to the constraint which drives dental harmony. The constraint requiring output segments to be specified for [distributed], Spec[distributed], must also outrank *[αnasal, +distributed] at the word level. Additional evidence that the constraint against dental nasals is demoted at the word level comes from consonant mutation processes in which geminate dental nasals surface outside of harmonic contexts. The data in (32) illustrate the addition of a process morpheme which gives verbs an inchoative meaning. A stem-final dental stop becomes nasalized when the process morpheme is added, leading to a dental nasal on the surface, even though there is no other dental in the form. 15 (32) Anywa (Reh 1996) pɔɔd̪ 'be smooth' pòon̪ n̪ 'become smooth' In Anywa, the detransitivized forms in (26), e.g. detransitived [d̪ ìd̪ ò] from [d̪ ɪ̄r] 'to jostle sth.', may be formed at the stem level or at the word level. If the detransitizing morpheme is added at the stem level, harmony will not determine the [distributed] value of a coronal stop derived from a liquid, as the harmony-driving constraint is low ranked in the stem-level grammar. Harmony will be enforced when the form undergoes word-level evaluation where the harmony-driving constraint, *[αdist][-αdist], is highly ranked and rules out disharmonic surface forms. The process derivation illustrated in (32), however, must take place at the word level. Stem-level constraint ranking will rule out dental nasals from surfacing, even if a [+distributed] feature is present in the input, as illustrated in the analysis of dental harmony. The existence of word-level processes that can lead to dental nasals appearing in surface forms, outside the context of dental harmony, leads support to the proposal that the constraint which penalizes dental nasals is ranked lower at the word level than at the stem level. The proposal that the process derivation is wordlevel is contrary to Trommer's (2011) analysis in which the process/inchoative derivation is attributed to the stem-level. Trommer distinguishes word-level from stem-level processes partly on the basis of the degree of morphophonological interaction with stems. For example, the coda-condition can be violated by word-level affixation but not by stemlevel affixation. His analysis of Anywa does, however, include underspecified word-level affixes which cause gemination and do not result in coda-condition violations (e.g. the 2pl suffix). It is not clear that the process derivation is incompatible with the stem-level ranking. I therefore take the contrastive hierarchy analysis here as a provisional argument in favour of a ascribing the process derivation to the word level, with further consideration of the issue within the context of Anywa morphophonology left to future research. 16

Disharmonic prefixes
The previous section has shown that a successful analysis of dental harmony in Anywa requires reference to a multi-level evaluation. In order to avoid the ranking paradox that results from an attempt to model non-structure-preserving harmony in a single evaluation, the analysis presented here proposes that dental harmony in Anywa is enforced at the word level, after stem-level evaluation has filtered the rich base to include only contrastively specified members of the Anywa inventory. Data from the interaction of harmony and consonant mutation provides further support for the word-level analysis of Anywa dental harmony. It is not the case, however, that Anywa dental harmony holds throughout all morphologically complex forms. While coronal stops and nasals created through mutation processes are subject to harmony, harmony does not extend to regular segmental prefixes, as shown in the following agentive nouns formed with the prefix /dɪ̀-/.

Conclusion
This paper has provided an analysis of dental harmony in the Nilotic languages, Dholuo, Päri, Shilluk, and Anywa. All have a contrast between dental and alveolar coronals and all have a system of dental harmony which bars the co-occurrence of dentals and alveolars. Details of the patterning of dental harmony and the structure of the coronal inventory vary between languages. According to the analysis proposed here, differences between the languages follow from three distinct aspects of the phonological grammar; differences in the shape of the inventory, differences in the hierarchy of features according to the theory of the contrastive hierarchy (e.g. Dresher 2009), and differences in the level at which harmony applies within a stratal model of OT (e.g. Kiparsky 2000;Bermúdez-Otero 2003).
Differences between Päri and Shilluk, on one hand, and Dholuo and Anywa, on the other, follow from the structure of the inventory. In Päri and Shilluk, the inventory contains two coronal nasals which minimally contrast in [distributed]. The feature [distributed] is contrastive among nasals, regardless of the ordering of features in a contrastive hierarchy, and the nasals participate in dental harmony. The inventory of Päri and Shilluk thus differs from that of Anywa and Dholuo, both of which have only a single coronal nasal. Anywa and Dholuo, have inventories which are alike in relevant respects. In both languages, the dental/alveolar contrast which is present among coronal stops is lacking in the nasal series. The grammars of Anywa and Dholuo differ in two ways. First, they have different feature hierarchies. In Dholuo, the feature [nasal] is ordered above the feature [distributed] and in Anywa the order of these features is reversed. As a result, the nasals are contrastively specified for [distributed] in Anywa but not in Dholuo.
The proposed contrastive specifications are not themselves sufficient to model crosslinguistic differences in dental harmony in an explicit theory of phonological operations. In addition to differences in the feature hierarchy, Dholuo and Anywa differ in the level at which harmony applies in a stratal model of OT. In Dholuo, harmony applies at the stem level whereas in Anywa harmony applies at the word level. Although these languages differ with respect to the level at which harmony applies, differences in the feature hierarchy remain crucial to the analysis. If Anywa had a feature hierarchy like that of Dholuo, the input to the word level would contain nasals unspecified for [distributed], the harmonydriving constraint would be vacuously satisfied, and allophonic dental nasals would fail to surface. This analysis makes typological predictions about the range of harmony patterns expected to be found crosslinguistically. In Dholuo, harmony occurs at the stem level, as shown by the existence of disharmonic forms arising through mutation processes at the word level (35).
Dholuo (Tucker 1994) t ̪uol 'snake' t ̪uo n de 'snakes' In Shilluk, consonant mutation feeds harmony, as illustrated in (36) (repeated from (18). The analysis proposed in Section 4.3 accounts for this pattern of mutation and dental examples show the possessive marker which involves the addition of a final vowel as well as mutation in which final liquids are realized as nasal-stop clusters. The final consonants created through mutation are subject to harmony. This is consistent with harmony being active at the stem level with the possessive form also created at the stem level. These data are also consistent with harmony applying later, at the word level, subsequent to stemlevel morphological processes.
(40) a. Päri (Andersen 1988) dèːl 'skin' dèːnd-á 'my skin' t ̪ùol 'snake' t ̪ùon̪ d̪ -à 'my snake' The proposed analyses of dental harmony allow for structure-preserving harmony to occur at the stem level, as in Dholuo, or at the word level, as in Mayak. Non-structurepreserving harmony, as in Anywa, however, is predicted to be impossible at the stem level where a ranking paradox arises if harmony, the inventory, and contrastive specifications are modeled with a single constraint ranking. The ranking needed for the nasal to participate in harmony, and for allophonic dental nasals to surface, must apply after contrastive specifications have been achieved. To my knowledge, this prediction is correct. There are no attested cases of non-structure-preserving dental harmony applying at the stem level within Nilotic.
This paper has demonstrated that contrastive specifications consistent with the theory of the contrastive hierarchy can be achieved as outputs of OT grammars with no restrictions on the set of possible inputs. However, in order to analyze non-structure-preserving harmony, as in Anywa, a multi-level evaluation, as in Stratal OT, is required. Challenges that non-structure-preserving processes pose for Classic OT have been recognized in previous work. The arguments for a serial evaluation presented here closely resemble those of Bermúdez-Otero (2007). His analysis of Catalan voicing assimilation also shows the need for a multi-level evaluation and draws a connection between challenges that the analysis of opacity poses for Classic OT and challenges posed by non-structure-preserving processes. This paper makes similar arguments from the analysis of dental harmony in Nilotic but, unlike Bermúdez-Otero (2007), the distinction between contrastive and redundant features relied on here is determined on the basis of an explicit theory of contrast that allows for differences in contrastive specifications between languages with similar inventories. An analysis of non-structure-preserving voicing assimilation in Czech is provided in Hall (2007). This analysis is undertaken within the framework of the contrastive hierarchy and uses a single-level evaluation in OT. Hall avoids the ranking paradox that arises in the analysis of non-structure-preserving assimilation by reformulating feature co-occurrence constraints which limit the scope of non-contrastive features as constraints which limit identical alignment between particular features. Such constraints are not violated by the co-occurrence of relevant features if the features do not have the same span, for example, if one feature is linked to multiple segments as a result of assimilation. This approach is able to adequately model non-structure-preserving harmony but fails to make any predictions about the interaction of phonological processes, such as harmony, with word-formation processes. In contrast, the stratal OT analysis here relies on the theory of the contrastive hierarchy and predicts that non-structure-preserving harmony, as found in Anywa, cannot be restricted to the stem level, as is the case for structure-preserving harmony in Dholuo.
The proposed analysis of dental harmony in Anywa, Dholuo, Päri, and Shilluk demonstrates that, while a multi-stage version of OT is necessary in order to achieve contrastive specifications as outputs, this does not require reference to any additional level beyond