Abstract

Dinka has two patterns of vowel-lengthening morphology: lengthening by one mora and imposition of a bimoraic template. Flack (2007) claims that these data provide conclusive evidence for morphemespecific indexed markedness constraints. In this article, I reanalyze the Dinka data in Colored Containment Theory (van Oostendorp 2006), effectively showing that the Dinka data are consistent with a more restrictive approach to the morphology-phonology interface: a markedness constraint may not refer to specific morphemes; rather, it may refer only to morphological colors (i.e., whether two phonological objects are part of the same morpheme or not).

1 Introduction

Western Nilotic languages use virtually all crosslinguistically attested phonological techniques of vowel length manipulation to express morphological categories. Dinka (Andersen 1995) marks 3SG forms of verbs by lengthening short vowels to long, and long vowels to extralong (additive lengthening, (1a)), whereas it derives benefactive forms by imposing a bimoraic template—that is, lengthening short vowels, but not extending long vowels to extralong (templatic lengthening, (1b)). Anywa (Reh 1993) expresses the antipassive by shortening of long vowels (2a) and forms the frequentative by length polarity: underlyingly long vowels are shortened, and underlyingly short vowels are lengthened (2b). (All these categories show additional nonconcatenative exponence (e.g., for tone and phonation type); see section 1.2 for discussion.) Finally, Dinka and Shilluk (Remijsen et al. 2009) have morphological categories that trigger bimoraic additive lengthening: short vowels become extralong (see section 2.2).1

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There is broad consensus in the literature that additive and templatic patterns of vowel length manipulation as in Dinka should be captured by some type of affixation,2 in line with a restrictive research program that limits morphological exponence to the concatenation of phonological representations and general processes of phonological alternation. I will call this research program—which implicitly underlies classical Autosegmental Morphology (Goldsmith 1976, McCarthy 1979, Marantz 1982) and is explicitly formulated under different names in Lieber 1992, Stonham 1994, Wolf 2007, Bermúdez-Otero 2012, and Bye and Svenonius 2012, and which I will adopt here—the Concatenativist Hypothesis.

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  • The Concatenativist Hypothesis

  • Morphology = Concatenation + Phonological alternations

Under the moraic analysis of vowel length (see Hayes 1989; also see Odden 2011 for further references), vowel shortening and vowel length polarity in Anywa pose obvious problems for the Concatenativist Hypothesis since they constitute morphological operations that inherently involve removal, not addition, of phonological (moraic) base material (see Bye and Svenonius 2012 for related problems arising from templatic morphology). In fact, one of the earliest formal discussions of Western Nilotic length polarity (Anderson and Browne 1973) argues for an account in terms of special morphophonological rules that are formally roughly equivalent to procedural rules of word formation (Matthews 1974, Anderson 1992). Similarly, the most influential current analyses of subtractive and polarizing morphology at the segmental level are based on the massive use of morpheme-specific (‘‘morphologically indexed’’) constraints (see Horwood 2001, Kurisu 2001 on subtractive morphology in Muskogean and Uto-Aztecan, and Alderete 1999, 2001, Kurisu 2001 on voicing polarity in Dholuo). However, morphological indexing of constraints ( Pater 2000, 2007) or its rough equivalent, the assumption of different cophonologies for specific morphological constructions (Inkelas and Zoll 2005), substantially undermines the empirical content of the Concatenativist Hypothesis since it allows phonology to perform most of the operations usually assumed in rule-based approaches to morphology in a morphologically distinctive way (see Bermúdez-Otero 2012 for discussion).

The Dinka data in (1) threaten the Concatenativist Hypothesis in a second, more intricate way, which also seems to lead inevitably down the road to morpheme-specific constraints (or constraint rankings). Thus, Flack (2007) claims that it is in fact the cooccurrence and interaction of additive lengthening and templatic lengthening in Dinka that provides definite evidence for morpheme-specific constraints, and especially indexed markedness constraints. She argues that both patterns derive from affixation of a floating mora, but the benefactive mora induces violations of a markedness constraint blocking trimoraic vowels (5) while the 3SG mora does not (4).3

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What forces Flack to index the constraint *V is not the bimoraic benefactive template itself, which would naturally follow from *V ≫ MAX-μ, but the fact that it must not apply to moraic affixation in 3SG forms that fail to obey it. Importantly, morpheme-specific markedness constraints are a substantial extension to the standard inventory of indexed constraints assumed in Optimality Theory (OT), which is usually limited to faithfulness constraints that refer only to general morphological morpheme types such as affix and root, not to the identity of individual morphemes (see e.g., Urbanczyk 2006).

In this article, I show that the differences in the realization of moraic affixes in Dinka reduce to a standard parameter of morphological affixation: the fact that affixes instantiate either prefixes, suffixes, or circumfixes (see Trommer 2011, 2014 for a generalization of this result to Anywa). In particular, I will import Flack’s analysis of additive lengthening in Dinka as simple moraic affixation (see (4)), but will argue that templatic lengthening follows from moraic circumfixation (i.e., attaching an affix that is composed of a moraic prefix and a moraic suffix), which triggers deassociation (and hence phonetic noninterpretation) of the base moras because of an undominated constraint, CONTIGUITY, requiring morphological contiguity (6).

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The only reference to morphological structure this analysis requires is the affiliation of phonological material to different morphemes, a standard assumption in OT made formally explicit by the morphological colors of Colored Containment Theory (van Oostendorp 2005): distinct morphemes have different morphological ‘‘colors,’’ and all phonological objects affiliated with a given morpheme wear its color—indicated for the moraic circumfix in (6) by background shading. Coloring makes it possible to determine whether two phonological entities belong to the same morpheme or not (or to no morpheme at all), but doesn’t give phonological constraints the power to identify specific morphemes such as benefactive and 3SG affixes. Thus, the theoretical hypothesis I put forward here as a safeguard for the restrictiveness of the Concatenativist Hypothesis is that the phonological computation has much more limited access to morphological information than Flack claims.

In what follows, I will show that morphological colors not only are sufficient to capture the distinctive lengthening of benefactive and 3SG morphology, but also account for the second phenomenon used by Flack as evidence for constraint indexation: the blocking of cumulative lengthening. Thus, 3SG forms of benefactives do not show templatic lengthening to bimoraic/ long and additive lengthening to trimoraic/extralong vowels; rather, they show only the effect of the bimoraic benefactive template (e.g., teηtê̤⧗/*tê̤⧗⧗η ‘dust.BEN.3SG’, mì⧗tmî̤⧗t/*mî̤⧗⧗t ‘pull.BEN.3SG’; Andersen 1995:19, 28). In Flack’s analysis, this is a consequence of undominated , but here I will show that it follows from constraints that restrict vowels and syllables to moras of maximally two colors (*V3□ and *σ3□). Just like moraic CONTIGUITY, *V3□ and *σ3□ require the information encoded in morphological coloring, but no access to the affiliation of moras to specific morphemes. In effect, the Dinka lengthening data are not evidence for extending the coverage of indexed constraints from faithfulness to markedness constraints—rather, they are evidence for eliminating morphological constraint indexation altogether.

The article is organized as follows. The remainder of this section introduces the formal framework I will assume (section 1.1) and crucial properties of Dinka morphology and phonology (section 1.2). The next two sections provide detailed analyses of the vowel-length-changing patterns in Dinka: additive lengthening (section 2) and templatic lengthening (section 3). Section 4 provides a general discussion of morphological colors.

1.1 The Framework: Autosegmental Colored Containment Theory

My analysis is based on what is essentially the original implementation of OT proposed by Prince and Smolensky (1993), which assumes hierarchical autosegmental representations and the Containment restriction on candidate generation. In a departure from Prince and Smolensky, I adopt the representation of epenthesis by morphological colors from Colored Containment Theory (van Oostendorp 2006, Revithiadou 2007) and generalize the Containment assumption to association lines (Radical Containment). Crucially, this framework employs in all essential respects (autosegmental representations, phonological constraints referring to morphological affiliation and underlying representations) the same or a proper subset of the formal mechanisms used by Flack (2007).

1.1.1 Morphological Colors and the Morphology-Phonology Interface

Following van Oostendorp (2006) and Revithiadou (2007), I assume that morphological structure is minimally reflected in phonological representations by coloring. At the interface of morphology and phonology, every morpheme M of an underlying representation UR is assigned a unique color C (i.e., a color that is distinct from all other colors C′ in UR), and every phonological component (i.e., every node and every association line) of M is also assigned C. (7) illustrates coloring with two hypothetical morphemes a and l. Color is notated here and in the following by background boxes with distinctive shading (i.e., shading and no shading). Starting with input (7a) and adding epenthetic [i], syllables, a mora, and epenthetic association lines results in candidate (7b). (7c) shows the same candidate, highlighting the epenthetic character of association lines by making them dashed lines.

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Colors have two important consequences for phonological computation. First, colors make it possible to distinguish underlying from epenthetic material: epenthetic material is colorless (in (7) without background box), and by the Containment assumption GEN does not allow changing or removing the color of underlying material. Second, colors make it possible to determine whether two phonological elements belong to the same morpheme or not. Crucially, I assume that the access of phonology to morphological information is restricted to these types of morphological information by the condition in (8).

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  • Color Map Hypothesis

  • Morphological color is the only morphological information visible to phonological constraints.

By (8), the phonological computation is like a traveler consulting a map that marks different countries by different colors, but does not identify them by name. By the map, a traveler wouldn’t know whether a specific city such as Juba or Jimma is part of Ethiopia or Southern Sudan, but the traveler could determine that each is located in a different country. Similarly, according to (8), phonological constraints may distinguish morphemes, but not identify them. Thus, the phonology cannot access whether l in (7) is a 3SG affix or a noun root; it only ‘‘knows’’ that l and a are part of different morphemes.

Representing distinctive morphological affiliations by coloring captures the intuition that morphemic affiliation is a dimension that is common to all phonological objects, but at the same time orthogonal to their purely phonological properties. This notation is closely related to the important classical mathematical problems of graph coloring, which generalize the specific problem of coloring a map using a finite set of colors such that every pair of adjacent countries differs in color (see Jensen and Toft 2011 for an overview of the mathematical literature, and Ristad 1993 for a detailed application to natural language).

Mathematically, there is nothing inherently visual about coloring. It can also be understood as assigning arbitrary indices (or any arbitrary set of mutually distinct objects) to the morphemes and the corresponding minimal parts of a phonological representation. The Color Map Hypothesis then amounts to the claim that at the morphology-phonology interface, morphological indices in phonological representations are retained, but their counterparts (the corresponding indices in morphological representation) become inaccessible. The notation in terms of colors, not indices, highlights this inaccessibility. Another way to understand coloring is in terms of McCarthy’s (1979, 1981) autosegmental approach to morphemic affiliation, where morphemes are represented as autosegmental nodes and affiliation to morphemes by association lines. Thus, a Dinka verb undergoing lengthening by a 3SG affix (9a) would be represented as in (9b) (where boxes indicate morphemes). The Color Map Hypothesis can then be viewed as the claim that phonological constraints are based on representations in which the specific features of morphemes have been deleted, as in (9c).

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The autosegmental notation quickly becomes unreadable for bigger representations, but interpreting coloring as a notational variant of the autosegmental formalism highlights an important formal aspect of coloring: under the Color Map Hypothesis, coloring is a process that does not add new information; rather, it restricts access to morphological information to a subset of the features available in morphology. Thus, colors might be considered a rudimentary memory device that keeps track of the tautomorphemic or heteromorphemic affiliation of phonological material in a modular architecture of grammar where all other morphological information is dispensed with once the output of morphosyntax is fed to phonological evaluation.4 Coloring thus grants the bare minimum of accessibility phonology may have to morphological structure, and effectively rules out the possibility of morpheme-specific rules or constraints such as the ones proposed by Flack (2007) and Pater (2000, 2007, 2009) (see section 4 for detailed discussion). In the following, I will assume that colors are phonological objects on a par with nodes and association lines, an assumption that will play an important role in the formal analysis of Dinka vowel length morphology (see section 2.3).

1.1.2 Containment and Possible Operations of GEN

By the Containment assumption, phonological material can never be literally removed from phonological input representations in the course of phonological computation (Prince and Smolensky 1993, van Oostendorp 2008:1365). The candidate-generating function GEN is thus restricted to performing the following changes on underlying forms:

(10) Possible operations of GEN

  • a.

    Insert epenthetic nodes (prosodic nodes, feature nodes, segmental root nodes) or phonetically visible association lines between nodes.

  • b.

    Mark an underlying association line as phonetically invisible.

(10a) implements the slightly implicit assumptions made about Containment and GEN in the earliest version of OT (Prince and Smolensky 1993), whereas (10b) replaces deletion of association lines by a less invasive operation: marking for phonetic invisibility. Phonetic visibility is conceived here simply as an elementary phonological attribute of association lines: all association lines are either [+phonetically visible] or [−phonetically visible]. Postphonological phonetic realization (see below) and phonological constraints may be sensitive to this distinction and therefore disregard phonetically invisible lines, but there is no literal deletion of association lines in phonology. Thus, in the following the double strikethrough (‘‘=’’) in autosegmental graphs does not imply derivational phonological removal of a line; rather, it indicates that an association line is marked as [−phonetically visible].

(11b) shows some representative candidates generated by GEN for the input in (11a). (11bii–iii) contain epenthetic association lines licensed by (10a). In (11biii), the association line between the second μ-node and [e] is marked as phonetically invisible according to (10b). Note that the graphical marking of epenthetic association lines by dashing is redundant because their epenthetic status is a direct consequence of the fact that they are colorless.

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1.1.3 Deletion as Phonetic Nonrealization

(Non)pronunciation of underlying material is implemented as noninterpretation of phonological material at the phonology-phonetics interface following the axioms in (12).5

(12) Axioms of phonetic realization

  • a.

    Nodes: A phonological node is phonetically realized if and only if it is dominated by the highest prosodic node of the candidate through an uninterrupted path of phonetically visible association lines.

  • b.

    Association lines: An association line is phonetically realized if and only if it is marked as phonetically visible and connects two phonetically realized nodes.

Highest in (12a) refers to the familiar prosodic hierarchy . . . ≻ Prosodic Word ≻ Foot ≻ σ ≻ μ ≻ ●. Thus, the highest prosodic node in all examples of (11b) is the σ-node because the representations do not contain Foot or Prosodic Word nodes.6 (13b) shows the part of (11biii) (repeated as (13a)) that is spelled out by phonetic interpretation. [e] and the second μ-node of (13a) are not in (13b) because the upper association line through which they are dominated by the σ-node is phonetically invisible. (11bi) shows a slightly different manner of deletion: [i] and the first μ-node are not phonetically realized because they are not dominated by a σ-node at all.

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1.1.4 Markedness Constraints

All markedness constraints come in two varieties (or clones), one applying only to phonetically realized material of a candidate (the phonetic clone of the constraint), and one applying to all phonological material of a candidate, whether phonetically realized or not (the general clone of the constraint). Thus, the phonetic clone *V (14b) implements the standard ban on phonetically trimoraic vowels (see Flack 2007). The general clone *V (14a) generalizes this constraint to phonetically unrealized structure in the computation of constraint violations. Throughout the article, the phonetic clone is marked by underlining.

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  • a.

    *V

    Assign * to every V-node that is dominated by more than two μ-nodes.

  • b.

    *V

    Assign * to every V-node that is dominated phonetically by more than two μ- nodes.

General constraint clones such as (14a), which I will call generalized markedness constraints, give rise to an especially simple analysis of templatic overwriting. Section 3 shows how this proposal applies to templatic lengthening in Dinka.7

1.2 Dinka Morphology and Phonology

Morphemes in Western Nilotic are typically monosyllabic. Lexical roots end in single consonants and show contrasts in vowel length, whereas affix syllables are open and allow only short vowels. Moreover, there are no complex onsets or codas apart from combinations of single-onset consonants with following glides (see below for details). Segmental affixation is restricted to maximally a single suffix and a single prefix per word. In the following, I will assume that all these statements are surface-true for Dinka, although there are some peripheral exceptions not relevant to the data discussed here. The prosodic structure of word forms is then a Prosodic Word containing maximally one foot whose head is the root syllable ( prefixes are peripheral to the system and tend to form independent Prosodic Words; see Trommer 2011 on Anywa).8

Dinka is also typical for Western Nilotic in a second respect: morphological categories are expressed to a large degree by a complex combination of different nonconcatenative exponents. Thus, the Dinka benefactive not only lengthens short base vowels, but also shifts creaky vowels to breathy and effects various tonal changes (tὲηtὲ̤⧗η ‘to dust’; Andersen 1995:28). In this article, I will systematically disregard all nonconcatenative (and concatenative) morphology that does not affect vowel length (which includes all prefixation). See Trommer 2011 for detailed discussion.

Dinka is one of the few of the world’s languages with a three-way vowel length contrast (see Andersen 1987, 1993, 1995, Remijsen and Gilley 2008, Remijsen and Manyang 2009, for detailed evidence). However, extralong vowels are restricted to morphologically complex forms (vowels may be creaky or breathy, but I will leave creaky vowels unmarked; thus, [e] = [ḛ]).

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The canonical shape of lexical roots in Dinka is Consonant (Glide) (Glide) Vowel Consonant, where a vowel (of any length) may be preceded by one or two glides (e.g., jwjê̤⧗n ‘rope’; Andersen 1995:4–5).

Since there is no evidence for weight of consonantal codas (weight by position), and prevocalic glides are invisible to vowel length alternations, I assume that only the head vowels of syllables are dominated by moras. Adopting the standard syllable model of moraic phonology (see Sherer 1994, Morén 1999, and references there), prevocalic glides and syllable-final consonants are dominated directly by the σ-node.

I assume that moraic association of vowels and consonants in Dinka is governed by the constraint ranking in (16), where undominated *V3μ̆ effectively blocks quadrimoraic syllables, *V̆ restricts (extra)long vowels to lexical roots, and *Cμ excludes moraic consonants. FAITH-μ is a placeholder for all faithfulness constraints on underlying mora-segment association. Constraint definitions are given in (17); nonhead refers to any mora that is not the head of a syllable, and unstressed to any vowel that is not the head of a Prosodic Word.

(16) {*V3μ̆, *V̆, *Cμ} ≫ FAITH-μ ≫ *V

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2 Additive Lengthening

2.1 Monomoraic Additive Lengthening

A number of derivational and inflectional morphological categories in Dinka induce vowel lengthening: short (monomoraic) vowels become long (bimoraic) ((18a), (19a)), and long vowels become extralong (trimoraic) ((18a), (19a)). (18) shows examples from 3SG, and (19) examples from centrifugal morphology (Andersen 1995, Flack 2007).10 In the following, I assume that the base forms of Dinka verbs correspond in the default case to the output forms labeled simple or ∅-forms in Andersen 1995—that is, the verb forms that are used as main verbs in finite clauses.

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I specify both, the 3SG and the centrifugal, morphologically as moraic suffixes, as shown in (20) in the notation familiar from work in Distributed Morphology (Halle and Marantz 1993, Harley and Noyer 1999).11

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  • a.

    3SG ↔ -μ

  • b.

    CF ↔ -μ

I implement affixation autosegmentally: just as a segmental suffix attaches to the last element of the segmental root node tier of its base, so a moraic suffix is concatenated to the rightmost mora of its base form. Since (20a) and (20b) are not lexically preassociated to segments or syllables, moraic suffixation here results in a floating mora following all base moras (21a). Association and hence lengthening are the consequence of phonologically epenthetic insertion of an association line (21b) (for convenience, I indicate color here and in following cases only for affix moras).

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As shown in (22), the integration of moras in additive lengthening follows from the constraints μ → ● and σ ← μ (23) dominating all faithfulness constraints on association (24).12 (23a), written in running text as μ → ●, and (23b), written as σ ← μ, implement the categorical imperative of Autosegmental Phonology (Goldsmith 1976, McCarthy 1979, Marantz 1982) to associate elements of a specific tier to elements of other appropriate tiers (see Myers 1997, Yip 2002, Elfner 2007, McCarthy 2008 for correspondence-theoretic implementations of equivalent constraint types). Crucially, both constraints are generalized constraints; that is, they can be satisfied by phonetic association lines, but also by morphological association lines that are not phonetically realized.13

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14

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The derivation for verbs with underlyingly long vowels is completely parallel. I assume that *V3μ̆ is ranked above and *V3μ̆ below the constraints shown here (see (17)). Thus, moraic affixation is in principle free to create trimoraic vowels if it integrates floating moras. On the other hand, Dinka has no morphemes with trimoraic vowels;15 hence, affixation of a single mora cannot lead to quadrimoraic vowels and to a violation of *V3μ̆.

There is one potential complication: whereas in 3SG and centrifugal forms the floating mora is not accompanied by segmental material that might host it, verbs in passive clauses with a circumstantial topic show both the suffix -è̤ and vowel lengthening.16

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Thus, the passive circumstantial topic affix consists of a vowel (with a preassociated _-node) preceded by an unassociated μ-node. The passive circumstantial topic of wèc ‘kick’ would be represented as follows:

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In principle, the floating mora in this case might attach to the vowel of the suffix instead of associating to the base verb. But this is excluded by the ban on long vowels in unstressed position, * ((17c), repeated in (27)). (Unstressed refers to the head of the Prosodic Word; recall from section 1.2 that in root-suffix structures, the root syllable is the head of the single foot in a Prosodic Word.)

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  • *

  • Assign * to every unstressed V-node that is phonetically dominated by more than one μ-node.

2.2 Bimoraic Additive Lengthening

Besides his detailed documentation of monomoraic additive lengthening, Andersen (1995) briefly mentions a pattern in the causative and the multiplicative of Dinka in which short-vowel roots of a specific tonal verb class are lengthened by two degrees (short vowels become extralong), hence augmentation by two moras.

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I derive this in exactly the same way as simple additive lengthening by representing causative and multiplicative as sequences of two floating moras (or two monomoraic suffix exponents).

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Again, high ranking of σ ← μ and μ → ● enforces association of the floating affix moras, as shown in (30).

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The multiplicative and causative data must be treated with some caution since Andersen doesn’t comment on them in any detail. In particular, Andersen doesn’t discuss what effects multiplicative and causative morphology have for underived long (bimoraic) base vowels and roots with other tone patterns. What is clear is that trimoraic stems do not become quadrimoraic in the multiplicative and causative because Dinka systematically bans quadrimoraic vowels (Andersen 1995:37). Under the assumption that Dinka eschews not only quadrimoraic vowels, but also quadrimoraic syllables in general, owing to undominated *σ3μ̆, the analysis developed here predicts that bimoraic bases also become extralong (trimoraic) in the multiplicative and causative (if μ → ● and σ ← μ dominate and as argued in section 3.1, it is one of the base vowels that deassociates to grant association of the affix moras).

2.3 The Blocking of Cumulative Lengthening

Since the 3SG and centrifugal each induce monomoraic lengthening, and the multiplicative and causative data discussed in section 2.2 show that bimoraic lengthening of simple bases is in principle possible, we expect that verbs with 3SG and centrifugal morphology should exhibit cumulative lengthening by two moras as in (31).

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However, as the data in (32) show, centrifugal 3SG forms exhibit simple additive lengthening, not cumulative lengthening (short vowels become long, not extralong).

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Now recall that one of the basic claims of Colored Containment Theory adopted here is that colors are real phonological objects that are expected to function largely in parallel to other phonological entities. Thus, in parallel to the constraints on maximal moraic binarity in (33), we expect to find constraints like those in (34) that require maximal chromatic binarity for vowels and syllables (where a phonological node N dominates (is dominated by) a color C if and only if it dominates (is dominated by) a phonological node N′ of color C).

(33) Constraints on moraic binarity

  • a.

    *V3μ

    Assign * to every V-node that is dominated by more than two μ-nodes.

  • b.

    Assign * to every σ-node that dominates more than two μ-nodes.

(34) Constraints on chromatic binarity

  • a.

    *V3

    Assign * to every V-node that is dominated by (μ-nodes of ) more than two colors.

  • b.

    3□

    Assign * to every σ-node that dominates (μ-nodes of ) more than two colors.

In fact, the constraints in (34) ranked above μ → ● and σ ← μ correctly derive the blocking of cumulative lengthening (35). The double-lengthening candidate (35c) is excluded because it would imply that the base vowel and syllable are associated to moras of three different colors (the colors of 3SG, centrifugal, and the verb root itself ).

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This analysis is also consistent with the fact that verb forms that combine independent doublelengthening (causative or multiplicative) morphology with a single-lengthening category such as nonfinite inflection, show together double (not triple) lengthening (e.g., throw.MULT.NF’; Andersen 1995:37).

As shown in (36), *σ3□ and *V3□ leave only the choice of whether to associate the moras of the bimoraic (36a) or the monomoraic (36b) morpheme, and maximization of moraic association by μ → ● and σ ← μ decides in favor of fully realizing the bimoraic morpheme.

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Consider finally a potential alternative approach to the blocking of cumulative lengthening. Following a suggestion by Ricardo Bermúdez-Otero (pers. comm.), it might be argued that the centrifugal affix blocks the 3SG affix in a purely morphological way. This would be parallel to the case of the English plural affix /-z/, which blocks the homophonous possessive affix (Yip 1998, Nevins 2011).17 It is difficult to test this hypothesis for the combination of centrifugal and 3SG directly because it is not clear whether the 3SG mora blocks the centrifugal mora or vice versa. However, there is indirect but unequivocal evidence from another combination of vowellengthening affixes showing that phonological material of both morphemes is realized phonetically, whereas cumulative lengthening of the base vowel is blocked. The centripetal has two further exponents apart from lengthening of base vowels (37): the base tone is replaced by low tone (38), and the base vowel becomes breathy ([spread glottis]) (39). (The base forms in (38) are nonfinite forms, which, according to Andersen (1995), are the only verb forms consistently showing the underlying tone of verb roots.)18

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Nontopic subject (NTS) inflection, a further morphological category triggering monomoraic additive lengthening (40),19 additionally shifts underlying tones to high (41) (where the tonally underlying forms are again nonfinite forms), but has no effect on the laryngeal setting of stem vowels (42).

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Again, as expected, the combination of centripetal and NTS leads to single, not double, lengthening.

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Under the assumption that cumulative lengthening is blocked because the NTS affix morphologically blocks the centripetal affix, we would expect the resulting forms to have all properties characteristic of simple NTS forms—hence, high tones and the underlying laryngeal features of their base vowels. Conversely, if the centripetal blocked the NTS affix, the resulting forms should have consistent low tone, and breathy voice on the vowel, independently of the laryngeal features of the underlying vowel. In fact, the behavior of centripetal NTS forms is mixed: as the data in (43) show, their tone is the high tone of the NTS, whereas their base vowels consistently become breathy as is expected from centripetal morphology. Thus, we have evidence for both an underlying centripetal affix and an NTS affix cooccurring with the blocking of cumulative lengthening. Independently of whether we assume that the lengthening mora in centripetal NTS forms is an exponent of NTS or of centripetal, the other morpheme must also be present in the underlying representation of the form. Consequently, blocking must be due to phonological, not morphological, mechanisms.

Centripetal NTS forms also provide important evidence regarding the interpretation of constraints on (chromatic) complexity. Under a liberal reading, these forms violate *σ3□ as shown in (44), where the σ-node immediately dominates the high tone exponent of the NTS suffix and indirectly dominates the breathy ([spread glottis]) feature associated to the segmental root node (via the moraic tier omitted here).

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In the following, I will assume that constraints on autosegmental complexity assign constraint violations strictly locally to configurations occupying a single autosegmental plane (i.e., elements on two tiers directly connected by association lines). This assignment convention does not have noteworthy consequences for constraints such as *σ3□, since segmental root nodes and moras are on connected tiers, but it makes constraints such as *σ3[spread glottis], which would penalize syllables with more than two [spread glottis] specifications, uninterpretable (σ-nodes and segmental features are not directly linked by association). Moreover, it has the effect that a constraint such as *σ (where π is a variable ranging over arbitrary phonological nodes) would be violated by a syllable dominating three tones, and by a syllable dominating three moras, but not by a syllable dominating two moras and a single additional tone (tones and moras are not on the same tier). This convention also has immediate consequences for constraints on chromatic complexity. Recall that a phonological node N dominates (is dominated by) a color C if and only if it dominates (is dominated by) a phonological node N′ of color C. This means that *σ3□ assigns violations to the syllables in (45a) and (45b), but not to the one in (45c).

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For similar reasons, *σ3□ is not violated by centripetal NTS forms because the σ-node in (44) does not dominate three mutually heteromorphemic tones, and does not form an autosegmental plane with [spread glottis]. On the other hand, undominated *σ3□ predicts that Dinka should not tolerate verbs that carry tonal exponents of two different affixes. This prediction is in fact borne out. For example, the tonal affix exponent associated with 3SG is a low tone (e.g., the simple 3SG wèc ‘she/he kicks’), and the exponent associated with CF is a high tone (e.g., uninflected CF wé⧗c), whereas centrifugal 3SG forms carry only the high tone of the centrifugal (wé⧗c) and Dinka in principle allows contour tones on long vowels (see Trommer 2011 for detailed discussion).

3 Templatic Lengthening

In benefactive forms, short vowels are lengthened to long whereas long vowels retain their length.20 Thus, as Flack (2007) observes, benefactive morphology imposes a bimoraic template on roots of any underlying vowel length.

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As Flack shows in detail, there is a simple OT analysis of benefactive morphology in terms of affixation of a single floating mora. Crucially, *V must be ranked above MAXAf (and μ → ●/σ ← μ) such that short/monomoraic vowels may lengthen, but long/bimoraic ones may not. The problem with this analysis (and supposedly any constraint ranking that correctly excludes lengthening of long vowels to extralong) is that it predicts the same for the 3SG and the centrifugal (see section 2), which actually require lengthening. This is exactly the ranking paradox that leads Flack to postulate constraints indexed to specific morphemes (see section 1).

3.1 Basic Analysis: Overwriting as a Contiguity Effect

Here, I argue instead that it is the underlying representation of the benefactive that crucially differs from those of the 3SG and centrifugal. Under this analysis, templatic lengthening in Dinka is an effect of complete overwriting of base moras by two affix moras. The benefactive is a moraic circumfix—that is, the combination of a moraic prefix and a moraic suffix—as shown in (47).

(47) BEN ↔ μ- -μ

Affixation prefixes the first moraic exponent to the first base mora, and suffixes the second mora exponent to the last base mora, resulting in the input representations in (48a) and (48b). Overwriting means that all base moras are deassociated from vowels and syllables, whereas the affix moras establish phonetic association lines to the base, resulting in the outputs in (48a) and (48b).

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The specific overwriting effect of the benefactive derives from the very fact that it is circumfixal. Intuitively, affix moras strive to form a contiguous phonetic string on the moraic tier, which can only be achieved by deleting the moras of the base (i.e., by making them phonetically invisible). Technically, this effect derives from the contiguity constraint in (49), which is a straightforward Colored Containment translation to the moraic tier of the constraint M-O-CONTIGUITY defended in detail by Landman (2002) for segments (see also Finley 2009 for a version of CONTIGUITY that applies to autosegmental features).

(49) □CONTIGUITYμ

Assign * to every phonetic triple of μ-nodes (M1, M2, M3) such that

  • a.

    M1 ≺ M2 ≺ M3, and

  • b.

    Color(M1) = Color(M3) ≠ Color(M2).

For segmental morphophonology, there are two sources of independent evidence for morphological contiguity. First, as is well-known, circumfixes are crosslinguistically marked structure. Contiguity constraints of the type exemplified in (49) are the conceptually minimal implementation of this observation. Second, as Landman (2002) shows in detail, many languages avoid phonological epenthesis in morpheme-internal positions. For example:

In Chukchee, schwa epenthesis splits up what would otherwise surface as a tautosyllabic cluster, for example, /miml+qaca+n/ place near water, surfaces as [mim.lə.qa.can], and not *[miml.qa.can]. Interestingly, epenthesis is restricted in that it systematically avoids a morpheme-internal position, for example, /miməl.qa.can/ surfaces as [miməl.qa.can], and not *[miməl.qa.can], although both outputs avoid potential tautosyllabic clusters through epenthesis. (Landman 2002:3)

(50) shows how ranking □CONTIGUITYμ above the constraints introduced so far derives the correct output for a monomoraic base. The only way to associate all affix moras without violating CONTIGUITY as in (50b) is to deassociate the base moras.21

(50)

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(51) shows the derivation for a bimoraic base that is exactly parallel. In fact, (51b) is independently excluded by *σ3μ̆ and *V3μ̆.

(51)

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The constraint evaluation in (51) also highlights an important aspect of the approach to overwriting adopted here, which is crucially tied to the adoption of the Containment Assumption: from the point of view of phonetic realization, (51c)—which associates only one affix mora and keeps all base moras—should be superior to the winning candidate (51a) because it realizes more moras without violating CONTIGUITY. But the fact that μ → ● and σ ← μ are generalized constraints extending in scope to phonetically unrealized structure has two crucial consequences. First, phonetic deassociation of (underlyingly—i.e., morphologically associated) base moras does not violate these constraints, because of Containment. Second, the only way licensed by GEN to satisfy μ → ● and σ ← μ for the floating affix moras is to associate them phonetically (i.e., to insert a phonetic association line; see the definition of GEN in (10)). The combination of these factors in Autosegmental Colored Containment Theory gives floating material a systematic strategic advantage in the battle for phonetic realization that is crucial for understanding the result of the evaluation in (51), but also gives rise to a general theory of morphophonological overwriting.22 (See Trommer 2011 for an application of the same mechanism to tonal overwriting.)

3.2 Templatic Lengthening Blocking Cumulative Lengthening

Undominated *V3□ and *σ3□ predict that benefactive overwriting should be incompatible with additional lengthening morphology, since this would require that the syllable and the vocalic root node of the base be associated to more than two colors (the colors of the base morpheme, the BEN affix, and a further affix). This prediction is in fact borne out. The imposition of the bimoraic template also blocks further augmentation of bases by morphological categories otherwise inducing lengthening. Thus, 3SG forms of benefactives have long, not extralong, vowels.

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The tableau in (53) shows how *V3□ and *σ3□ block the lengthening of a short root vowel in the benefactive 3SG by two more moras to extralong. Associating all three affix moras (53e) fatally violates *V3□ and *σ3□. The same problem results from leaving the first benefactive mora unassociated and the root mora associated (53f). Crucially, the association of the base vowel to its mora remains visible for *V3□ and *σ3□ even when the association line becomes phonetically invisible. Associating only the 3SG mora to the base vowel (53g) avoids violating *V3□ and *σ3□, but leads to more violations of μ → ● and σ ← μ. Hence, (53g) is also inferior to (53a) (this is crucial for input roots with two moras, where the candidate corresponding to (53g) would involve lengthening).

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Again, the fact that bimoraic benefactive forms cannot be further lengthened by morphological categories otherwise triggering additive lengthening cannot be due to purely morphological blocking. Thus, benefactive NTS forms show templatic lengthening just like simple benefactive forms, but with the high tone contributed by the NTS affix (see the data in (41)).23

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4 Discussion and Summary

Flack’s (2007) argument regarding Dinka addresses one of the central questions in research on the morphology-phonology interface: what amount of access do phonological rules and constraints have to the morphological affiliation of phonological material? The minimalist null hypothesis advocated in most versions of Government Phonology (see Kaye 1995, Scheer 2008, and references there) is that phonological computation has no direct access to morphological information whatsoever, whereas The Sound Pattern of English (Chomsky and Halle 1968) allows virtually full phonological access to morphemes via the percolation of morphological features to single segments. In the OT literature, which seems to take a somewhat intermediate position, three substantial types of restrictions on the accessibility of morphemic affiliation to constraints have been proposed.

(55) Restrictions on constraint accessibility to morphemic affiliation

  • a.

    Constraint type

    Only specific constraint types are eligible for indexing (e.g., only faithfulness constraints in Itô and Mester 1999 or only alignment constraints in Bermúdez-Otero 2012).

  • b.

    Feature type

    Only specific morphosyntactic features are accessible to indexing (e.g., the morphological status of a morpheme as root or affix in Urbanczyk 2006).

  • c.

    Locality

    A constraint indexed for morpheme M only incurs violations if the locus of violation is identical to or overlaps with phonological material affiliated to M (Pater 2007).

Flack argues that to capture Dinka lengthening morphology, all restrictions in (55) must be abandoned in favor of a fully unrestrictive position. First, her major claim is that access to morphology cannot be restricted to faithfulness constraints, a position explicitly advocated by (e.g.) Itô and Mester (1999), but must extend to markedness constraints such as (see below for discussion). Second, under her analysis, phonological constraints not only must access general grammatical features of morphemes, but also must be able to identify specific morphemes (e.g., 3SG or centripetal).24 Third, and maybe most strikingly, Flack’s analysis also requires abandoning the weakest form of (55c), a locality restriction that is usually considered a main tenet of the theory of indexed markedness constraints, which I will call here the Overlap Condition. This restriction requires that indexed markedness constraints ‘‘apply if and only if the locus of violation contains some portion of the indexed morpheme’’ (Pater 2007:275, 2009; see Jurgec 2010 for critical discussion).

To see this, consider Flack’s account of complex forms that combine templatic lengthening and additive lengthening morphology such as benefactive 3SG forms, where is indexed for benefactive. Under the Overlap Condition, would block association of the vowel to the benefactive mora as in (56a), but not to the 3SG mora as in (56b) because in the latter candidate the locus of constraint violation (the vowel and the three moras to which it is associated) does not overlap with (contain part of) an exponent of benefactive. Thus, under the Overlap Condition, Flack’s analysis would incorrectly predict additive lengthening for benefactive 3SG forms. Consequently, she rejects this restriction, stating that ‘‘is violated by any trimoraic vowel that surfaces in a benefactive verb, regardless of the morphological source of the three moras’’ (Flack 2007:754, emphasis in original).

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In fact, benefactive 3SG forms are also the base of Flack’s argument that Dinka lengthening morphology cannot be captured by indexed faithfulness constraints. A ranking such as MAX3SG ≫ *V ≫ MAXBEN can account for additive lengthening in simple 3SG forms, and for templatic lengthening in simple benefactive forms, but again predicts incorrectly that benefactive 3SG forms show additive lengthening (due to undominated MAX3SG).

In this article, I have shown that the Dinka data require not more, but actually less finegrained phonological access to morphemic affiliation than is standardly assumed in OT, and I have argued for the Color Map Hypothesis in (8), which basically restricts reference to morphology to whether two phonological elements are tautomorphemic or heteromorphemic. The Color Map Hypothesis is more restrictive than the restriction of constraints to specific feature types (55b) since lexical constraint indexation gives the phonology a superset of the information provided by morphological colors: if phonological constraints may identify phonological material as belonging to specific morphemes such as 3SG and centrifugal, they may a fortiori also determine that different phonological material belongs to different morphemes. Thus, constraint indexation logically implies the availability of all information provided by morphological coloring. Conversely, colors do not allow the morphosyntactic features of single morphemes to be identified and hence substantially restrict the access of phonology to grammatical features. Coloring also implies the standard restrictions on constraint types accessible to indexing (55a) since indexing of standard markedness constraints to specific morphemes or classes of morphemes becomes impossible if the only information available to phonology is abstract colors.25

On the other hand, morphological colors seem to allow the theoretical minimum access to morphology necessary to capture the blocking of cumulative lengthening in Dinka. This becomes especially clear when we compare bimoraic affixation (section 2.2) and cumulative monomoraic affixation (section 2.3), which differ only by the fact that the first involves affixation of two tautomorphemic moras and the latter, affixation of two heteromorphemic moras. It is hard to imagine how this difference could be captured in a framework that embraces a maximally restrictive position that does not allow phonological computation to distinguish at least whether two given pieces of phonological material belong to the same morphemic unit or not—which is exactly what morphological colors accomplish.26 Morphological colors are also essential in the implementation of templatic lengthening via moraic CONTIGUITY. Of course, this does not come as a surprise since the formalization of any form of CONTIGUITY (including the well-documented segmental contiguity effects discussed by Landman (2002)) requires some means of identifying morphemic affiliation that is at least as powerful as adopting morphological colors.

Notice also that each constraint necessary to reanalyze Dinka lengthening morphology in terms of morphological colors (moraic CONTIGUITY, *σ3□, and *V3□) refers only to colors (colored phonological material) in its own locus of violation; thus, together they instantiate an even stricter form of locality than required by Pater’s (2007) Overlap Condition. We might call this form of locality Fixed Overlap: sensitivity to morphemic affiliation is bound to specific parts of the locus of violation specified by the constraint. Thus, in Flack’s (2007) indexed constraint against trimoraic vowels, , there are 15 different ways in which the locus might overlap with M to satisfy Pater’s version of the Overlap Condition (either only with one of the μ-nodes, or only with the vocalic root node, or with all nodes, or with any two-member or three-member subset of this set).27 On the other hand, *V3□, which penalizes phonological configurations of exactly the same size and structure as (one vocalic root node associated to three moras), allows only one option for overlap: every mora of the constraint locus must instantiate a distinct color.

Thus, as far as the analyses of Western Nilotic length-manipulating morphology in this article prove successful, they show that coloring is the minimally and maximally necessary amount of access the phonology module must have to morphosyntax. This is in line with evidence from derived environment effects, which also crucially reduce to the differential treatment of tautomorphemic and heteromorphemic association by phonological constraints (see van Oostendorp 2007).

Note finally that the formal mechanisms I have used in the reanalysis of Dinka lengthening morphology apart from morphological colors are either standard in the OT literature or close equivalents to standard mechanisms, especially the autosegmental representation of moras, and the specifications of affixes as prefixes, suffixes, and circumfixes. The adoption of Autosegmental Colored Containment Theory allows an especially natural analysis of moraic templates. Thus, the implementation of overwriting by the bimoraic circumfix in section 3 follows from the structural preference the theory gives to unassociated material via the constraints μ → ● and σ ← μ—that is, the fact that ‘‘deletion’’ (deassociation) of underlyingly associated material does not violate them, whereas the only possibility for floating moras to satisfy them is by phonetic association. However, a similar overwriting effect could also be achieved in Standard Correspondence Theory by assuming high-ranked constraints that require the output realization of underlyingly floating material (e.g., MAX FLOAT in Wolf 2005, 2007 or MAX SUBSEGMENT in Zoll 1996). Thus, the reanalysis of Dinka based on morphological colors does not require any substantially new formal mechanisms.

Notes

I am grateful to Ricardo Bermúdez-Otero, Marc van Oostendorp, Bert Remijsen, Eva Zimmermann, and the audience of the 19th Manchester Phonology Meeting for helpful discussion. All remaining errors are my own.

1 Abbreviations, glosses, and symbols used in the article are 1/2/3 = 1st/2nd/3rd person, AP = antipassive, BEN = benefactive, CAUS = causative, CF = centrifugal, CP = centripetal, CT = circumstantial topic, F = falling tone, FQ = frequentative, H = high tone, L = low tone, MASC = masculine, MULT = multiplicative, NF = nonfinite, NTS = nontopic subject, PAS = passive, PL = plural, SG = singular, ● = segmental root node, μ = mora, σ = syllable, □ = morphological color.

2 See Lombardi and McCarthy 1991, Samek-Lodovici 1992, Davis and Ueda 2005, 2006, and Saba Kirchner 2010 on moraic affixation in general and Flack 2007 on moraic affixation in Dinka.

3 I have adapted the notation of Flack’s constraints to the notation used in this article.

4 In Bermúdez-Otero’s (in preparation) terms, phonology accesses an impoverished morphological representation.

5 The axioms in (12) are equivalent to the operation Stray Erasure of pre-OT and early OT phonology (Steriade 1982, Itô 1988, Prince and Smolensky 1993).

6 I assume that GEN does not generate candidates that contain more than one highest prosodic node (say, two σ- nodes, but no Foot or Prosodic Word nodes).

7 Just like corresponding phonetic constraints, generalized markedness constraints penalize phonologically marked surface structure, but in addition they have a number of subtle side effects, all of which correspond to well-documented phonological phenomena (see Trommer 2011, 2014 for details).

First, they enforce overwriting effects by underlyingly floating material (see section 3).

Second, in deletion contexts, they lead to counterbleeding opacity. Thus, the counterbleeding pattern in Bedouin Hijazi Arabic in which assimilation of velars to following front vowels is rendered opaque by deletion of high vowels in nonfinal open syllables (e.g., /ħa⧗kim-i⧗n/ ⇒ [ħa⧗kjm-i⧗n/* ħa⧗km-i⧗n] ‘ruling-MASC.PL’; McCarthy 2007:11) can be captured by a generalized version of a constraint requiring velar consonants to share the [coronal] feature of a rightadjacent vowel.

Third, the generalization of standard markedness constraints to phonetically unrealized material makes it possible to capture ‘‘grandfather’’ effects in the sense of McCarthy 2003. Consider, for example, *VOICEDOBSTRUENT (Kager 1999:40). The generalized version of this constraint is violated by any obstruent O that is either underlyingly or phonetically voiced. If O is underlyingly voiced, no operation of GEN could possibly avoid a violation of the constraint because Containment disallows the literal removal of underlying material. On the other hand, if O is underlyingly voiceless, generalized *VOICEDOBSTRUENT will penalize the voicing of O. Thus, the predicted output for high-ranked generalized *VOICEDOBSTRUENT is one where underlyingly voiceless obstruents are blocked from voicing whereas underlyingly voiced obstruents are freely allowed. This is exactly the pattern observed in voicing assimilation in Mekkan Arabic captured in McCarthy 2003 by the comparative-markedness constraint NNOVCDOB. (See van Oostendorp 2006 for a more general discussion of comparative-markedness effects in Containment.)

However, it is important to note that cloning restricts the options of possible OT constraints in Containment since it restricts generalized markedness constraints to clones of constraints that are well-motivated in their nongeneralized version, and disallows constraints that make arbitrary reference to morphological color. Thus, presupposing Containment Theory, cloning is actually a restriction, not an extension to the inventory of possible constraints (see also Finley 2008 for a detailed argument that Containment-based constraints give rise to substantial restrictions on possible grammars).

8 I adopt the standard assumption of Prosodic Phonology that every nonterminal prosodic node immediately dominates exactly one strong node of a lower prosodic level (Nespor and Vogel 1986:7). I will call a phonological node N the head of a prosodic constituent P if and only if P dominates N by a path that contains only strong nodes.

9 Andersen cites these and many other verb forms with the declarative particle a that appears as a proclitic to verbs in declarative clauses. I systematically omit a here and in the following data.

10 Centrifugal is a derivational category that ‘‘indicates that the action is directed away from the deictic center, which is typically the speaker. . . . Conversely . . . centripetal indicates that the action is directed towards the deictic center’’ (Andersen 1995:9–10). Other morphological categories that trigger monomoraic additive lengthening besides 3SG and centrifugal are centripetal, nonfinite, nontopic subject, 1SG, and passive circumstantial topic (Andersen 1995:45). All these categories also induce complex patterns of tonal changes on roots.

11 Since Dinka syllable structure is symmetric (moraic vowels are followed and preceded by nonmoraic segments), 3SG and centrifugal could in principle also be analyzed as moraic prefixes. See Trommer 2014 on Anywa for a situation where moraic prefixes and suffixes lead to different changes in vowel length.

12 See Bermúdez-Otero 2001 for an overview of the literature on slightly different versions of moraic faithfulness constraints (especially Morén 1999:36–46) and for critical discussion of the typological predictions. For present purposes, the exact implementation of moraic faithfulness is irrelevant since the relevant constraints are crucially dominated in Dinka.

The constraint definitions in (24) are Containment-based implementations of the constraints NO-SPREAD and NODELINK in McCarthy 2000:160.

13 With Flack (2007) and most other researchers working on prosodic affixation (see, e.g., Davis and Ueda 2006, McCarthy 2000, Bye and Svenonius 2012), I assume that lexical bases have syllabic and moraic structure at the point of affixation. I leave it open whether this is due to cyclic phonological evaluation or to Lexicon Optimization. See Saba Kirchner 2010 and Bermúdez-Otero 2012 for discussion of this point.

14 I use the symbol ‘‘●’’ to denote segmental root nodes.

15 A natural way to ensure this gap in the inventory of Dinka roots in Autosegmental Colored Containment Theory would be to posit a high-ranked constraint that blocks the phonetic association of a vowel to more than two tautomorphemic moras (i.e., moras of the same color).

16 Passive circumstantial topic clauses in Dinka are passives in which the preverbal topic is neither subject nor object. See Andersen 1995:sec. 3 for discussion.

17 That the blocking of plural by possessive /-z/ must be morphological, not phonological, is evident from minimal pairs such as cats ([kæts], possessive form [kæts]), where the plural [-s] triggers blocking of the possessive formative, and the proper name Katz ([kæts], possessive form [kætsez]) where the nonmorphemic [s] does not.

18Andersen (1995) assumes that Dinka has four phonological verb classes, differing with respect to underlying vowel length and tone: short vowel/low tone (tèη), short vowel/falling tone (wêc), long vowel/high tone (té⧗m), and long vowel/falling tone (lé⧗r). According to this classification, the underlying tone of a verb surfaces uniformly in nonfinite forms (see (38)). In Trommer 2011, I argue that wec and té⧗m have underlying high tone, teη and lé⧗r underlying low tone. Thus, there are only two underlying tonal classes that perfectly crossclassify the vowel length contrast, but there is no single form in the verbal paradigm that exhibits the underlying tone. For the argument here, it is irrelevant which underlying tones are assumed.

19 Nontopic subject forms are used in Dinka finite active clauses that have a topic that is different from the subject of the clause. See Andersen 1995:sec. 3 for details.

20 Benefactive is the morphological marking of transitive verbs as ditransitive (Andersen 1995:11). In addition to imposing a bimoraic template and causing tonal changes, the benefactive renders the vowels of verb roots breathy.

21 The □CONTIGUITYμ violation might also be circumvented by metathesis of moras. I assume that this is in principle impossible (according to the definition in (10), reordering of elements on an autosegmental tier is not a possible operation of GEN). As Zimmermann (2009) has convincingly shown (see also Moskal 2009), segmental metathesis is universally excluded; hence, it is natural to assume that the same is true for moras. However, in principle the analysis of templatic lengthening developed here is compatible with the a priori availability of metathesis, which would simply require undominated faithfulness constraints against linear reordering.

22 Of course, overwriting by floating moras is contingent on the high ranking of σ ← μ, μ → ●, and □CONTIGUITYμ. In a language where dominate these constraints, overwriting is systematically blocked.

23 Note that Flack (2007:754) derives the blocking of cumulative lengthening in benefactive 3SG forms by high ranking of the constraint (see (4)), a derivation that does not extend to the analogous case of centrifugal 3SG (see section 2.3). Thus, Flack must stipulate a further constraint requiring that an affix mora must always appear adjacent to a mora of the head to which it affixes (Flack 2007:752).

24 An anonymous reviewer suggests capturing the ban on cumulative lengthening in Dinka by subcategorization specifications requiring that affix moras be adjacent to root moras. Under an implementation of subcategorization requirements as phonological constraints, this amounts to the use of markedness constraints that do not access the affiliation of phonological material to specific morphemes, but instead access the partition of morphemes into roots and affixes. This analysis would hence be more restrictive than Flack’s (2007) proposal, along the lines proposed by Urbanczyk (2006), but would imply more fine-grained access to morphosyntactic information than the color-based analysis proposed here, which does not require reference to the root/affix distinction.

25 The difference between morphological coloring and constraint indexation is roughly parallel to the two major devices Chomsky and Halle (1968) use to achieve phonological access to morphosyntactic information: boundary symbols and indexing of segments for morphological affiliation by percolation of indices. The reason why they use both instruments is probably that the theory also makes massive use of readjustment rules that manipulate boundary symbols and thereby make boundary symbols much more powerful than morphological coloring, which is subject to the Containment assumption.

26 Note especially that the asymmetry between bimoraic and cumulative monomoraic affixation (see (32)) cannot plausibly be derived by assuming a cyclic, stratal, or serial organization of morphophonology that interleaves phonology and affixation (see, e.g., Wolf 2008, Bermúdez-Otero 2012). If centrifugal 3SG forms are created in two serially ordered steps of affixation whereas multiplicative or causative affixation takes place in one step, the prediction would instead be that affixation of two moras at the same time should be worse than monomoraic affixation.

27 In general, a constraint locus specifying a set S of n phonological objects leads to 2n − 1 distinct options for overlap with a morpheme, the cardinality of the power set (the set of subsets) of S less the empty (sub)set. Thus, specifies four phonological objects (the vocalic root node and the three moras), resulting in 24 − 1 = 15 distinct overlap options.

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