OCP Effects in Dagaare*

OCP effects in Dagaare*

Abstract

In tone languages, adjacent high tones are often avoided. Different languages resolve the problem in different ways, but different resolutions can be found even in one and the same language. Dagaare (Gur, Niger-Congo) exhibits four different responses to a sequence of high tones: the second tone dissimilates, the second tone is downstepped, the two tones merge, or adjacent high tones are simply tolerated. The choice is morphologically and lexically conditioned. We present evidence that adjacent high tones are resolved only if they belong to the same tonal foot. We account for the different resolution patterns by assuming that morphemes may specify partial rankings: the tone of the complex word is the concatenation of the tones of its constituent morphemes, evaluated by the union of their partial rankings.

* [Acknowledgements suppressed.] The following abbreviations are used: 3.SG ‘third person singular’, A ‘adjective’, COMP ‘complementiser’, DEF ‘definite article’, DEM ‘demonstrative’, FACT ‘factitive marker’, IMPF ‘imperfective aspect’, N ‘noun’, NOM ‘nominalization’, PERF ‘perfective aspect’, PL ‘plural’, SG ‘singular’.

1 1 Introduction

In tone languages, adjacent high tones are often avoided. For example, Myers (1997) notes that different Bantu languages resolve HH sequences in different ways and different resolutions can be found even in one and the same language. One of the tones can be deleted or retracted from the other (Shona, Rimi, Chichewa); the tones can merge into a single high tone (Shona, Kishambaa); processes that would create such sequences are blocked (Shona); and sometimes adjacent high tones are simply tolerated (Kishambaa). Myers shows how all these outcomes can be derived from the OBLIGATORY CONTOUR PRINCIPLE (OCP, Goldsmith 1976, Leben 1973) which prohibits adjacent identical elements, but crucially only if the OCP is interpreted as a violable constraint in the sense of Optimality Theory (Prince & Smolensky 1993/2004). In this paper, we examine the lexical tone system of Dagaare (Gur, Niger-Congo), a two- tone language of northwestern Ghana and adjoining areas of Burkina Faso. There is relatively little earlier work on Dagaare phonology. The essentials are described in Kennedy 1966; subsequent work includes Anttila & Bodomo 2000, Bodomo 1997, 2000, Dakubu 1982, and Hall 1977. Kennedy notes that the tone system of Dagaare can be conveniently described by postulating two levels of the register type and a downstepped high unit. In the simple word, which is usually disyllabic, the first syllable can carry either high or low tone, and the second syllable can carry either high, downstepped high, or low tone. The complexity of the system resides in the morphologically and lexically conditioned tonal alternations. These are described by Kennedy in some detail and are further explored in this paper. We will focus on tonal alternations that arise from the concatenation of two high tones. Dagaare exhibits at least four different responses to HH sequences depending on the morphological and lexical environment: the second tone dissimilates (tonal polarity), the second tone is downstepped, the two tones merge, or adjacent high tones are simply tolerated. These four responses are illustrated in (1) in terms of autosegmental representations.

(1) Four different responses to the input /H-H/

(a) Dissimilation (b) Downstep (c) Merger (d) No change

! yí -rì bU@- má kúlí pI@-kU@U@-rç$

H L H !H H H H L

‘house-SG’ ‘thing-PL’ ‘go.home-PERF’ ‘sheep-kill-IMPF’

We first present evidence that HH sequences undergo tonal alternations only if they belong to the same tonal foot, but else remain inert. We then account for the different resolution patterns by assuming that morphemes may specify partial rankings: the tone of the complex word is the concatenation of the tones of its constituent morphemes, evaluated by the union of their partial rankings.

The paper is structured as follows. In section 2, we describe the tone patterns of Dagaare nouns and verbs, illustrate the different responses to HH sequences, provide evidence for tonal feet, and note how the lexical tonology differs from the postlexical tonology. In section 3, we derive the different responses to HH sequences and show how the tone pattern of a complex word results from the tone patterns of its constituent morphemes. In section 4, we point out some implications of our proposal for morphological theory. Section 5 concludes the paper. Our data represent the dialect of the second author, a native speaker of the Central dialect of Dagaare.

2 The facts

2.1 Tone in nouns

The Dagaare noun consists of a root followed by a number suffix. The simple word is maximally disyllabic and the tone-bearing unit (TBU) is the syllable (Kennedy 1966). The majority of nouns fall into the three tonal classes in (2) which are similar to those found in the closely related Moore (Kenstowicz et al. 1988) and Dagbani (Hyman 1993).1

(2) Three major tone patterns in nouns

SINGULAR PLURAL TONE (a) kùù-rí kù-é LH ‘hoe’ (b) yí-rì yí-è HL ‘house’ (c) nyU@ç@-rI@ nyç@-E@ HH ‘nose’ (d) -- -- LL --

In the examples in (2), the singular suffix is –ri/-rI, the plural suffix is –e/-E, depending on ATR harmony. Examples (2a) and (2b) illustrate TONAL POLARITY, a phenomenon attested in several Gur languages. If the root tone is L, the suffix surfaces as H; if the root tone is H, the suffix surfaces as L. Kenstowicz et al. (1988) analyze tonal polarity in the closely related Moore as follows: the number suffix is underlyingly H; if the root is L, the resulting L-H surfaces with no changes (kùù- rí, kù-é); if the root is H, the resulting H-H undergoes dissimilation and the suffix becomes L (yí-rì, yí-è). Kenstowicz et al. (1988) posit two ordered rules: Association which links tones to syllables, one to one, left to right, and Dissimilation which changes H-H to H-L, a process known as Meeussen’s Rule (Goldsmith 1984). The derivations are illustrated in (3).

1 ! The following tone marks are written over every vowel: @ = H(igh) tone, $ = L(ow) tone, ^ = HL (falling) tone, = downstep. Unless otherwise noted, we follow the orthographical conventions of Kennedy 1966. Nasalization has been omitted for simplicity. There are a number of additional noun types that will not be discussed in this paper. In particular, recent borrowings can be longer than two syllables, e.g. tábU$l-I$ ‘table-SG’ and báásàkúú-rì ‘bicycle-SG’. There also exist polysyllabic native nouns which may be etymologically compounds, but which are synchronically difficult to distinguish from simple words, e.g. bádE@r-I@ ‘spider-SG’, ku$nku@n-í ‘tortoise-SG’ and fúmì-ní ‘needle-SG’. We have also observed a marginal disyllabic pattern with three tones (LHL) where the first syllable is closed by a sonorant consonant, e.g. kpàŕ-rI$ ‘shirt-PL’. In this paper, we focus on canonical disyllabic simple nouns.

(3) Tonal polarity as dissimilation

UR ASSOCIATION DISSIMILATION OUTPUT (a) /kuu -ri/ kùù-rí kùù-rí kùù-rí -- L H L H L H

(b) /yi -ri/ yí -rí yí -rì yí -rì

H H H H H L H L

Tone dissimilation can be understood as a consequence of the OCP which prohibits adjacent identical tones (Goldsmith 1976, Leben 1973, 1978; see also McCarthy 1986, Myers 1997, Odden 1986, Yip 1988, among others). As we will see in a moment, tone dissimilation is only one of several possible responses to an OCP violation in Dagaare. The third example nyU@ç@-rI@ ‘nose-SG’ and nyç@-E@ ‘nose-PL’ in (2c) raises the question why the H-H-sequence does not undergo dissimilation here. Kenstowicz et al. (1988) show that in Moore the corresponding H-H nouns only have one multiply associated H tone which originates from the suffix and the root is underlyingly toneless. This is illustrated in (4). The analysis requires an additional rule of Spreading which applies after Association, linking the H tone to the remaining toneless syllables.

(4) Toneless roots

UR ASSOCIATION SPREADING DISSIMILATION OUTPUT (a) /nyUç -rI/ nyU@ç@ -rI nyU@ç@ -rI@ -- nyU@ç@ -rI@

H H H H

This analysis has several correct consequences. First, dissimilation is predicted not to apply to H-H nouns because there is only one H tone. Second, the nonexistence of L-L nouns follows because there are no L suffixes. Third, the analysis explains a puzzling alternation in noun-adjective compounds where a noun root is followed by one or more adjectives of which only the last is inflected for number. Examples are given in (5). The tonally alternating syllable is highlighted.

(5) Noun-adjective compounds

N-SG A-SG A-SG N-A-SG (a) kùù-rí vI$l-a$a@ kù-vI$l-a$a@ ‘hoe-good-SG’ (b) yí-rì vI$l-a$a@ yí-vI$l-a$a@ ‘house-good-SG’ (c) nyU@ç@-rI@ vI$l-a$a@ nyç$-vI$l-a$a@ ‘nose-good-SG’ (d) pç@g-ç@ bíl-é vI$l-a$a@ pç$g-bìl-vI$l-a$a@ ‘woman-small-good-SG’

4 The polarity nouns in (5a) and (5b) are tonally stable: /kù-/ ‘hoe’ is always low and /yí-/ ‘house’ is always high. The H-H nouns in (5c) and (5d) undergo tonal alternations: /nyç-/ ‘nose’ and /pçg-/ ‘woman’ surface as H when immediately followed by the number suffix, but lose the H tone when an adjective follows. Example (5d) shows that the same happens in adjectives as well: /bil-/ ‘small’ loses the H tone when it is followed by another adjective. These patterns can be explained if the roots are underlyingly toneless and the H tone comes from the number suffix. We thus have a third correct consequence of the toneless root analysis. The fact that this analysis generalises to several Gur languages (see e.g. Hyman 1993 for Dagbani and Cahill 1999:53-56 for Kçnni) is strong evidence in its favor and we will adopt it here. In addition to the three major tone patterns, Dagaare has three minor patterns that involve downstep (!H). These patterns are illustrated in (6). Downstep may occur on the singular suffix ((6a)), on the plural suffix ((6b)), or on both ((6c)), depending on the noun.

(6) Three minor tone patterns in nouns

SINGULAR PLURAL TONES ! ! (a) pI@ -rU@U@ pI@I@-rI$ HH HL ‘sheep’ (b) sáán-à sáá!m-á HL H!H ‘stranger’ ! ! ! ! (c) sU@- á sU@ç@ n-I@ H H H H ‘rabbit’

We must first address the question whether !H should be analyzed as a genuine mid tone, as in the related Buli (Akanlig-Pare & Kenstowicz 2003), or as a H tone which is phonetically lowered. The crucial observation is that there is no three-way contrast H vs. !H vs. L on the initial syllable (Kennedy 1966:43). Instead, !H only occurs after H, suggesting that !H is a contextual variant of H (Hyman 1979). Evidence from a number of African tone systems suggests that !H arises when two H tones come into contact: both tones remain H, but the second is interpreted phonetically at a lower pitch value than the first, schematically /HH/ Æ H!H; see e.g. Carlson 1983 (Supyire), Liberman et al. 1993 (Igbo), and Odden 1982, 1986 (Kishambaa). If this interpretation of downstep is correct, it leads to the claim that tonal polarity and downstep are two different responses to the same underlying configuration /H-H/. Thus, all the examples in (6) have the same underlying tones /H-H/, but the outcomes differ depending on morpholexical environment (noun class, number). An alternative interpretation of downstep is that there is a floating L tone sandwiched between the two H tones, which results in the lowering of the second H, schematically /HLH/ Æ H!H (Clements & Ford 1979, Pulleyblank 1986). Under this hypothesis, polarity-triggering roots would be underlyingly H, e.g. /yí-rí/ Æ yí-rì ‘house-SG’ (/H-H/ Æ HL), whereas downstep- ! ! triggering roots would be underlyingly HL, e.g. /sU^-á/ Æ sU@- á ‘rabbit-SG’ (/HL-H/ Æ H H). The mixed roots that trigger either polarity or downstep depending on the number would have to be diacritically marked one way or the other. The floating tone hypothesis can be tested by placing these roots before a H tone in a compound. The prediction is that the putative HL root should trigger downstep on the following H, whereas the putative H root should not. The results are shown below in (7)-(9).

(7) Downstep

(a) yí-rì bíl-é yí-!bíl-é ‘house + small’ ‘small house’ ! ! (b) sU@- á sI@I@-rE@ sU@ç@- sI@I@-rE@ ‘rabbit + skinner’ ‘rabbit skinner’

(8) No downstep

(a) yí-rì dúó-rò yí-dúó-rò ‘house + climber’ ‘house climber’ ! (b) sU@- á@ kU@U@-rç$ sU@ç@-kU@U@-rç$ ‘rabbit + killer’ ‘rabbit killer’

(9) No downstep

! ! (a) sáá-nà pI@ -rU@U sáá-pI@ -rU@U ‘stranger + sheep’ ‘hospitality sheep’ ! ! ! (b) náá- ú kU@ç@ r-áá náá-kU@ç@ r-áá ‘bullock + farmer’ ‘farming bullock’

These examples show that the two types of roots behave identically: both trigger downstep in (7); neither triggers downstep in (8)-(9). This provides evidence against the floating tone hypothesis. However, the data pose another puzzle: why is there downstep in (7), but not in (8)-(9)? The descriptive generalization is straightforward: downstep occurs if the head of the compound has one single tone (H), but not if it has two tones (H-L, H-!H) (cf. Kennedy 1966:44). The head of the compound can be identified by the locus of number inflection which is invariably final. This suggests the following analysis: tones are grouped into binary constituents, starting from the head of the word, and an OCP violation is only resolved within a constituent. We call these constituents TONAL FEET. The idea of tonal constituency is not new; precedents include Akinlabi and Liberman 2000, Clements 1983, Leben 2001, Odden 1982, and Zec 1999, among others. The grouping of tones into tonal feet is illustrated in (10)-(12) where tonal feet are indicated by parentheses.

(10) Downstep within a tonal foot

! pI@-sII-rE@ Æ pI@- sI@I@-rE@ ‘sheep skinner’, lit. ‘sheep-skin-IMPF’

H H (H !H)

(11) Polarity within a tonal foot, no resolution across feet

pI@-kU@U@-rç@ Æ pI@-kU@U@-rç$ ‘sheep killer’, lit. ‘sheep-kill-IMPF’

H H H H (H L)

(12) Downstep within a tonal foot, no resolution across feet

! náá-kU@ç@r-áá Æ náá-kU@ç@ r-áá ‘cattle farmer’, lit. ‘cattle-farm-IMPF’

H H H H (H !H)

The tonal foot is a genuine tonal constituent. Its size is determined by the number of tones, not by the number of syllables. For example, in (10) vs. (11)-(12) the number of syllables is the same, but the number of tones is different, hence the difference in the distribution of downstep. The analysis predicts that there should be no sequences of two adjacent downsteps, i.e. *H!H!H, which would require a ternary tonal foot (H!H!H). Instead, a sequence of three H tones must be parsed either H(H!H) or (H!H)H. To the best of our knowledge, this prediction is correct for Dagaare. We now summarise our discussion of tone in Dagaare nouns. We have seen three different responses to an OCP violation: /HH/ Æ HL (tonal polarity), /HH/ Æ H!H (downstep), and /HH/ Æ HH (no resolution). We proposed that tones are grouped into binary tonal feet; that an OCP violation is resolved only within a foot; and that the choice between the two resolutions (tonal polarity, downstep) is morpholexically conditioned.

2.2 Tone in verbs

Dagaare verb roots fall into three tonal classes: Class 1 is underlyingly toneless; Classes 2 and 3 have an underlying H tone. A similar division into toneless and H verbs is found in Dagbani (Hyman & Olawsky 2000). The three tonal classes are illustrated in (13). Each verb is presented in four morphological forms: citation form, imperfective aspect, perfective aspect, and nominalization. All morphological categories except the citation form have an underlying H suffix.

(13) Tone patterns in verbs

CITATION IMPF PERF NOM -- H H H

(a) CLASS 1 -- LL LH LH HH bùrì bùr-ó bùrí búr-úú ‘soak’

(b) CLASS 2 H HH HL HH HL kúlí kúl-ò kúlí kúl-ùù ‘go home’

! ! ! (c) CLASS 3 H HL H H H H H H búrì bú!r-ó bú!rí bú!r-úú ‘fetch’

The key insight in (13) is that the underlying tone inventory is extremely simple: roots are either toneless or H, and suffixes are all H. The various surface patterns result from morpholexically conditioned tonal alternations. In what follows, we lay out the principles that are responsible for these alternations by examining each verb class in turn.2

2 The perfectives in (13) are the transitive perfectives (Bodomo 1997:90). Their intransitive counterparts are tonally slightly different: in toneless verbs, there appears to be no H suffix at all, e.g. bùr-èè (Class 1) and all H verbs are tonally identical to Class 3 transitive perfectives, e.g. kú!l-éé (Class 2), bú!r-éé (Class 3). We also note that the transitive perfective and the following factitive suffix lá may optionally coalesce resulting in both tonal and segmental changes. This may be a fast speech phenomenon and needs further study. Finally, the verbs tàá ‘have’ and wàá ‘be’ appear to have unique tonal paradigms and will not be discussed in this paper.

7 Class 1 verb roots are toneless: the surface L is simply absence of lexical tone. This gives us an opportunity to observe the behavior of suffix tones in isolation. In imperfectives and perfectives the suffix H tone is strictly aligned to the right edge of the word; in nominalizations the suffix H tone spreads. The paradigm of toneless verbs is illustrated in (14) in terms of autosegmental representations.

(14) The paradigm of toneless verbs (Class 1)

CITATION IMPERFECTIVE P ERFECTIVE NOMINAL bùrì bùr-ó bùrí búr-úú ‘soak’

H H H

The right-edge alignment of the H suffix in finite verbs can be clearly seen by varying the length of the verb. In short (CV) verbs, the H suffix covers the entire verb. In longer (CVV, CVCV, CVCCV, CVVCV) verbs, H is only realised on the last vowel. Examples from the perfective paradigm are shown in (15).

(15) The right-edge alignment of the perfective H tone

CITATION PERFECTIVE dì dí ‘eat’ bàà bàá ‘grow’ bùrì bùrí ‘soak’ kànnI$ kànnI@ ‘read’ mààlI$ mààlI@ ‘make’

Nominalizations are different: the H tone spreads across the whole word. As we have seen earlier, this is a general property of toneless nouns. The tonal difference between nouns and verbs is particularly clear in compounds where the imperfective form of a verb can be used as a noun to mean ‘someone who Vs’ (Kennedy 1966:45). In the verbal use, the H tone is strictly aligned to the right edge; in the nominal use, the H tone spreads across the whole word. This is shown in (16).

(16) (a) tùù-ró ‘follow-IMPF’ (verb)

(b) bì-túú-ró ‘child-follow-IMPF’, i.e. ‘child-follower’ (noun)

We now turn to the two remaining verb classes. In both Class 2 and Class 3, the verb root is underlyingly H. The differences result from the morpholexically conditioned tonal alternations illustrated in (17) and (18) in terms of autosegmental representations.

(17) The paradigm of Class 2 H-toned verbs

CITATION IMPERFECTIVE P ERFECTIVE NOMINAL kúlí kúl -ò kúlí kúl-ùù ‘go home’

H H L H H L

(18) The paradigm of Class 3 H-toned verbs

CITATION IMPERFECTIVE P ERFECTIVE NOMINAL búrì bú!r-ó bú!rí bú!r-úú ‘fetch’

H H !H H!H H !H

The situation is simplest in the citation form where there is only one underlying tone: the root tone. In Class 2, the root tone spreads and both syllables surface as H. In Class 3, the root tone sticks to the left edge and the second syllable remains toneless. In the imperfective, perfective, and nominal there are two underlying H tones: the root tone and the suffix tone. The response to the underlying H-H sequence is morphologically conditioned: Class 2 verbs undergo tonal polarity, except in the perfective where the two H tones merge. Class 3 verbs undergo downstep everywhere.3 The verb paradigms provide further evidence for tonal feet. In (19), we show the verb forms with underlying H-H sequences parsed into tonal feet. In the finite forms (imperfective, perfective), we have included the factitive particle lá which immediately follows the finite verb. The observed pattern of downsteps is correctly predicted.

(19) Downstep in verbs

IMPERFECTIVE PERFECTIVE NOMINAL Class 1: bùr-ó !lá bùrí !lá búr-úú ‘soak’

(H !H) (H !H) H

Class 2: kúl -ò lá kúlí !lá kúl-ùù ‘go home’

(H L) H (H !H) (H L)

Class 3: bú!r-ó lá bú!rí lá bú!r-úú ‘fetch’

(H !H) H (H!H) H (H !H)

3 There appears to be some variation in the perfective and nominal forms of some Class 3 verbs. The perfective of búrì ‘fetch’ may occasionally surface as either bú!rí (lá) or búrí (!lá); the nominal form may occasionally surface as either bú!r-úú or búr-ùù. This variation may be related to speech rate. The forms reported here are the carefully pronounced elicitation forms.

9 In sum, we have seen four different responses to an OCP violation: /HH/ Æ HL (tonal polarity), /HH/ Æ H!H (downstep), HH Æ H (merger), and /HH/ Æ HH (no resolution). We have argued that an OCP violation is only resolved within a tonal foot and that the choice among the three possible resolutions is morphologically conditioned. In the rest of this paper, we will work out an analysis of these conditions based on universal tonal constraints.

2.3 A note on postlexical tonology

While we have not undertaken a detailed study of Dagaare postlexical tonology, it is clear that OCP violations are systematically tolerated across a word boundary. This is illustrated in (20) where the two adjacent H tones surface at level pitch.

(20) (a) a dç@b-ç@ pç@g-bç@ the man-PL woman-PL ‘the men’s wives’

H H

However, the actual generalization appears to be subtler. Another environment where OCP violations are systematically tolerated is the future tense of toneless verbs. The future tense is expressed by the pre-verbal particles nà ‘will’ and kU$ng ‘will not’. Kennedy (1966:47-48) notes that these particles “perturb a following low tone [i.e. toneless root of Class 1] to a high tone”. This is shown in (21). The tonally alternating syllable is highlighted.

! ! (21) (a) à bí-é dìg-ré lá sU@ç@ N-áá the child-SG chase-IMPF FACT rabbit ‘The child is chasing a rabbit’

! ! (b) à bí-é nà díg-ré lá sU@ç@ N-áá the child-SG FUT chase-IMPF FACT rabbit ‘The child will be chasing a rabbit’

! (c) à bí-é kU$ng díg-ré sU@ç@ N-áá the child-SG FUT.NEG chase-IMPF rabbit ‘The child will not be chasing a rabbit’

We propose that the future particles are underlyingly LH, but only the initial L can actually be realised on the monosyllabic particle itself. If the particle is placed before a toneless verb, the trailing H tone becomes audible by docking onto the following vacant syllable. This analysis is illustrated in (22) in terms of autosegmental representations.

(22) Adjacent H tones within a verb

bi -e na dig -re Æ bí -é nà díg -ré

H LH H H L H H

The result is a H-H sequence within a word. Crucially, the OCP violation is not resolved: the H-H sequence surfaces at level pitch. We suggest that this is because the H-H sequence was not created in morphology, by combining a root with a suffix, but in syntax, by combining a tense particle with a word. This suggests that tonal feet are constructed in the lexical phonology, but not in the postlexical phonology.

2.4 Summary

Table (23) summarises the attested tone patterns in disyllabic simple words:

(23) Tone in disyllabic simple words

ROOT SFX SURFACE PATTERN MORPHOLEXICAL CATEGORY

(a) -- -- X.X toneless Class 1 verbs: citation form (b) L H L.H faithful Class 2 nouns (c) H -- H=H spreading Class 2 verbs: citation form H.X left align Class 3 verbs: citation form (d) -- H H=H spreading Class 1 nouns X.H right align Class 1 verbs: imperfective, perfective (e) H H H.L polarity Class 2 nouns; Class 2 verbs: imperfective H!H downstep Class 3 nouns; Class 3 verbs: imperfective, perfective H=H merger Class 2 verbs, perfective H.H faithful Postlexical tonology

Patterns (a) and (b) are the simplest ones: the underlying tone sequence always yields the same surface sequence. Pattern (c) shows that an underlying H root may surface in two different ways: spreading vs. left alignment. Pattern (d) shows that an underlying H suffix may also surface in two different ways: spreading vs. right alignment. Finally, pattern (e) shows that there are four possible responses to a H-H sequence: polarity vs. downstep vs. merger vs. no change. Different resolutions of an OCP violation are thus possible not only across languages, but even within one and the same language. There remain two questions that need to be addressed. First, why do we get just these tonal patterns instead of a different set of patterns? Are the patterns in (23) in some sense a natural class and something we might have expected, or could we just as well have expected a different set of patterns? Second, how is the tone of a complex word derived from the tones of its parts? In Dagaare, the answer clearly involves something more than a simple concatenation of underlying tones followed by some tone rules that apply across the board. Answers to these questions will be provided in the next section.

3 Analysis

3.1 Constraints

We now identify the tonal constraints that are responsible for the alternations described in the previous sections. We do this by first identifying the constraints that are never violated in Dagaare. This leaves us with a handful of constraints that are systematically violated. It is the latter group of constraints that will play a crucial role in explaining the morphologically conditioned tonal patterns. We start by considering the standard faithfulness constraints (McCarthy & Prince 1995), starting from correspondence constraints.

(24) Correspondence constraints on tone

(a) MAX-IO(T) (“No deletion”) Each input tone has an output correspondent. (b) DEP-IO(T) (“No insertion”) Each output tone has an input correspondent. (c) UNIFORMITY(T) (“No merger”) Each output tone has at most one input correspondent. (d) INTEGRITY(T) (“No split”) Each input tone has at most one output correspondent.

In the absence of evidence for tone deletion, tone insertion, and tone split, we assume that MAX- IO(T), DEP-IO(T), and INTEGRITY(T) are undominated. The only correspondence violation we have seen is the merger of two adjacent H tones in the perfective of Class 1 verbs, which constitutes a violation of UNIFORMITY(T). Turning to identity constraints, the constraint IDENT(T) ‘Do not change the value of a tone’ is clearly violable in Dagaare: tonal polarity starts out with an underlying /H-H/ sequence and changes the value of the suffix tone to L. The fact that root tones never change suggests the activity of another identity constraint which bans tone changes in roots: IDENT-ROOT(T). This constraint is undominated in Dagaare.

(25) Identity constraints on tone

(a) IDENT(T) Do not change the value of a tone. (b) IDENT-ROOT(T) Do not change the value of a root tone.

The tonal grammar must also contain constraints that govern the mapping between tones and tone- bearing units (TBUs). We assume that the unmarked mapping is one-to-one: every tone has exactly one TBU and every TBU has exactly one tone. This implies four logically possible violation types listed in (26), with their respective constraints:

(26) Tone-TBU mapping constraints

PATTERN VIOLATES

(a) σ σ *SPREAD ‘Every tone has at most one TBU.’

T (b) σ *CONTOUR ‘Every TBU has at most one tone.’

T T

(d) σ *TONELESS ‘Every TBU has at least one tone.’

Two of these constraints are violable in Dagaare: *SPREAD is systematically violated in toneless nouns and Class 2 verbs ((23c,d,e)). *TONELESS is systematically violated in Class 1 and Class 3 verbs ((23a,c,d)). We are not aware of any compelling evidence for either contours or floating tones and will therefore assume that *CONTOUR and *FLOAT are undominated in the lexical phonology of Dagaare.4 Finally, there is evidence for two additional constraints. Fundamental to our discussion is the OCP which militates against two adjacent identical tones within the tonal foot. The OCP is ! violated in downstep: /HH/ Æ (H H). We have also seen evidence for an ALIGN constraint that requires suffix tones to be linked to the word-final syllable. This constraint is never violated in Dagaare and can thus be considered undominated.

(27) (a) OCPφ Avoid adjacent identical tones within a tonal foot. (b) ALIGN-RIGHT-SUFFIX Every suffix tone is linked to the word-final TBU.

The outline of the analysis is now complete. We have considered twelve standard constraints on tone. Seven are never violated and can thus be considered undominated: MAX-IO(T), DEP-IO(T), INTEGRITY(T), IDENT-ROOT(T), *CONTOUR, *FLOAT, ALIGN-RIGHT-SUFFIX. Five are occasionally violated, hence dominated: UNIFORMITY(T), IDENT(T), OCP, *SPREAD, *TONELESS. This yields the schematic constraint ranking in (28).

4 The statement that *CONTOUR is undominated needs some justification. There are at least two environments where a sequence of two tones might be interpreted as a contour: word-final (C)VV and (C)VN, e.g. yí-è ‘house-PL’, kú-è ‘hoe- SG’, sàá ‘father.SG’, vI$l-àá ‘good-SG’, I$rU@N$ ‘culture’, and word-final (C)VC that results from optional vowel elision, e.g. gánI$ ~ gán$ ‘book-SG’, wóg-ì ~ wôg ‘tall-SG’. As for word-final (C)VV sequences, these are at least in some cases syllabified CV.V (Kennedy 1966:10-11). This means that words like yí-è are in fact disyllabic and the contour is only apparent. Word-final (C)VC sequences are also considered disyllabic by Kennedy (1966:6), primarily due to the fact that the final consonant carries tone, although he notes that “consonants occurring word final have presented something of an interpretation problem”. As for optional word-final vowel elision, the process seems gradient and sensitive to speech rate, which suggests it is postlexical. We thus conclude that Dagaare has no contours in its lexical phonology. This makes Dagaare similar to the closely related Dagbani (Hyman 1993).

(28) A preliminary constraint ranking for Dagaare

STRATUM 1 STRATUM 2

MAX-IO DEP-IO UNIFORMITY INTEGRITY IDENT IDENT-ROOT >> OCP *CONTOUR *SPREAD *FLOAT *TONELESS ALIGN-RIGHT-SUFFIX

3.2 Possible tone patterns

The schematic tonal grammar in (28) defines a limited space of possible tone patterns. We will now check how well the predicted patterns match the actual patterns, repeated in (29).

(29) Tone in disyllabic simple words

ROOT SFX SURFACE PATTERN MORPHOLEXICAL CATEGORY

First, we consider inputs with no tones ((29a)). Since the undominated DEP-IO(T) bans tone insertion, the output will remain toneless and nothing more needs to be said. This is the pattern attested in the citation form of Class 1 verbs, e.g. bùrì ‘soak, where the low tone is phonologically absence of tone. There are two inputs with one tone: words with a H root ((29c)) and words with a H suffix ((29d)). The predictions are shown in (30) and (31). The leftmost constraint column records severe violations where a candidate either violates an undominated Stratum 1 constraint or is harmonically bounded. No rankings are intended among the five Stratum 2 constraints.

(30) H root + toneless syllable

STRATUM 1 STRATUM 2 /H.X/ UNIF IDENT-(T) OCP *SPREAD *TLESS Æ H=H * L=L IDENT-RT H.H DEP-IO L.L DEP-IO H.L DEP-IO L.H DEP-IO X.H IDENT-RT Æ H.X * X.L IDENT-RT L.X IDENT-RT X.X MAX-IO

(31) Toneless syllable + H suffix

STRATUM 1 STRATUM 2 /X.H/ UNIF IDENT-(T) OCP *SPREAD *TLESS Æ H=H * L=L bounded * * H.H DEP-IO L.L DEP-IO H.L DEP-IO L.H DEP-IO Æ X.H * H.X ALIGN-S X.L bounded * * L.X ALIGN-S X.X MAX-IO

In each tableau, only two candidates survive. In each case, these are exactly the attested patterns. If H comes from the root, it either spreads (H=H) or is left-aligned (H.X); if H comes from the suffix, it either spreads (H=H) or is right-aligned (X.H). These correspond to the empirical patterns (29c) and (29d). Finally, there are two inputs with two tones: /L-H/ ((29b)) and /H-H/ ((29e)). The presence of two input tones opens up the possibility of merger. This is a real possibility in Dagaare: recall that in the perfective of Class 1 verbs two adjacent H tones merge into one (/H1-H2/ Æ H12). It is thus necessary to contemplate the possibility of merger in every case. For this reason, we have systematically included merger candidates in the tableaux and coindexed input tones with their output correspondents.

15 The tableau for /L-H/ is shown in (32). The only possible output is L-H. This candidate is both perfectly faithful and perfectly unmarked and will therefore win irrespective of ranking. This corresponds to the empirical pattern (29b).

(32) /L-H/

STRATUM 1 STRATUM 2 /L1.H2/ UNIF IDENT-(T) OCP *SPREAD *TLESS H=H1,2 IDENT-RT L=L1,2 bounded * * * H1.H2 IDENT-RT H1,2.H DEP-IO H.H1,2 DEP-IO L1.L2 bounded * * L1,2.L DEP-IO L.L1,2 DEP-IO H1.L2 IDENT-RT H1,2.L DEP-IO H.L1,2 DEP-IO Æ L1.H2 L1,2.H DEP-IO L.H1,2 DEP-IO X.H1,2 IDENT-RT H1,2.X IDENT-RT X.L1,2 IDENT-RT L1,2.X ALIGN-S X.X IDENT-RT

The tableau for /H.H/ is shown in (33). In this case, there are three possible outputs: merger (H=H1,2), OCP violation (H1.H2), and tonal polarity (H1.L2). Recall our assumption that a surface H-H sequence is phonetically realised with downstep if the two tones constitute a tonal foot (H!H), else as a level tone. This results in the four empirically attested tone patterns in (29e).

(33) /H-H/

STRATUM 1 STRATUM 2 /H1.H2/ UNIF IDENT-(T) OCP *SPREAD *TLESS Æ H=H1,2 * * L=L1,2 IDENT-RT Æ H1.H2 * H1,2.H DEP-IO H.H1,2 DEP-IO L1.L2 IDENT-RT L1,2.L IDENT-RT L.L1,2 IDENT-RT Æ H1.L2 * H1,2.L DEP-IO H.L1,2 DEP-IO L1.H2 IDENT-RT L1,2.H IDENT-RT L.H1,2 IDENT-RT X.H1,2 IDENT-RT H1,2.X ALIGN-S X.L1,2 IDENT-RT L1,2.X IDENT-RT X.X IDENT-RT

We now have an analysis that predicts the space of attested tone patterns in Dagaare. These tone patterns form a phonologically natural class: they are all and only those patterns that satisfy the Stratum 1 constraints in (28). Two important questions remain. First, how are specific morphological categories associated with their characteristic tone patterns? For example, the input /H-H/ surfaces as H-L in ! ! Class 2 imperfectives (kúl-ò ‘go.home-IMPF’), but as H- H in Class 3 imperfectives (bú r-ó ‘fetch- IMPF’). Similarly, the input /X.H/ surfaces as H=H in nouns (nyU@ç@-rI@ ‘nose-SG’), but as X.H in finite verbs (bùr-ó ‘soak-IMPF’). This suggests that individual morphological categories have a limited amount of freedom in choosing their tone pattern and this choice has to be represented somewhere in the grammar. The second question has to do with tonal combinatorics: if the root chooses one tone pattern and the suffix chooses another, what is the tone pattern of the complex word? These questions will be answered in the next section.

17 3.3 Tonal composition

How are specific morphological categories associated with their characteristic tone patterns? We take the view that a morpheme is not just a piece of phonological material, but it also includes a piece of grammar that characterises its phonological behavior. In Dagaare, the space of available tonal options is defined by the constraints of Stratum 1. Within this space, each individual morpheme may choose a characteristic tonal pattern by specifying a partial ranking of the constraints in Stratum 2. We will now illustrate this in detail. The available tonal options can be obtained by computing the factorial typology of the five constraints in Stratum 2. This can be easily done with the aid of OTSoft (Hayes et al. 2003). Note that the inputs /X.X/ and /L.H/ need not be considered since they are invariably mapped onto X.X and L.H, respectively. Thus, we only need to consider the three inputs where ranking makes a difference. The resulting factorial typology is shown in (34). Six distinct patterns are predicted.

(34) Factorial typology of {UNIFORMITY, IDENT, OCP, *SPREAD, *TONELESS}

INPUT 1 2 3 4 5 6 (a) /X.H/ H=H H=H H=H X.H X.H X.H (b) /H1.H2/ H.L H.H H=H12 H.L H.H H=H12 (c) /H.X/ H=H H=H H=H H.X H.X H.X

The key observation is that different columns of the factorial typology can be identified with different morphological paradigms. Columns {1,2} match nominal number: in toneless nouns ((a)) the H tone of the number suffix spreads; in H nouns ((b)) the H tone of the number suffix undergoes tonal polarity or downstep, depending on the noun class. Columns {4,5} match the imperfective aspect: in toneless verbs ((a)) the H tone of the imperfective is strictly right-aligned; in H verbs ((b)) the H tone of the imperfective undergoes polarity or downstep, depending on the verb class. Finally, columns {5,6} match the perfective aspect: in toneless verbs ((a)) the H tone of the perfective is strictly right-aligned; in H verbs ((b)) the H tone of the perfective undergoes downstep or merges with the root tone, depending on the verb class. Inflectional paradigms thus carve up the space of possible tone patterns as shown in (35).

(35) Inflectional paradigms

NUMBER IMPERFECTIVE PERFECTIVE

INPUT 1 2 3 4 5 6 (a) /X.H/ H=H H=H H=H X.H X.H X.H (b) /H1.H2/ H.L H.H H=H12 H.L H.H H=H12 (c) /H.X/ H=H H=H H=H H.X H.X H.X

Root classes can be mapped onto the factorial typology in an analogous manner. Columns {1,2} match nouns; columns {1,3,4,6} match Class 2 verbs, and columns {2,5} match Class 3 verbs. In (36), inflectional categories are laid out across the top, root categories across the bottom.

18 (36) Inflectional paradigms and root classes

NUMBER IMPERFECTIVE PERFECTIVE

INPUT 1 2 3 4 5 6 (a) /X.H/ H=H H=H H=H X.H X.H X.H (b) /H1.H2/ H.L H.H H=H12 H.L H.H H=H12 (c) /H.X/ H=H H=H H=H H.X H.X H.X

NOUN CLASS 2 VERB CLASS 3 VERB

The tone pattern of a complex word can now be defined as the intersection of the tone patterns of its constituent morphemes. For example, the imperfective of a Class 2 verb has the input /H1.H2/. The predicted form is found in column {4} which is the intersection of {1,3,4,6} (Class 2) and {4,5} (imperfective). The predicted output is H.L, e.g. kúlò ‘go.home-IMPF’. The picture in (36) conveys the intuition behind the analysis, but more needs to be said. Morphological categories cannot be literally associated with columns in the factorial typology because factorial typologies are not grammatical objects: they are surface patterns derived from the grammar. We propose to characterise each morphophonological pattern as a PARTIAL RANKING, i.e. as a set of ordered pairs of constraints (see e.g. Anttila 2002 and Zamma 2005). The partial rankings for Dagaare are given in (37).

(37) Partial rankings for morphological categories

NUMBER *TLS >> *SPR; *SPR >> ID(T) spreading, polarity, downstep IMPERFECTIVE *SPR >> *TLS; *SPR >> ID(T) polarity, downstep PERFECTIVE *SPR >> *TLS; ID(T) >> *SPR downstep, merger NOUN *TLS >> *SPR; *SPR >> ID(T) (same as NUMBER) CLASS 2 VERB OCP >> *SPR; OCP >> ID(T) polarity, merger CLASS 3 VERB ID(T) >> OCP; *SPR >> OCP downstep

We now define the tone of a complex word as a function of its constituent morphemes. We call the combinatorial operation RANKING COMPOSITION:

(38) RANKING COMPOSITION: The phonology of a complex word is the concatenation of the underlying forms of its constituent morphemes, evaluated by the union of their partial rankings.

We will now give concrete examples of ranking composition. First, consider a Class 2 verb combined with the imperfective suffix, e.g. kúlò ‘go.home-IMPF’. The ranking composition is illustrated in (39)-(40).

(39) Morphemes

Underlying form: /kul-, H/ Partial ranking: OCP >> *SPR; OCP >> ID(T) Meaning: ‘go home’

Underlying form: /-o, H/ Partial ranking: *SPR >> *TLS; *SPR >> ID(T) Meaning: IMPERFECTIVE

(40) Ranking composition

(a) Union of rankings (b) Intersection of columns

[kúlò] *SPR >> *TLS *SPR >> ID(T) OCP >> *SPR [kúlò] OCP >> ID(T) {4}

/kul-, H/ /-o, H/ /kul-, H/ /-o, H/ OCP >> *SPR *SPR >> *TLS {1,3,4,6} {4,5} OCP >> ID(T) *SPR >> ID(T)

(40a) illustrates tonal composition in terms of the union of partial rankings; (40b) does the same in terms of intersection of columns in the factorial typology. Tableau (41) shows the composite ranking that correctly predicts the tone of the complex word.

(41) Tableau for kúlò ‘go.home-IMPF’

/H1.H2/ OCP *SPREAD *TLESS IDENT-(T) UNIF H=H1,2 *! * H1.H2 *! Æ H1.L2 *

In the above example, the verb root has both an underlying tone and a partial ranking. Now, let us consider a verb root that has neither. The hallmark of Class 1 toneless verbs is the strict right edge alignment of suffix H tones, e.g. bùr-ó ‘soak-IMPF’ and bùrí ‘soak-PERF’. However, this pattern is clearly not a property of the verb roots themselves because in nominalizations the suffix H tone spreads: búr-úú ‘soaking’. The strict right edge alignment must thus be a property of the imperfective and perfective suffixes and spreading must be a property of nominalizations. The upshot is that Class 1 verb roots are tonally completely unmarked and the tone pattern of the complex word depends on the suffix. The ranking composition is illustrated in (42)-(43).

20 (42) Morphemes

Underlying form: /bur-/ Partial ranking: -- Meaning: ‘soak’

Underlying form: /-o, H/ Partial ranking: *SPR >> *TLS; *SPR >> ID(T) Meaning: IMPERFECTIVE

(43) Ranking composition

(a) Union of rankings (b) Intersection of columns

[bùró] *SPR >> *TLS [bùró] *SPR >> ID(T) {4,5}

/bur-/ /-o, H/ /bur-/ /-o, H/ *SPR >> *TLS {1,2,3,4,5,6} {4,5} *SPR >> ID(T)

(44) Tableau for bùró ‘soak-IMPF’

/X.H/ OCP *SPREAD *TLESS IDENT-(T) UNIF H=H *! Æ X.H *

We now turn to nouns. The analytical challenge is to account for the phonologically unpredictable behavior of /H-H/ sequences: the choice between tonal polarity and downstep depends on both the root and the number suffix. The relevant examples are repeated in (45). In all these cases, the underlying tone is /H-H/.

(45) The four surface realizations of /H-H/ in nouns

SINGULAR PLURAL TONE (a) yí-rì yí-è HL HL ‘house’ ! ! (b) pI@ -rU@U@ pI@I@-rI$ HH HL ‘sheep’ (c) sáán-à sáá!m-á HL H!H ‘stranger’ ! ! ! ! (d) sU@- á sU@ç @n-I@ H H H H ‘rabbit’

The patterns in (45) can be easily reconstructed in terms of ranking composition. We start by classifying nominal morphemes according to how they resolve H-H sequences:

(46) A three-way classification of nominal morphemes (noun roots, number suffixes)

(a) Morphemes that trigger/undergo polarity: yí- (root); -rí, -é -á (suffixes) (b) Morphemes that trigger/undergo downstep: súóN- (root); -má, -rU@U@ (suffixes) (c) Morphemes that do either: pI@-, sááN- (roots); -úú ’nominaliser’ (suffix)

The noun classes can be derived by associating the morphemes in (46a) with the polarity ranking OCP >> ID(T), the morphemes in (46b) with the downstep ranking ID(T) >> OCP, and the morphemes in (46c) with neither. Note that the decisive ranking may come from either the morpheme that triggers the alternation or from the morpheme that undergoes it. The source is irrelevant as long as the ranking appears in the phonology at the word level. The partial rankings are shown in (47):

(47) Rankings for nominal morphemes

(a) POLARITY NOUN/NUMBER *TLS >> *SPR; *SPR >> ID(T); OCP >> ID(T) (b) DOWNSTEP NOUN/NUMBER *TLS >> *SPR; *SPR >> ID(T); ID(T) >> OCP (c) OTHER NOUN/NUMBER *TLS >> *SPR; *SPR >> ID(T)

Particularly interesting are mixed morphemes that allow both tonal polarity and downstep. An example of a mixed root is /sááN-/ ‘stranger’ which triggers polarity in the singular (sáán-à ! ‘stranger-SG’), but downstep in the plural (sáá m-á ‘stranger-PL’). In this case, the root does not have the decisive ranking, but relies on the number morpheme to determine the outcome.

(48) A mixed root

Underlying form: /saaN-, H/ Partial ranking: *TLS >> *SPR; *SPR >> ID(T) Meaning: ‘stranger’

Underlying form: /-na, H/ Partial ranking: *TLS >> *SPR; *SPR >> ID(T); OCP >> ID(T) Meaning: SINGULAR

Underlying form: /-ma, H/ Partial ranking: *TLS >> *SPR; *SPR >> ID(T); ID(T) >> OCP Meaning: PLURAL

(49) Ranking composition

(a) sáán-à ‘stranger-SG’

[sáán-à] *TLS >> *SPR *SPR >> ID(T) [sáán-à] OCP >> ID(T) {1}

/saaN-, H/ /-na, H/ /saaN-, H/ /-na, H/ *TLS >> *SPR *TLS >> *SPR {1,2} {1} *SPR >> ID(T) *SPR >> ID(T) OCP >> ID(T)

! (b) sáá m-á ‘stranger-PL

! [sáá m-á] *TLS >> *SPR ! *SPR >> ID(T) [sáá m-á] ID(T) >> OCP {2}

/saaN-, H/ /-ma, H/ /saaN-, H/ /-ma, H/ *TLS >> *SPR *TLS >> *SPR {1,2} {2} *SPR >> ID(T) *SPR >> ID(T) ID(T) >> OCP

! (50) Tableau for sáá m-á ‘stranger-PL’

/H1.H2/ *TLESS *SPREAD IDENT-(T) OCP UNIF H=H1,2 *! * Æ H1.H2 * H1.L2 *!

An example of a mixed suffix is /-úú/ ‘nominaliser’ which undergoes polarity with Class 2 verbs ! (kúl-ùù ‘go.home-NOM’), but downstep with Class 3 verbs (bú r-úú ‘fetch’). In this case, both the root and the suffix allow multiple output possibilities, but their union is unambiguous.

(51) A mixed suffix

Underlying form: /-uu, H/ Partial ranking: *TLS >> *SPR; *SPR >> ID(T) Meaning: NOMINALISER

Underlying form: /bur-, H/ Partial ranking: ID(T) >> OCP; *SPR >> OCP Meaning: ‘fetch’

Underlying form: /kul-, H/ Partial ranking: OCP >> ID(T); OCP >> *SPR Meaning: ‘go home’

(52) Ranking composition

(a) kúl-ùù ‘go.home-NOM’

[kúl-ùù] *TLS >> *SPR *SPR >> ID(T) OCP >> ID(T) [kúl-ùù] OCP >> *SPR {1}

/kul-, H/ /-uu, H/ /kul-, H/ /-uu, H/ OCP >> ID(T) *TLS >> *SPR {1,3,4,6} {1,2} OCP >> *SPR *SPR >> ID(T)

(b) bú!r-úú ‘fetch’

! [bú r-úú] *TLS >> *SPR *SPR >> ID(T) ! ID(T) >> OCP [bú r-úú] *SPR >> OCP {2}

/bur-, H/ /-uu, H/ /bur-, H/ /-uu, H/ ID(T) >> OCP *TLS >> *SPR {2,5} {1,2} *SPR >> OCP *SPR >> ID(T)

(53) Tableau for bú!r-úú ‘fetch’

/H1.H2/ *TLESS *SPREAD IDENT-(T) OCP UNIF H=H1,2 *! * Æ H1.H2 * H1.L2 *!

There remains one case where the analysis underpredicts the outcome. Both Class 2 and Class 3 verbs are predicted to allow two possible citation forms: H=H (spreading) and H.X (right align). In reality, Class 2 verbs choose the former (kúlí ‘ go home’) and Class 3 verbs the latter (búrì ‘fetch’). This does not follow from any ranking posited so far. The analysis can be completed by associating the citation form of Class 2 verbs with the ranking *TLS >> *SPR and the citation form of Class 3 verbs with the ranking *SPR >> *TLS.

4 Implications for morphological theory

We have proposed that the phonological representation of a morpheme consists of two parts: an underlying form and a partial ranking. As we have seen, it is not necessary for both to be actually present. Three kinds of morphemes are conceptually possible: morphemes that only have an underlying form; morphemes that only have a ranking; and morphemes that have both. This theoretical typology allows us to reconstruct some aspects of morphological typology that have traditionally been problematic. The first type corresponds to morphemes as items (agglutination); the second type corresponds to morphemes as processes (truncation, subtraction, metathesis, ablaut, and other kinds of “process morphology”); the third type encompasses everything that traditionally goes under the name of morphophonemics.

(54) Three types of morphemes

UNDERLYING FORM PARTIAL RANKING MORPHEME TYPE (a) /x/ -- item (b) -- a >> b process (c) /x/ a >> b item and process

“Process morphemes” are problematic for pure item-based theories of morphology where a morpheme is conceived of as a piece of phonological material. The natural move within the item- based framework is to try to reanalyze apparent morphological processes as abstract items. This is often possible in cases like truncation and ablaut which can be reconstructed in terms of abstract templates, underspecification, and featural affixation. A more radical response is to reject morphemes as items in favor of morphemes as processes (e.g. Zwicky 1985, Anderson 1992, Stump 2001). The present proposal opens up a third way to think about “process morphology”: morphemes as rankings. This approach generalises the notion of morpheme beyond the item-based view: any systematic phonological pattern statable as a ranking is in principle a possible morpheme. It should be noted that morpheme-specific rankings seem necessary anyway in order to deal with run-off-the-mill morphophonemics (Anttila 2002, Zamma 2005). Thus, morphemes that only consist of a ranking are simply the limiting case of what is already available.

25 An independent issue is how partial rankings should be combined. In this paper, our working hypothesis has been ranking composition: the ranking of a complex word is the union of the rankings of its constituent morphemes. This makes for a simple and transparent combinatorics. All constituent morphemes are treated equally; there are no phonological asymmetries between stems and suffixes; and all rankings of the parts are inherited by the ranking of the whole. Ranking composition works for Dagaare tone, but it may well be too restrictive for general purposes. In her work on lexical accent systems, Revithiadou (1999) points out the existence of systematic head- dependent asymmetries where the accentual properties of morphological heads typically suppress the accentual properties of morphological dependents. In particular, category-changing derivational suffixes tend to impose their accentual requirements on the entire word. In many tone and lexical accent languages it is also customary to distinguish between DOMINANT and RECESSIVE affixes based on their tonal/accentual behavior (see e.g. Halle & Vergnaud 1987, Inkelas 1998): a dominant morpheme dictates the tone/accent of the word and the tone/accent of a recessive morpheme only emerges if the word contains no dominant morphemes. Crucially, dominant affixes do not appear to form a morphologically natural class, but include both derivation and inflection (Inkelas 1998). These are prima facie examples of phonological asymmetries among morphemes. To what extent these asymmetries are analyzable in terms of ranking composition remains a topic for future work.

5 Conclusion

The avoidance of adjacent high tones is a cross-linguistically common tendency often attributed to the universal constraint ‘Avoid adjacent identical elements’ (OCP). The problem is to reconcile the universality of this constraint with the fact that different languages employ different strategies to avoid adjacent high tones. The problem is particularly acute in Dagaare where different avoidance strategies are found depending on the morphological and lexical environment. In this paper, we have shown how the language-specific facts of Dagaare can be derived from universal phonological constraints. Two theoretical assumptions were necessary. First, we argued that adjacent high tones are resolved only if they belong to the same tonal foot, but are else left unresolved. This supports the hypothesis that tones are grouped into constituents. Second, we outlined a combinatorial theory of the phonology-morphology interface that allows one to operate with a small number of universal constraints and reduce the morphological and lexical aspects of phonological patterns to differences in constraint ranking.

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