Tone and morphological level ordering in Dagaare

Abstract Dagaare is a language of northern Ghana and adjoining areas of Burkina Faso. There are two tones, H and L, and contrastive downstep H!H that involves a non-automatic pitch drop between two H tones. The challenge is to explain the extensive morphological conditioning of tonal processes, including dissimilation, downstep and spreading. Our solution involves level ordering: tones are introduced at different morphological levels (stems, words and phrases) and later processes can make earlier processes opaque. Tonal differences between nouns (spreading) versus verbs (no spreading) and stems (dissimilation) versus words (downstep) arise from constraint ranking differences within and across levels. There are two kinds of downsteps: stem-level downsteps are underlying L tones affiliated with some morpheme; word-level downsteps are L tones inserted by a general process of word-final lowering. Only one downstep per word is allowed. If more would arise, the morphologically inner downstep blocks the morphologically outer downstep.


Introduction
Dagaare is a Mabia (formerly known as Gur) language of northern Ghana and adjoining areas of Burkina Faso.Earlier descriptions include Kennedy (1966), Hall (1977), Kropp Dakubu (1982), Delplanque (1983), Bodomo (1997) and Ali et al. (2021).For general overviews of this language group, see BendorSamuel (1971), Manessy (1975), Naden (1989), Miehe (2012) and Eberhard et al. (2020).The tone system of Dagaare can be briefly described as follows.There are two tones: H and L. Simple words are typically monosyllabic or disyllabic.Monosyllables surface as either H or L. Disyllables show the expected four surface patterns HH, HL, LH and LL.In addition, there is a fifth pattern H ! H with a pitch drop between the two H tones that is conventionally marked by a raised exclamation point.This is contrastive downstep common in tone languages south of the Sahara (Connell 2011).Each downstep sets a new ceiling for subsequent H tones making Dagaare a 'terracedlevel' language (Welmers 1959; Winston 1960; Clements 1979; Connell 2011).Trisyllabic and longer words are often compounds or recent borrowings.
Several common processes target H tones, including dissimilation (Meeussen's Rule), spreading and absorption.What makes Dagaare tone analytically challenging is that tone alternations are often triggered or blocked by morphological and lexical conditions.Our goal in this article is to show that once morphology is properly understood, phonology turns out simple.Dagaare tone operates elegantly just as one would expect tone to operate.The apparent complexity arises because tones are introduced at different morphological levels (stems and words) and undergo processes specific to that level.The levels interact serially: stemlevel phonology feeds word level phonology and wordlevel phonology feeds postlexical phonology in the way familiar from Lexical Phonology and Morphology and Stratal Optimality Theory (Kiparsky 1982, 2000, 2015; Pulleyblank 1986).
(1) The organisation of morphology and phonology

Stem Phonology
Word Phonology Postlexical Phonology Phonology applies inside out in tandem with morphology, and later processes can make earlier processes opaque.Downstep turns out to provide key evidence that helps unlock the apparently complex tone system and its interaction with morphology.
The article is structured as follows.§2 gives a brief sketch of Dagaare morphology that serves as a backdrop for the subsequent phonological analysis.§3 introduces downstep.§ §4-6 divide the tone alternations into stem, word and postlexical pro cesses.The phonological generalisations are stated in terms of informal rules intended to serve as a descriptive lingua franca readily understood by phonologists.§7 proposes an analysis in terms of Stratal Optimality Theory that instantiates the organisation shown in (1) and correctly derives many of the descriptive generalisations.§ §8 and 9 discuss alternative hypotheses and residual problems.§10 concludes.

Inflection
Dagaare is a suffixing language where nouns inflect for number/class and verbs inflect for aspect. 1 The number/class suffix immediately follows the noun root which determines the choice of the suffix allomorph and its phonological shape.In class (2a), the singular adds a vowel to the root (Anttila & Bodomo 2009).The plural is marked by /ri/ or /rɪ/, depending on ATR harmony, and the root vowel is lengthened if high.In class (2b), this pattern is inverted.The singular is marked by /ri/ or /rɪ/ and the root vowel is lengthened or diphthongised, this time in a lexically conditioned manner.The plural is marked by /e/ or /ɛ/ depending on ATR harmony.The tonal behaviour of the suffix depends on the root tone in a way to be explained below.Grimm (2021) proposes that the choice between (2a) and (2b) correlates with the lexical semantics of the root.The upshot is that the root conditions the suffix in two ways: lexically/semantically (choice of allomorph) and phonologically (ATR harmony and tone).
The imperfective aspect suffix /rV́/ also immediately follows the verb root and undergoes both ATR and rounding harmony.Consider the verb paradigms in (3): (3) The suffix /rV́/ copies the root vowel except that a high vowel becomes mid: dàà rá 'buyIPFV' vs. búúrò 'measureIPFV', tárà 'reachIPFV' vs. kʊ ̀rɔ ́'giveIPFV'.Root vowel length is lexically conditioned.In (3a), the vowel lengthens if low or high and diphthongises if mid.In (3b), there are no alternations.In (3c), the vowel undergoes shortening and ablaut: /gààrV́/ → gɛ ̀rɛ ́'goIPFV'.There is no obvious phonological or semantic rationale behind the threeway choice which seems to be simply a lexical property of the root.Any analysis of Dagaare phonology must find a way of dealing with such lexically specific alternations.
In sum, both the number/class and imperfective suffixes appear immediately after the root and interact with the root in multiple ways: lexically, semantically and phonologically.This is typical stemlevel behaviour.

Enclitics
Enclitics are phonologically part of their host but syntactically separable and show no morpholexical conditioning.An example from Dagaare is the postverbal focus particle lá, which has an underlying H tone. Its regular location is after the inflected verb, immediately after the aspect suffix, but it can be separated from it by light object pronouns.Such pronouns are underlyingly toneless.They are probably themselves enclitics, an assumption we will make but will not attempt to defend here.Subject and object are only distinguished in the first person singular N vs. ma.A light pronoun recipient intervenes between the inflected verb and lá as shown in (6).If both the recipient and the theme are light pronouns, both can be sandwiched between the inflected verb and lá as shown in (7) where the resulting clitic cluster /ma=ʊ/ 1SG=3SG coalesces into [mʊʊ], with some tonal variability.Alternatively, and perhaps preferably, the serial verb construction in (8) is used.The focus particle lá is thus always the rightmost element of the verb and occurs outside both suffixes and (other) clitics.The phonological dependence of lá on the verb is not reflected in vowel harmony because /a/ does not participate in ATR harmony (pace Ozburn et al. 2018).Instead, we will see tonal evidence for the dependence of lá on the verb shortly.
To complete the picture, tense and negation are expressed as preverbal parti cles that appear to be independent words.Tense particles include /dà/ 'PAST', /záà/ 'ONE.DAY.PAST' and /dáá/ 'TWO.DAYS.PAST'.The negation particle is /bá/ 'NEG', the unmarked future is /nǎ/ 'FUT' and the negative future is /kʊ̌ŋ/ 'NEG.FUT'. 3The two future particles are phonetically low but carry a trailing H tone that interacts with the following verb tone as we will see in a moment.Other preverbal particles seem to have no special tonal effects.
In sum, the focus marker lá comes after the inflected verb and any other enclitics.Unlike suffixes, lá appears to have no morpholexical conditioning.It is syntactically separable from the inflected verb by light object pronouns but phonologically depen dent on it as we will see shortly.This is typical clitic behaviour.The two morphological levels, stem level vs. word level, correspond to affixes vs. enclitics, and suffixes come before enclitics.This is exactly the linear ordering expected in a stratal grammar.

Compounds
Compounding is productive in Dagaare (BendorSamuel 1971: 172; Bodomo 1997: 49) Are compounds formed at the stem level, at the word level, or postlexically?The fact that (12) means 'bad child follower', not 'follower of a bad child', suggests the rightbranching structure [ bì [ fà [ túúró ]]], where túúró 'follower' is modified by fà 'bad', which in turn takes bì 'child' as its complement.This implies that inflectional morphology happens inside compounds. 4The fact that ATR harmony often fails in compounds, as in yízɪ ̀ɪ̀ rɪ ́'red houses' and bìdɔ ́ɔ́' son', where the first part is [+ATR] and the second part [−ATR], suggests that compounding cannot happen at the stem level where ATR harmony is regular, yet there are individual compounds where ATR harmony is possible.We will later present tonal evidence suggesting that compounding happens at the word level.A more rigorous study of Dagaare compounds is much needed.Kennedy (1966: 42) was the first to observe that Dagaare has 'two levels of the register type and a downstepped high unit' and that the TBU is the syllable. 5In addition to H and L, a downstepped !H is possible after a H tone, resulting in a threeway surface contrast after H as illustrated in (13).These examples illustrate some key tone alternations.In (13a), the suffixal H spreads to the toneless root resulting in a level H tone.In (13b), a H root combined with a LH suffix sets the L tone afloat, triggering downstep on the suffix.In (13c), the suffixal H undergoes dissimilation after a H root (Meeussen's Rule) resulting in a HL sequence.In (13d), the root and suffix tones simply combine with no alternation.

Downstep
Before proceeding, it is necessary to establish why !H is not a midtone.First, !H is only possible after H. Positing a M tone would predict a wordinitial contrast H vs. M vs. L which is not found in Dagaare (Kennedy 1966: 43).Second, Dagaare is a 'terracedlevel' language (Welmers 1959; Winston 1960; Clements 1979; Connell 2011) where each downstep sets a new ceiling for subsequent H tones.The downstep analysis predicts that a !HH sequence should surface with level pitch, which is correct.Analysing downstep as M would predict a pitch rise, which is incorrect. 7(14) a. kpá̰ á̰ !ʊ̰ ǵuineafowlSG yírì houseSG 'It is these things that he wants.'While some downsteps are underlying, we will see that others arise by the final lowering of a wordfinal H tone (Gussenhoven 2004: 110-113; see Childs 1995: 48 for Kisi).Our proposal is that underlying downsteps are introduced at the stem level, whereas final lowering occurs at the word level.The number of downsteps is in principle unlimited in an utterance (cf.Rialland & Somé 2000, 2011  In both examples, the first downstep comes from wordfinal lowering, and the second downstep arises from an underlying L tone (/nǎ/ = LH 'DEM', /sʊ̰ ́ɔ̰ ŋ/ = HL 'rabbit').8Only one downstep per word is allowed, however.In cases where multiple downsteps might be expected to arise within a word, the leftmost one wins, an effect we will attribute to level ordering.

Stemlevel tone
Dagaare has the stemlevel processes in (17); see Kenstowicz et al. (1988)  The singular and plural have an underlying H suffix which surfaces as H in (19a), dissimilates to L by Meeussen's Rule in (19b) and spreads to the toneless root in (19c).9In the compound, the roots H and L surface intact, but toneless roots become low by default.
Dagaare systematically distinguishes between nominal and verbal tones at the stem level.Toneless nominals (nouns and adjectives) get a tone by H spreading from the suffix, but there is no H spreading in toneless verbs.Instead, we get the default low, just like in compounds.This is particularly clear in nominalisations (Anttila & Bodomo 2019).Consider the contrast between the imperfective /rV́/, which is a verbal suffix, and the homophonous agentive /rV́/, which is a nominal suffix (cf.In compounds, the suffix H only spreads to the immediately adjacent toneless root.Toneless roots further to the left remain toneless and receive the default low (cf.Kennedy 1966: 45).This suggests that H spreading is a stemlevel process that does not extend to compounds, which are formed at the word level.The source of the downstep is the root /kʊ ́ɔr / in ( 22) and the plural suffix /mǎ/ in (23).This can be seen by placing the roots before a H adjective such as /wóg/ 'long, tall'.The root /kʊ ́ɔr / 'farmer' triggers downstep, whereas the root /sá̰ á̰ / 'stranger' does not.
(24) a.Where does the downstep on fáá 'bad.SG' come from?The noun cannot be its source: /yí/ 'house', /kyúú/ 'moon' and /wɛ ǵ/ 'log' must be underlyingly H because their number/class suffix undergoes Meeussen's Rule (HH → HL), yielding yírì 'houseSG', kyúúrì 'moonPL' and wɛ ́grɪ ̀'logPL'.If the nouns were underlyingly HL, we would incorrectly predict downstep on the number/class suffix: *yí !rí, *kyúú !rí, *wɛ ́g !rɪ ́.The adjective itself can also be excluded as the source of downstep.This becomes evident when we embed 'bad' in a compound where it reveals its underlying tone: (27) à DEF bìbìlfàwóg childsmallbadtall.SG !ná DEM 'that bad tall toddler' The three initial roots bìbìlfà have the corresponding singular forms bíé 'child.SG', bílé 'small.SG' and fáá 'bad.SG', where the H tone comes from the number/class suffix.In the compound, where there is no suffix, they receive the default low, showing that all three roots are underlyingly toneless (/bi/ 'child', /bil/ 'small' and /fa/ 'bad'). 10he downstep on fáá in ( 27) must thus have some independent source.Our proposal is that a wordfinal H undergoes automatic downstep.This is stated as the informal rule in (28), which introduces a floating L after a H tone before a wordfinal H tone.
The rule portrays stemlevel and wordlevel downsteps as materially the same: both involve a floating L tone.The difference is that stemlevel downsteps arise from underlying L tones that belong to some morpheme, whereas wordlevel downsteps arise from epenthetic L tones that have a structural origin. 11 Despite their different sources, the two types of downstep are impressionistically indistinguishable and occur at the same location in the surface string.This is illustrated in (30) by 'sheep', 'sheep skinner' and 'bad sheep'.The downstep in (30a) 'sheep' is underlying and comes from the suffix: H + LH = H(L)H.The downstep in (30b) 'sheep skinner' and (30c) 'bad sheep' is structural and results from wordfinal lowering: ∅ → (L) / H H] Word .Note that even though the downstepped H tone in (30b) is not on the final syllable, it is still the final autosegmental H.
The structural downstep is restricted to the word edge.In (31a)-(31c), the word final H undergoes downstep.In (31d)-(31f), the wordfinal tone is L, and the preceding H tones surface with no intervening downsteps.
An anonymous reviewer suggests that instead of wordfinal lowering, the downstep in compounds might be a morphological linking element L parallel to the associative H in Etsako and Bini (Akinlabi 1996: 259-272).That seems unlikely: there is no evidence for a linking L in the compoundinternal sequences HH and HHH (31d)-(31f).Only the final H is downstepped, suggesting that the downstep is not a morpheme but has a structural origin.
Wordfinal lowering also applies to enclitics.The focus marker lá, which has an underlying H tone, encliticises to the verb and undergoes downstep.12(32) a.The tonal configurations are shown in (34).We get downstep on !lá in (34a), but not in (34b), where it is preceded by the earlier downstep on !rí. 1334) a. bùrí This leaves us with the question of why it is the downstep on the left, i.e. the underlying floating tone, that blocks the downstep on the right, i.e. wordfinal lowering.Just saying that the leftmost downstep must be realised would provide no rationale for the asymmetry.One natural hypothesis is level ordering: the stemlevel downstep in bú !rí is privileged because it is 'old' (derived earlier), whereas the word level downstep is dispensable because it is 'new' (derived later). 14inally, Dagaare shows evidence for the common process of tone absorption that simplifies LHH sequences (Hyman & Schuh 1974: 90-91) and is also found in the related Buli (AkanligPare & Kenstowicz 2002).In Dagaare, tone absorption appears with the intransitive perfective suffix /èé/ followed by /lá/.The verbs are /kúl/ 'go home' (H) and /di/ 'eat' (toneless).The intransitive perfective and the future (to be discussed below) are the only environments where we have observed tone absorption so far.In /kúlèé/, the suffix triggers a stemlevel downstep on itself which blocks the wordlevel downstep on lá.In /dièé/, the suffix H simply vanishes: it is 'absorbed' into the clitic H.The process can be described by the informal rule in (37): (37) Tone Absorption: LHH → LH Note that in (36a), downstep at the stem level yields kú !léé, bleeding tone absorp tion.This implies that tone absorption is either wordlevel or postlexical.
The nature of tone absorption is not clear to us.Various possibilities are discussed by Hyman & Schuh (1974: 91).An anonymous reviewer notes that in related lan guages, contour tones are often only allowed wordfinally or phrasefinally, providing a possible phonological motivation for tone absorption here.This is consistent with our proposal that contours are not allowed in the lexical phonology of Dagaare and an underlying LH is repaired by tone absorption.We must leave the analysis of tone absorption for future work.

Postlexical tone
The postlexical level introduces no new cases of dissimilation or downstep.A H##H sequence with a word boundary between the two H tones surfaces with level pitch.The key tone alternation at the postlexical level involves the three preverbal particles /nàá/ 'EMPH.FUTURE', /nǎ/ 'FUTURE' and /kʊ̌ŋ/ 'NEG.FUTURE'.All three have an underlying LH tone.The vowel sequence in nàá accommodates the entire LH tone.In contrast, the short vowels of nà and kʊ ̀ŋ leave the H component floating and subject to deletion except in suitable contexts to be discussed below.The majority of Dagaare verbs are HL, H or toneless.Before HL and H, the trailing H is simply absorbed, but before a toneless root, it docks onto the verb (Kennedy 1966: 47-48) This is explained by level ordering: the H H] Word sequence was created postlexi cally, counterfeeding final lowering, which applies at the word level.
Another case of opacity emerges in the imperfective paradigm.Recall that the imperfective is realised as the stemlevel suffix /rV́/ with an underlying H tone.The stemlevel status of the /rV́/ suffix is evident from the fact that it undergoes Meeussen's Rule (HH → HL) after H roots, e.g./dʊ ́grV́/ → dʊ ́grɔ ̀'brewIPFV'.Now, consider a toneless verb with the H imperfective suffix: (44) digre H 'chaseIPFV' Adding the preverbal future particle /nǎ/ results in a HH sequence across a stem suffix boundary, but Meeussen's Rule does not apply.Again, this is explained by level ordering: the HH sequence was created postlexically, counterfeeding Meeussen's Rule, which applies at the stem level.The downstep on !lá is also predicted: the stemlevel ré triggers wordlevel downstep because stemlevel phonology feeds wordlevel phonology.
In addition to its postverbal uses, the focus particle lá 'FOC' also encliticises to fronted subjects in cleft sentences, but for some reason this time without downstep.The absence of downstep in this context remains an outstanding puzzle.It would be expected if the sequence ʊ ́nɔ ́lá were created, not at the word level, but postlexically, since postlexical phonology counterfeeds wordlevel phonology, but at this point we do not have independent evidence for such an assumption.
Finally, downstep may surface between words if it is underlying.Consider the underlyingly LH demonstrative pronoun nǎ 'that', which triggers downstep on itself: (47)

Preliminaries
The preceding sections have laid out the empirical generalisations in terms of informal rules.We now take the first steps towards deriving them from general principles in Stratal Optimality Theory (Kiparsky 2000(Kiparsky , 2015)).The key observation is that morphology plays an important role in Dagaare tone.Recall the main generalisations: (49) To simplify presentation, we start by identifying four highranked constraints.This allows us to simplify subsequent tableaux by omitting the candidates that violate them.The first constraint guarantees that root tone values cannot be changed.We will generalise this constraint to impose faithfulness to material inherited from the previous level: IDENT(T)ROOT applies at the stem level; IDENT(T)STEM applies at the word level; and IDENT(T)WORD applies at the postlexical level.Giving privileged status to 'old' material through faithfulness in this way is reminiscent of the familiar principle of the cycle.Making *CONTOUR undominated guarantees that a syllable (TBU) can be associated with at most one tone.This seems like a reasonable null hypothesis that is not obviously contradicted by anything in the phonological system as a whole; see fn. 5 for alternative analyses.

Stemlevel tone
Here are the six constraints that play a key role in Dagaare tone alternations: 'Tone values (H, L) cannot be changed' OCP(H) (e.g.Hyman 2011: 1096) triggers dissimilation at the stem level.17The tableau in (52) derives Meeussen's Rule.We use comparative tableaux (Prince 2002a, 2002b; McCarthy 2008: ch. 2), where losing candidates have their constraints labelled W for 'favours the winner' or L for 'favours the loser'.
(52) Meeussen's Rule: yírì 'houseSG' A ranking is guaranteed to work (i.e. to make the desired winner optimal) if all Ls are dominated by some W. A comparative tableau is useful for making ranking arguments because it transparently shows the necessary rankings.In this case, Meeussen's Rule requires that OCP(H) ranks above IDENT(T), as shown by loser (52a), and that either DEP(T) or *FLOAT rank above IDENT(T), as shown by loser (52b).The constraints are neither totally ranked nor totally unranked: the ranking is genuinely partial.The dashed vertical lines between constraints are used simply for convenience.We highlight harmonically bounded candidates (i.e.candidates that only have Ws) by greying out the entire row.The fact that dissimilation applies to suffixes, not to roots, is guaranteed by ranking IDENT(T)ROOT above OCP(H).
Meeussen's Rule applies even when the suffix is simply H. Consider /kúlíH/ 'go homePFV'.The candidate *kúlì is ruled out because of the highranked IDENT(T) ROOT. 18This leaves us with three candidates, none of which violate IDENT(T)ROOT, since they remain H. Since the root must remain H and inserting a medial downstep (L) is not an option at the stem level due to the ranking DEP(T) ≫ {*SPREAD, IDENT(T)}, the result is dissimilation.The suffix H becomes L but remains floating, correctly predicting downstep on a following /lá/ 'FOC' at the word level.Examples where the downstep on /lá/ 'FOC' does not arise from a suffix but wordfinal lowering will be presented in the next section.Finally, recall that at the stem level, we observed a difference between nouns and verbs in toneless roots: the suffix H spreads in nouns but not in verbs where the root remains toneless and receives a low tone at a later level, to be discussed shortly.We derive this by positing two minimally different COPHONOLOGIES within the stemlevel grammar, in this case different rankings of *TONELESS and *SPREAD, following e.g.Anttila (2002) and Inkelas & Zoll (2007); see Jenks & Rose (2011, 2015) and Sande et al. (2020) for an extension of cophonologies to the phrasal domain.

Wordlevel tone
Wordlevel tone differs from stemlevel tone in two ways.First, HH sequences do not dissimilate (Meeussen's Rule) but instead trigger floating L insertion (downstep).Second, there is no H spreading.The required rankings are visible in the tableau in (59), which derives the wordfinal downstep in bùrí= !lá 'soak.PFV=FOC'. 2020 An anonymous reviewer brings up the possibility that the difference between stems and words might be prosodic.Perhaps root-affix combinations correspond to nonrecursive prosodic words and wordclitic combinations to recursive prosodic words.It is not clear to us how such an analysis would differ empirically from ours.We would still need a twoway distinction grounded in morphology.
At the word level, OCP(H) and IDENT(T) must rank above both DEP(T) and *FLOAT, and *SPREAD must rank above *TONELESS.Changing the perfective H to L would violate the highranked IDENT(T)STEM, which requires faithfulness to 'old' material -here the output of the stemlevel phonology -as would any other change in the stemlevel tones. 21Inserting a H tone on the root would violate OCP(H).Note that IDENT(T)STEM is not violated by the spreading in (59c) because the root syllable is toneless and without tone value.Instead, (59c) is ruled out by *SPREAD.
The tableau in (60) shows that nothing happens to the stemlevel kúlí(ˋ) 'go.home.PFV' with a trailing (L) when combined with /lá/ 'FOC' at the word level.IDENT(T)STEM maintains the stem tone H(L), and any change would make things worse.
The 'old' stemlevel downstep survives by satisfying the highranked IDENT(T) STEM.Inserting a 'new' wordlevel downstep is blocked by * !H ! H, implying that this constraint must be ranked above OCP(H).Dissimilating the clitic to L is ruled out by IDENT(T) ≫ OCP(H).
In compounds, H spreading is limited to one root and never crosses compound boundaries.Roots further to the left remain toneless.The analysis predicts that the initial syllable of bìtúúró 'child follower' is lexically toneless.Its low pitch must thus have a postlexical or phonetic origin.The evidence will be presented in the next section.
Finally, in our preliminary rulebased description, we stipulated that downstep is inserted before a wordfinal H tone preceded by a H tone: ∅ → (L) / H H] Word .This results in a downstep in pɪ ́! sɪ ́ɪ́ rɛ ́'sheep skinner' but not in pɪ ́nɛ ́nɪ ̀'mutton'.It is not clear to us why such a restriction should hold.In the OptimalityTheoretic analysis, we must similarly assume that OCP(H) only applies to a sequence of two H tones at the right edge of a constituent, suggesting that we should rename the constraint OCP(H)]. 222 An anonymous reviewer suggests several interesting alternative formulations. On is 'to posit an explicit constraint requiring that the last tone in a domain is lower than the preceding tone (final lowering, vacuously satisfied by HL).[M]any languages have something like this (see, e.g., Liberman & Pierrehumbert 1984 on English and Laniran 1992 on Yoruba).'

Postlexical tone
The postlexical tone of Dagaare is relatively inert compared to related languages such as Moore (Kenstowicz et al. 1988) and Dagbani (Hyman 1993; Hyman & Olawsky 2004) where we see extensive rightward tone spreading across words.
The fact that H##H sequences survive intact across word boundaries implies that either *FLOAT or DEP(T) dominates OCP(H) in the postlexical phonology.The violations are shown in (65).The highranked IDENT(T)WORD keeps the wordlevel 'old' tones intact.The H docking simultaneously satisfies *FLOAT and *TONELESS.The winner vio lates OCP(H), but that cannot be helped.Dissimilation (Meeussen's Rule) is not an option in the postlexical phonology because the highranking IDENT(T)WORD rules out *nà dígrè.Changing the floating H to L would eliminate the OCP(H) violation but is ruled out by the ranking IDENT(T) ≫ OCP(H).The analysis correctly associates the trailing H tone from the future particle with the toneless syllable in the following verb root.Note that there is no general compulsion to fill toneless syllables by tone spreading from neighbouring syllables.This restriction is not yet accounted for under the present analysis.The editor suggests adding the ranking *SPREAD ≫ *TONELESS into the postlexical phonology, which would correctly block spreading into toneless syllables.Exploring the consequences of this additional ranking elsewhere in the data must be left for future work.
After H docking, the verb surfaces with a level HH tone with no intervening downstep.This provides evidence that the verb must have emerged as ∅H from the word level.If dìgré had been LH, we would have expected the root L tone to block H docking, or else the L would have been dislodged, triggering a downstep on the suffix: *nà díg !ré.Neither happens.We conclude that at the word level, the verb root remains toneless and receives a L tone in the postlexical phonology in virtue of an additional ranking *TONELESS ≫ DEP(T) or alternatively receives a default low pitch in the phonetics.Both analyses correctly predict that the low tone is phonologically inert and does not feed any phonological alternations.

Are cophonologies necessary?
We have seen that H spreads from suffixes to toneless roots in nouns but not in verbs: We derived this by positing two minimally different cophonologies within the stem level: *TONELESS ≫ *SPREAD for nouns and *SPREAD ≫ *TONELESS for verbs.An anonymous reviewer suggests an alternative: perhaps nominal affixes belong to the stem level and verbal affixes to the word level.This would immediately yield the right result, since H spreading is possible at the stem level but not at the word level.It would also simplify the analysis by eliminating levelinternal cophonologies.For an analogous approach to Korean noun-verb asymmetries, see Yun (2009).
The problem is that there is no independent evidence for separating nouns and verbs to different levels in Dagaare.Affix ordering provides no such evidence: verbal suffixes do not occur outside nominal suffixes.Nouns and verbs also share many phonological alternations, including lexically conditioned vowel lengthening, vowel harmony and tone dissimilation (Meeussen's Rule), all located at the stem level.Indeed, they only differ in H spreading.Postponing verb inflection to the word level would require us to replicate these processes at two separate levels.The opposite ordering, i.e. locating verbs at the stem level and nouns at the word level, as in Yun's (2009)   In addition, we get at least two more patterns: (80) ʊ ̀kʊ ́=mʊ ́=ʊ ́=! lá (81) ʊ ̀kʊ ̀=mʊ ́=ʊ ́=! lá Despite this variation, the focus clitic lá is always H, and there is always one downstep somewhere within the clitic sequence.A more systematic exploration of these patterns of variation is clearly needed.
Finally, we have not mentioned trisyllabic and longer words.Such words are often compounds but some seem simplex, e.g.tákóró 'windowSG', kùnkúní 'tortoiseSG' and fɪ ̀ntɪ ́lɛ ̀'lampSG'.In general, the same tonal processes apply and our analysis generalises to these longer words under the assumption that the initial syllable is simply ignored.A detailed analysis must be left for future work.

Conclusion
Dagaare is a twotone 'terracedlevel' language with nonautomatic downstep.There are two main analytical challenges: tone alternations are often triggered or blocked by morphological and lexical conditions and downstep has at least two sources: lexical and structural.We have shown that the apparent complexity arises because tones are introduced at different morphological levels (stems and words) and undergo processes specific to that level.The levels interact serially: stemlevel phonology feeds word level phonology and wordlevel phonology feeds postlexical phonology as in Lexical Phonology and Morphology and Stratal Optimality Theory.Phonology applies inside out in tandem with morphology and later processes can make earlier processes opaque.Downstep provides key evidence that helps unlock the apparently complex tone system and its interaction with morphology.
are very bad' 16 he who has come again'

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60) kúlí= !lá 'go.home.PFV', where perfective = H multiple downsteps follows from the highranked constraint in (61): (61) * !H ! H 'No multiple downsteps within a word.'This constraint licenses at most one downstep in a word, but does not stipulate its location.The left-right asymmetry by which a stemlevel downstep blocks a word level downstep falls out from level ordering.The tableau in (62) shows this for bú !rí=lá 'soak.PFV=FOC'.(62) No multiple downsteps within a word compounding occurs at the word level.At the stem level, the root /tu/ 'follow' combines with the suffix /rV́/ 'AGENTIVE' yielding the simple word túúró 'follower'.Compounding adds roots to the left edge of this word.If they are toneless, they remain so, because H spreading is no longer an option.The tone of túúró 'follower' was derived at the stem level and remains intact given the highranked IDENT(T)STEM.(64) No H spreading in compounds at the word level / bi[túúró H ] / IDENT(T) OCP(H) *SPREAD DEP(T) *TLESS *

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dɔ ́ɔ́# # pɔ ́gɔ ́→ dɔ ɔ́p ɔ ǵɔ ́'man's woman' / dɔ ɔH pɔ ́gɔ H / IDENT(T) *TLESS DEP(T) *FLOAT OCP(H) a. dɔ ɔH pɔ ́gɔ HThe only postlexical alternation for which we have robust evidence is the pairing up of toneless syllables and trailing H tones.This involves the LH morphemes /nǎ/ 'FUT' and /kʊ̌ŋ/ 'NEG.FUT', whose H tone docks onto a toneless verb root across a word boundary.(66)nǎ digré → nà dígré 'FUT chaseIPFV' , multiple tone linearisations are possible, perhaps depending on the speech rate.One tone linearisation for 'S/he gave it to me' is given below, with a hypothetical derivation . Nominal compounds typically consist of two roots, of which the second is inflected for number/class.Consider the following four compounds: Anttila & Bodomo (2009)n Moore.Each process has morphological or lexical conditions.Evidence for the tonelessness of roots like (18c) comes from noun-adjective compounds where the noun root surfaces without a number suffix.For the vowel alternations, seeAnttila & Bodomo (2009).
Dagaare roots can be toneless (= ∅), L, H, HL or LH, except that there seem to be no L verbs.Suffixes are usually H but can be LH.Examples of L, H and toneless roots are given in (18).H roots exhibit Meeussen's Rule; toneless roots exhibit H Spreading.
Most verbs are toneless, H or HL, but there are a few LH roots that trigger downstep on themselves.One such verb is /tàá/ 'have'.The H tone on the subject ʊ ́is the exponent of the hortative construction.
(Leben 2018)ave it.'5.Wordlevel toneDownstep can come from a variety of sources(Leben 2018).Dagaare stemlevel downsteps illustrate one common source: an underlying floating L wedged between H tones(Clements & Ford 1979; see Pulleyblank 1986: 34for Tiv).However, the downstep systematically present in compounds requires a different explanation: However, wordlevel downstep fails to materialise if there is a downstep earlier in the word.This ban on two downsteps in the same word can be seen by contrasting /buri/ 'soak' (toneless) and /búrì/ 'fetch' (HL).The verbfinal H is the perfective suffix.
. The toneless verb /gaa/ 'go' illustrates H docking: the verb surfaces with the default L after nàá, but with the trailing H after nǎ.Similarly, the toneless /buri/ 'soak' receives the default low after the negation particle bá, but the trailing H after the negative future kʊ̌ŋ.
The role of morphology in Dagaare tone a. Downstep is underlying at the stem level and structural at the word level.b.At the stem level, HH undergoes dissimilation (Meeussen's Rule).c.At the stem level, nouns and verbs differ in tone spreading.d.At the word level, H=H undergoes structural downstep (Final Lowering).e.At the postlexical level, H##H survives intact (no alternation).f.Only one downstep per word is allowed.g.Stemlevel downstep blocks wordlevel downstep.
analysis of Korean, fails for straightforward empirical reasons.It would incorrectly allow H spreading in toneless verbs once they reach the word level, but as It is as if the perfective H tone were realised one syllable too late, not on the verb but on the enclitic.Instead of *ngmɛ ́=! ʊ ́=lá, we get ngmɛ ̀=ʊ ́=! lá.The wordfinal downstep is as expected, as illustrated below.