2.1. Language and data

Laal is a language isolate spoken by about 800 people in Gori and Damtar, two villages along the Chari river in southern Chad, as well as in urban centres such as Sarh and N'Djaména. Prior work on the language was undertaken in the 1970s by Pascal Boyeldieu, who published a preliminary description of the sound system (Boyeldieu Reference Boyeldieu1977), as well as a description of the nominal and verbal systems (Boyeldieu Reference Boyeldieu1982, Reference Boyeldieu1987) which includes the first description of the M-lowering patterns described and analysed in this paper.

Unless explicitly stated, all the data presented in this paper come from my own fieldwork: about eighteen months between 2010 and 2020, with multiple speakers of various ages, both male and female, mostly in Gori, as part of a language documentation project funded by the DOBES (Documentation of Endangered Languages) program of the Volkswagen Foundation. Speaker participation and informed consent were obtained in accordance with IRB protocols #2011-03-3000 (University of California, Berkeley) and #10346 (Princeton University).

The data collected during the documentation project are archived and openly accessible as part of the DOBES collection in The Language Archive, hosted by the Max Planck Institute for Psycholinguistics in Nijmegen.Footnote ¹ Examples taken from archived text recordings are duly referenced. Examples without references are taken from my field notes or lexical database.

2.2. Phonological sketch

The 24 contrastive consonants and 12 contrastive vowel qualities of Laal are presented in (4). The stop inventory is reduced outside of the stem-initial position to one series of plain stops underspecified for voicing, realised as voiced word-internally, voiceless (and often unreleased) word-finally. The vowels /ia ua yo ya/ are most of the time realised as diphthongs, and are therefore systematically transcribed as such, but phonologically they are monomoraic vowels behaving exactly like /ɛ ɔ ø œ/ respectively. The low peripheral vowels /ia ua/ and the three front rounded vowels are attested only in stem-initial position. Finally, length is contrastive for all twelve vowel qualities, but in stem-initial position only. Length is transcribed by doubling the vowel, or the last vowel of a digraph, e.g. /aː/ = /aa/, /iaː/ = /iaa/.

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Laal requires every syllable to start with an onset. Vowel-initial syllables in stem-initial position are always realised with a prothetic glottal stop, which is otherwise not contrastive in the language. Attested syllable structures are CV, CVV, CVC, CVVC, where VV stands for a long vowel. No vowel sequences are allowed – the diphthongised vowels /ia ua yo ya/ are not phonologically vowel sequences or diphthongs, but single, monomoraic vowels phonetically realised as diphthongs.

Laal is characterised by strong stem-initial prominence (Lionnet and Hyman Reference Lionnet and Hyman2018: 651–655 and references therein), mostly of a distributional nature: the number of consonantal and vocalic contrasts is much greater stem-initially than elsewhere, as shown in (4) above. The stem is defined as a lexical root and any suffixes attached to it (there are no prefixes). Most morphological words involve only one stem, e.g. /nō/ ‘person’, /gùm-ál/ ‘melon-sg.’Footnote ² The very few multi-stem words consist of frozen compounds such as /gàà+kɨ̀rà/ ‘Pluvianus aegyptius (bird sp.)’, and reduplicative forms such as /cī+cām/ ‘today’ or /sí+sáál/ ‘bird of prey sp.’ Stems in Laal are maximally disyllabic. When a suffix is added to a disyllabic root, the second vowel of the root is deleted in order to avoid creating a trisyllabic stem, e.g. /tuágár-àn/ $\rightarrow$ tuágràn ‘break it’.Footnote ³

Two morphophonological strata can be identified in Laal. Stratum 1 suffixes include number-marking suffixes on both nouns and verbs, the deverbal suffix (e.g. pāj ‘be painful’ $\rightarrow$ pāj-āl ‘pain’), and the denominal suffix deriving nouns referring to ethnic or cultural characteristics (e.g. ndààm ‘Ndam (village name)’ $\rightarrow$ ndààm-ál ‘characteristic of the Ndam people’). All other inflectional and derivational suffixes belong to stratum 2: alienable possessive suffixes, object suffixes, gerund, ventive, associative, medio-passive, and passive, all of which will be illustrated and discussed in the paper. This is summarised in Table 1. These strata are defined by different morphophonological processes, or the application of the same processes under different conditions – in particular the vowel harmony processes discussed below. Stratum 1 morphophonology is mostly irregular and unpredictable, in contrast to stratum-2 morphophonology, which is extremely regular and knows no exception.

Table 1. Laal suffixes by stratum

Three vowel harmony processes are attested in Laal: perseverative [+high] harmony, anticipatory [ $\pm$ low] harmony, and anticipatory rounding harmony, illustrated in (5), (6), and (7) respectively.

1. (5)

   

The final /r/ of /-Vr/ suffixes is realised as [l] when following a stem ending with /l/.

1. (6)

   

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Rounding harmony applies unconditionally only in stratum-2 morphophonology (mostly verbal morphology). In stratum 1 (mostly number marking morphology on nouns and verbs), it applies under very strict conditions: the target vowel must be in the vicinity of a labial consonant, and the trigger and target vowels must be of equal height and [front] specifications (cf. Lionnet Reference Lionnet2017).

Finally, Laal has three contrastive tone heights: high (H), mid (M), and low (L), illustrated in the minimal triplet in (8) below.

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The tone-bearing unit is the mora, as shown by the fact that bitonal patterns are only found on CVV and CVR syllables (where R stands for sonorant), and the only case of a tritonal pattern attested on a monosyllabic stem is bòôr ‘pigeon sp.’, a trimoraic CVVR syllable.Footnote ⁶ As is shown in the next section, the three tones can combine into a limited number of stem-level patterns. The distribution of tones as well as aspects of the morphotonology of the language point to a marked status of the M tone, as compared to both H and L. This is the object of the next two sections.

4.1. Morphophonological M-lowering

Whenever a non–M-toned suffix is added to a M-toned root, the M tone is systematically changed to L. This lowering applies to avoid creating a complex stem-level tone pattern involving a M tone, i.e. to comply with the phonotactic constraint described above. This is illustrated in (10) with three suffixes carrying the three most frequent suffixal tone patterns: H, L, and LH.Footnote ¹¹

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As seen, the M tone of the verb root is systematically changed to L, irrespective of the nature of the following tone: H in (10a), L in (10b), LH in (10c). Only M tones are affected, as shown by the stability of H- and L-toned roots in (11).

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M-lowering applies with all stratum-2 suffixes (except the gerund and passive suffixes, whose tone is replacive; see §6.2): object suffixes as in all the above examples, but also inalienable possessive suffixes on nouns (both H-toned as in (12a) and L-toned as in (12b), associative as in (13), mediopassive as in (15), and ventive as in (14).Footnote ¹²

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The stem initial vowel shortening in nìnráŋ (instead of *nììnráŋ) is regular, and applies in to comply with a stratum-1 phonotactic constraint against *VVCC sequences, i.e. against non-final CVVC syllables.

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Note that M-lowering applies with both transitive and intransitive verbs (e.g. ‘swim’ in (13c) and (14c), and with suffixes that are not related to transitivity, such as the associative and ventive. M-lowering is thus not related to transitivity or argument structure, or in general to any morphosyntactic category. It is a general phonological operation that applies without exception in stratum-2 morphophonology.

As mentioned in the introduction, stratum 1 morphophonology is complex and mostly irregular, including in its tonal effects. Suffixation of a number-marking suffix (by far the most numerous stratum-1 suffixes) onto a M-toned root does not always result in lowering of the M to L. Out of 208 nouns that are M-toned in the singular or in the plural, this M pattern corresponds to an L-initial pattern (L or LH) in the other number category in 143 cases (69%; e.g. /kòòg/, pl /kuāg-mī/ ‘bone’, or /siāāg/, pl /sèèg-ú/ ‘milk’), to a M pattern (i.e. no tone change) in 36 cases (17%; /gār-āl/, pl /gə̄r-ī/ ‘Acacia spp.’), and to a H pattern in 29 cases (14%; e.g. /kūr-ā/, pl /kúr-ú/ ‘stick’, or /wúl-ú/, pl /wūl-māny/ ‘Kigelia africana, tree sp.’). That is, despite the relative unpredictability of the tonal alternations involved, no MX or XM pattern is ever created as a result of number-marking (and more generally stratum-1) suffixation. Furthermore, The expected M $\sim$ L alternation is found in over two-thirds of all cases, whereas the unexpected M $\sim$ H alternation accounts for only 14%.

4.2. Morphosyntactic M-lowering

M-lowering is also attested in two morphosyntactic contexts where it does not appear to be an effect of the *MX/XM constraint: on M-toned transitive verbs followed by an in-situ object (§4.2.1), and on the M-toned head of a genitive construction (§4.2.2).

4.2.3. M-lowering as inflectional morphology

Morphophonological M-lowering seems at first sight to be analysable as a syntactically conditioned phonological alternation: in certain specific syntactic contexts – transitive verb followed by its object, genitive head followed by its complement – M is changed to L. I show in this section that this is not the correct analysis. I argue that these two cases of morphosyntactic M-lowering are best analysed as head-marking inflectional morphology, i.e. specific forms of verbs and nouns exponing a specific morphosyntactic feature – in this case, the presence of a complement in situ: object of the transitive verb, genitive complement in a genitive construction, i.e. a form of non-extraction marking (cf. Lionnet Reference Lionnet2015).Footnote ²⁰

Two arguments can be put forth in favour of an inflectional analysis of M-lowering on transitive verbs: adjacency, and morphological systematicity.Footnote ²¹

Surface adjacency is not required between the verb and its object for M-lowering to occur. Indeed, the dative complement or adjunct frequently occurs before the object (this is its preferred position, if it is not too long), as shown in (42b). When it is pronominal, it obligatorily follows the verb, i.e. intervenes between the verb and its object, as in (43).

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The second argument is paradigmatic systematicity: M-lowering is indeed only one of two morphological exponents of this inflectional category, the second one being found with the gerund form. The gerund is a nominalised form of the verb which can be used as an argument as in (44a). It is required after certain aspectual and modal markers: imperfective tāá/tīí˜tēé, prospective ná/ní, itive wáā/wíī, prospective-itive náā/níī, injunctive-itive màá/mìí, counterfactual mɨ̀ná/mìní, and intentional mɨ́nà/mínì (all are number-sensitive: sg/pl). This use is illustrated with the prospective marker ná in (44b). The gerund has two forms: one that is homophonous with the simple form of the verb, used when there is no overt object in situ, as in (44a-i) and (44b-i), and one which is marked with a suffix and used only with transitive verbs followed by an in-situ object as in (44a-ii) and (44b-ii). The marked form of the gerund is used in exactly the same context as M-lowering: this parallelism is briefly illustrated in (44b) and (44c), repeated from (16b).

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This form is derived by the addition of the suffix /-V^L/, which consists of an underspecified vowel realised as a copy of the verb root's final vowel, and a replacive L tone that overwrites the underlying tone of the verb – i.e. all verb roots, irrespective of their underlying tone, are realised with a L tone when combining with this suffix (see §6.2 for more detail). Lexical tonal contrasts are thus completely neutralised in the marked gerund form, as shown in the bottom-right quadrant of Table 3 (cf. §6 for more detail).Footnote ²²

Table 3. Simple and gerund forms

The marked form of the gerund is used with exactly the same function as M-lowering: on transitive verbs with an overt object in situ. Just like M-lowering, it does not occur when the object is topicalised (45) or relativised (46).

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It is not used when the verb is followed by an adjunct locative noun, as in (47a); compare with the effect of an in situ object in (47b).

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Finally, like with M-lowering, the marked form of the gerund is used when a dative complement or adjunct intervenes between the verb and the object, as shown in (48), repeated from (40).

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Both M-lowering and the /-V^L/ suffix are thus exponents of the same inflectional category, in morphosyntactic complementary distribution: M-lowering on simple finite verbs (i.e. non-derived and not otherwise inflected), the suffix /-V^L/ on gerunds. This is summarised in Table 3.

As for M-lowering in the genitive construction, the same argument of paradigmatic systematicity can be used as evidence of its status as inflectional morphology. Indeed, there are ten nouns in Laal which have a specific construct form, usually obtained through truncation of the number marking suffix, and used in exactly the same context as M-lowering:

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Consequently, M-lowering, both in the verb phrase and in the genitive construction, must be analysed as the morphological exponent of a morphosyntactic category. This category can be defined as “non-extraction marking” (or “presence of complement in situ”).

4.3. Interim summary

The three-tone system of Laal displays a number of distributional restrictions on the M tone that the H and L tones are exempt from. The M tone is exclusive, i.e. there is a strong constraint against stem-level tone patterns involving a M tone (*MX/XM, with a few exceptions among function words and recent loanwords). To avoid creating this banned structure, M tones followed by H- or L-toned suffixes are systematically changed to L. Additionally, generalised M-lowering is observed as the exponent of a morphosyntactic category (presence of a complement in situ) in two specific morphosyntactic environments, in the absence of any violation of *MX/XM. This raises at least the following five questions:

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I show in the next section that a subtonal analysis of the Laal tone system offers a unified, straightforward account of all these phenomena.

5.1. Subtonal features

Using Pulleyblank's (Reference Pulleyblank1986: 125) version of Yip's (Reference Yip1980) two-feature model, I propose the following analysis of the Laal tone system:

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Specifically, M is analysed as the higher tone within the lower register, i.e. [–upper, +raised], while the [+upper] register is limited to H, analysed as [+upper, –raised]. Missing from this system is the subtonal specification [+upper, +raised]. This gap is reminiscent of similar segmental gaps (i.e. unattested featural combinations) in phonemic inventories, e.g. cross-linguistically frequent lack of a voiceless bilabial plosive or absence of front rounded vowels (cf. §5.6 for further discussion). This subtonal analysis will be justified in the following sections – in particular (i) the treatment of M as [–upper] and as the only [+raised] tone in the system, and (ii) the analysis of H as [–raised].

I further assume the tone geometry in (52), borrowed from Reference SniderSnider's (Reference Snider1999; Reference Snider2020) Register Tier Theory.

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The two subtonal features [upper] and [raised] are on two separate tiers. They are linked to a Tonal Root Node (TRN), which is a representation of a ‘full’ tone, i.e. H, M or L. The TRN is in turn associated with the TBU, i.e., the mora in Laal. This representation allows for both feature spreading and ‘full tone’ (i.e. TRN) spreading, both of which are necessary to account for the tonology of Laal, as I show in this and the next section.

I do not adopt Snider's features H, L, h, and l here. Indeed, while his two “tone features” H(igh) and L(ow) can be considered to be the exact equivalent of Pulleyblank's (Reference Pulleyblank1986) [+raised] and [–raised] respectively (and Yip's (Reference Yip1980) [+high] and [–high]), his two register features h(igh) and l(ow) are not equivalent to Yip and Pulleyblank's register feature [ $\pm$ upper]. The latter is defined on purely paradigmatic grounds: [+upper] tones are realised within a higher register than [–upper] tones. In contrast, Snider's h and l register features are defined in both paradigmatic and syntagmatic terms: they ‘effect a register shift h = higher and l = lower relative to the preceding register setting’ (Snider Reference Snider2020: 25, emphasis mine; see also pp. 151–153). This definition allows Snider to account for downstep and upstep phenomena with register features. Since downstep is not at issue here, I prefer to adopt a purely paradigmatic definition of the register feature.

5.2. Morphophonological M-lowering as [–raised] assimilation

Within the subtonal feature system proposed in (51) above, I propose to analyse M-lowering as the result of one simple process: [–raised] agreement/assimilation, which applies in response to a stem-internal constraint against sequences of disagreeing [raised] features: *[ $\alpha \,$ raised] [ $\beta \,$ raised]stem. This straightforwardly accounts for morphophonological M-lowering, and explains (i) why only M is targeted – it is the only [+raised] tone, i.e., the only possible target of [–raised] assimilation – and (ii) why both H and L trigger it – they both carry the assimilating feature [–raised]. This is illustrated in (53) below, with assimilation/agreement formalised as [–raised] spreading. H- and L-toned suffixes are represented together, the only featural difference between them being the value of the [upper] feature, which plays no role in [–raised] assimilation. The features [upper] and [raised] are shortened to [u] and [r] respectively in autosegmental representations, for lack of space.

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This analysis also naturally accounts for the fact that neither L nor H is targeted by any tonal changes in the same context: they are both already [–raised] and therefore (i) they do not violate the *[ $\alpha \,$ raised] [ $\beta \,$ raised]stem constraint when followed by a suffix carrying a [–raised] feature, and (ii) they are never targeted by [–raised] assimilation. This is shown in (54) and (55), where the root and suffix [–raised] features either stay as they are, or merge (depending on whether one wants to enforce an OCP-[raised] constraint within stems, which is not necessary in the present analysis).

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Evidence that the domain of application of this constraint is the stem rather than the phonological word comes from frozen nominal compounds. Compounding is not productive in present-day Laal, but 95 words in the lexicon can be identified as frozen compounds. In most cases, the elements of the compounds are not attested on their own, and cannot be ascribed a meaning anymore. They can only be identified as members of a compound because they occur in several words, and/or are marked for number separately (e.g. /mōō+gà+díígí/, pl /mùù-rí+gà+díígí/ ‘hippopotamus’, /gà+jàw/, pl /gà+jə̀w-ó/ ‘fish trap’, where the plural suffix /-o/ attaches to and triggers [ $\pm$ low] harmony on the second element of the compound only). If these frozen compounds were to be analysed as one-stem words, most would violate one or more stem-level phonotactic constraints, e.g. words longer than two syllables, long vowels in non-initial syllables, violations of vowel harmony, etc.Footnote ²³ Importantly for our discussion, many of these compounds violate stem-level tonotactic constraints as well in that they display complex tone patterns unattested on uncontroversial one-stem words, in particular ones involving M, as shown in (56) (see also the examples in (36) above). Once analysed as multi-stem words, these fall back into the realm of regular phonotactics, since each one of the stems they are made up of abides by all stem-level phonotactic constraints.

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5.3. Morphosyntactic M-lowering: floating [–raised] suffix

The same mechanism accounts for morphosyntactic M-lowering, analysed as the effect of a floating [–raised] suffix flagging the presence of an in-situ complement (on a par with the gerund suffix /-V^L/, or truncating morphology on the irregular nouns mentioned above).Footnote ²⁴ This is shown in (57) with the verb /dāg/ ‘drag’ and the noun /ɲāw/ both followed by a floating [–raised] suffix.

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With H- and L-toned roots, the [–raised] suffix is either stray-erased or fused with the root [–raised], as seen in (58), where L- and H-toned verb roots are represented together.

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5.4. Distributional constraint *MX/XM: bidirectional [–raised] assimilation

So far all examples illustrate leftward spreading. This is accidental and due only to the fact that there are no M-toned suffixes that would show rightward spreading of [–raised] from the root (the only M-toned suffix has a replacive tone, as we will see in §6). But the absence of LM and HM patterns in the lexicon (modulo the exceptions mentioned at the end of §3) proves that the structure the language seeks to avoid is not only stem-internal [+raised] [–raised], but also [–raised][+raised], i.e. the constraint is bidirectional: *[ $\alpha \,$ raised] [ $\beta \,$ raised]stem. In a constraint-based approach with parallel evaluation, ill-formed inputs with a stem-level LM or HM pattern would violate this constraint. Given the preponderance of M-lowering in the language and the absence of L-raising ([–raised] $\,\rightarrow \,$ [+raised]) or H-lowering ([+upper] $\,\rightarrow \,$ [–upper]), the only possible repair to posit in such cases is progressive [–raised] assimilation/spreading. All potentially ill-formed tone patterns are thus repaired in the same way, as schematised in (59).Footnote ²⁵

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Potential underlying tritonal patterns with one or more M tones would likewise surface with no M tone. This would involve leftward spreading (e.g. MHL $\rightarrow$ L_HL), rightward spreading (e.g. LHM $\rightarrow$ LHL), or both (e.g. MHM $\rightarrow$ LHL), as well as indistinct cases (e.g. HML $\rightarrow$ HLL $\rightarrow$ HL, with [–raised] spreading either from H or from L).

All cases of M-lowering (M instability), as well as the static constraint against complex stem-level patterns involving M (M exclusivity) are thus straightforwardly accounted for by one simple general phonological process ([–raised] assimilation) applying to comply with one simple phonotactic constraint (that against disagreeing [raised] feature sequences within a stem). M-lowering is thus a phonological phenomenon: morpheme concatenation simply creates the phonotactic context triggering [–raised] assimilation. In that sense, the root tone change in this case is no different from the root vowel changes involved in the anticipatory vowel harmony patterns described in (6) and (7) above. I come back to this parallel behavior in the conclusion.

5.5. The case of the ventive suffix

The ventive morphology on verbs can be used as another argument in favor of the subtonal approach defended in this paper. The ventive suffix on verbs is segmentally identical to the gerund seen in §4.2.3 above: it consists of a copy of the root vowel. It differs in its tonal behavior. It carries the same tone as the root with H- and L-toned roots. With M-toned roots, on the other hand, the entire ventive form is realised with a L tone – another case of M-lowering. This is shown in (60).

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The fact that this suffix is realised with a L tone in two cases out of three makes it tempting to analyse it as underlyingly L-toned. The H-toned realisation in combination with a H-toned root would then have to be analysed as a case of High tone spread: /kár-V̀/ $\rightarrow$ kárá. The problem with this analysis is that this specific High tone spread rule is unique to this suffix: it is not found with any other stratum-2 L-toned suffix following a H-toned root, e.g. /kár-àn/ $\rightarrow$ káràn ‘put-it’. While high tone spread is attested with L-toned inalienable possessive suffixes, as discussed in §6.3, the two processes are not identical. Indeed, in the case of possessive suffixes, the initial H tone of the root spreads only one mora to the right: /tɨ́m-àr/ $\rightarrow$ tɨ́már ‘his hand’, but /wúúr-àr/ $\rightarrow$ wúúràr ‘his thigh’ (cf. examples (71)-(72)). With the ventive suffix, on the other hand, spreading would have to be analysed as unbounded, as evidenced by the trimoraic form /máár-V̀/ $\rightarrow$ máárá ‘knead-ven’.

The featural representations proposed above to account for the behavior of the M tone offer a better alternative. I propose to analyse the ventive suffix as consisting of a copy vowel associated with a TRN specified as [–raised], but underspecified for [upper]. Specification of the upper feature comes from the root, which explains the H realisation after H-toned (i.e. [+upper]) roots, and the L realisation after M- and L-toned (i.e. [–upper]) roots, as illustrated in (61), (62), and (63). Additionally, the [–raised] feature of the suffix triggers [–raised] assimilation, thus causing M-toned roots to lower to L, as shown in (63).

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The advantage of this representational approach over the high-tone-spread analysis is that it does not posit a morpheme-specific tone rule, and does not treat the ventive suffix as exceptional in its tonal behavior. Rather, this behavior simply results from [–raised] assimilation, which is a general, independently attested tonological rule of the language, and spreading of features to unspecified elements, which is a general mechanism built into the theory of autosegmental phonology (Leben Reference Leben1973; Goldsmith Reference Goldsmith1976), which I use here to account for the tonology of Laal.

5.6. The emergence of subtonal features and the ambiguity of M

I assume that subtonal features, just like segmental distinctive features, are emergent (Boersma Reference Boersma1998; Mielke Reference Mielke2008), i.e. they are ‘created by learners in response to a phonological pattern’ (Mielke Reference Mielke2008: 101). The subtonal specification associated with a tone is not determined a priori by the theory. A featural analysis is thus necessarily a bottom-up approach, guided by empirical facts. Consequently, it is not expected that all featural combinations should necessarily be used in a language. Only the ones that are justified by the data are likely to emerge. Subtonal features are not even expected to be necessary in the analysis of all tonal systems. In the absence of any phonological pattern that would benefit from a featural analysis (e.g. tonal patterns showing natural class behavior that cannot be captured by tonal units alone), subtonal features are simply unnecessary to both the learner and the analyst.

The emergent nature of features allows us to address the third argument put forth against subtonal features, that is, the fact that the specification of the Mid tone in a three-tone system is necessarily ambiguous (cf. Hyman Reference Hyman2010; Clements et al. Reference Clements, Michaud and Patin2010; and references therein). A system with two binary features allows for four combinations, which is perfect for the characterisation of a four-tone system. In a three-tone system, one of these combinations is unattested. In principle, the missing category could be any one of the four possible combinations. There are thus four possible analyses of a three-tone system, as shown in Table 4, and the problem lies is in determining which combination is missing.

Table 4. Four possible three-tone systems

Yip (Reference Yip2001) rules out options A and D on the basis of the dispersion principle and the pressures it places on inventories: in order for contrastive tones to be maximally distinct phonetically, the two ends of the pitch range must be as far as possible from each other. Consequently, H is always encoded as the highest possible value on the featural scale, i.e. [+upper, +raised], and L as the lowest value, i.e. [–upper, –raised]. The M tone is necessarily one of the two intermediate values – in Reference YipYip's (Reference Yip2001: 162) terms, ‘the gap [is] a missing mid tone, not a missing H or L’.

I contend that dispersion is active in phonetic implementation (i.e. in translating the featural specifications into actual sounds), but not in determining feature specifications in the first place. In general, there need not be a one-to-one correspondence between specific featural specifications and specific pitch ranges. A system with three different subtonal feature combinations is expected to be interpreted as a partition of the total pitch range into three equidistant pitch targets, irrespective of the exact featural specifications of the three combinations. In other words, the highest tone does not have to be [+upper, +raised] in order to be interpreted as a pitch target located toward the higher end of the pitch range, maximally different from the pitch target corresponding to the lowest tone in the system.Footnote ²⁶

In an emergent approach, all four options in (4) are in principle possible, as long as they are evidenced by phonological patterns. The only (trivial) restriction needed is a form of paradigmatic phonetic naturalness: the relative position of the different featural combinations on the featural scale should correspond to the relative position of the corresponding pitch targets within the pitch range (i.e. H corresponds to the highest feature combination irrespective of its actual featural content, L to the lowest one, M to a combination intermediate between that of H and that of L). The choice of the missing combination is entirely determined by the phonological pattern under analysis.

Whether all four types in (4) are indeed attested or not cannot be confirmed at this point, given the very limited number of three-tone systems that have been given a featural analysis so far. Laal is a system of type A, as clearly shown by the behavior of the Mid tone: *MX/XM and M-lowering both characterise M as [–upper, +raised] ([+raised] because it is targeted by [–raised] assimilation, [–upper] because it merges with L under assimilation) and H as [+upper, –raised] ([–raised] because it triggers [–raised] assimilation, just like L, and [+upper] because it is higher than both M and L and in contrast with L which is also [–raised]). The feature combination [+upper, +raised] has no use in the system, and is thus naturally absent form the tonal inventory.

Snider (Reference Snider2020: 101) analyses Acatlán Mixtec as a language of type B,Footnote ²⁷ while Gjersøe et al. (Reference Gjersøe, Nformi and Paschen2019) propose to view Limbum as instantiating type C.Footnote ²⁸ I don't know of any language or analysis corresponding to type D, where the missing combination is the lowest on the featural scale, but in the emergent approach to subtonal features taken here, there is no reason to exclude it a priori.

To conclude, the subtonal specification of the mid tone in a three-tone system is not necessarily ambiguous. In the three languages mentioned above, the featural content of the mid tone can clearly be established by the analyst on the basis of its behavior with respect to the other tones. Systems in which the subtonal specification of the mid tone cannot be established might simply be cases where evidence for subtonal features is lacking, i.e. systems whose learning is unlikely to lead to the creation of something like a feature system in the learner's grammar, and whose analysis does not require it.

6.1. Base pattern reduction under suffixation

Stratum-2 suffixes require their base of affixation to bear only one tone, which has been the case in all the examples presented until now. If the base of suffixation bears a complex tone pattern, this pattern is simplified by deletion of all but its first tone: /T1T2-sfx/ $\rightarrow$ /T1-sfx/ (only the bitonal patterns LH and HL are ever attested in the relevant contexts). This reduction is observed irrespective of the nature of the base (noun or verb) or affix (inflectional, derivational), and irrespective of the base and suffix tones. This is shown in the examples below, where the LH (64) and HL (65) root patterns are systematically changed to L and H respectively upon suffixation, whether the suffix is L, as in (64a) and (65a), H, as in (64b) and (65b), or LH, as in as in (64c) and (65c).Footnote ²⁹

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Forms like /duàgál-àr/ $\rightarrow$ duàglàl or /sèègé-àn/ $\rightarrow$ siààgàn in (64a) may suggest that the tone reduction on the base is due to V2 deletion, applying to avoid creating a trisyllabic stem. However, the forms /gàáw-àr/ $\rightarrow$ gààw-àr or /sə̌ɲ-àn/ $\rightarrow$ sàɲ-àn clearly show that tone pattern reduction is independent of V2 deletion, and is only caused by the presence of the suffix. Furthermore, the existence of stem-level LHL and HLH patterns shows that reduction is not caused by the necessity to avoid tritonal stem patterns.

The examples above all involve pronominal suffixes. The following examples further show that pattern reduction occurs with the ventive, associative, and medio-passive suffixes, i.e. all stratum-2 suffixes except the gerund /-V^L/ and passive /-Vl^M/ suffixes, whose tones are replacive, as discussed in §6.2.

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We saw that the ventive suffix is tonally deficient: it is specified as [–raised] and gets its [upper] feature value from the last tone of the base of affixation. When following a LH root, as in (66a) /yùgár-V[–r]/, the [upper] specification inherited by the suffix is not the [+upper] of the final H tone of the root (*yùgr-á), but the [–upper] of the initial L tone (yùgr-à), after deletion of the H tone, i.e. after base reduction. This indicates that the spreading of the root [upper] feature to the underspecified vowel of the suffix occurs after V2 deletion – very likely postlexically, as do most default structure-filling rules.

Base pattern reduction can be represented as the deletion of all but the initial TRNs of the base of affixation (in effect, deletion of the second of two TRNs, since no tritonal pattern is attested in the relevant contexts). This is illustrated in (67).

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6.2. Full-tone spread in replacive tone patterns

Two suffixes display “replacive” tone (Welmers Reference Welmers1973: 132–133), i.e. they impose a single tone pattern to their stem, wiping out the underlying tone of the root to which they attach. These two suffixes are gerund /-V^L/ seen in §4.2.3 and Table 3, and passive /-Vl^M/. Both are illustrated in (68) with H-, M-, and L-toned verbs. In both cases, the vowel of the suffix is realised as a copy of the root vowel.

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These two suffixes contrast with all other segmental suffixes, whose tones are never replacive, e.g. /kár-àn/ $\rightarrow$ [káràn] (*[kàràn]) ‘put-it’, /ɟàr-án/ $\rightarrow$ [ɟàrán] (*[ɟárán]) ‘sacrifice-him’. This replacive pattern corresponds to what Rolle (Reference Rolle2018: 47) calls “replacive-dominant grammatical tone”, defined as a tone pattern associated with a specific morpheme or morphological construction which deletes and replaces the underlying tone of its target. It is beyond the scope of this paper to offer an analysis of dominance and replacive grammatical tone. The reader is referred to Rolle (Reference Rolle2018); Sande et al. (Reference Sande, Jenks and Inkelas2020); Trommer (Reference Trommerin press) for recent proposals (and references therein for previous accounts). For now, I simply represent the dominance of the tone pattern imposed by the gerund and passive suffixes with a diacritic mark on the TRN (‘d’ for ‘dominant’). The main point here is that these patterns involve spreading and deletion of entire TRNs, justifying the tone geometry in (52), as illustrated in (69) and (70).

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Neither the replacive L of the gerund nor the replacive M of the passive can be analysed as involving subtonal interaction alone. The universal change to L observed with the gerund requires both [–raised] (M $\rightarrow$ L) and [–upper] (H $\rightarrow$ L) assimilation/spreading, i.e. full assimilation, better represented as TRN spreading. As for the passive suffix, the systematic change to M that it triggers could be viewed as a case of regressive [+raised] assimilation/spreading.Footnote ³² This would straightforwardly account for the L-to-M change observed with L-toned roots. With H-toned roots, one additional step would be required: spreading the suffixal [+raised] to the root would create a [+upper, +raised] combination, unattested in the language. The [+upper] feature of the root would then have to be changed to [–upper] to comply with the constraints of the inventory. This abstract extra-step is unnecessary in the TRN-spreading analysis in (70) above. Furthermore, this would be the only case of [+raised] assimilation/spreading, all the more suspicious that it goes against the otherwise exceptionless [–raised] assimilation/spreading at work in the language.

The fact that there are no non-replacive M-toned suffixes is intriguing. One could hypothesise that the replaciveness of suffixal M is a last-resort solution to preserve the grammatical information conveyed by the suffix. Indeed, in order to comply with the unviolable *MX/XM constraint, there are two solutions: either change the suffixal M (e.g. to L, as in other cases of M-lowering), or change the lexical tone of the root to M, in order to keep the suffix intact – which appears to be what Laal does. The problem is that such an explanation is not available for the replacive L tone of the gerund, which has no need to be replacive. Like the other L-toned suffixes (e.g. third person neuter object /-àn/ seen in (10), (11) and (53)–(55)), it could indeed in theory be kept without violating any tonotactic constraint (other than *MX/XM when attaching to a M-toned root, in which case M-lowering of the root M would apply, as it does elsewhere). In other words, the last-resort analysis does not generalise to all cases of replacive tone. Replaciveness thus has to be accounted for in its own terms.

6.3. High Tone Spread in inalienable possessive morphophonology

When a H-toned noun root combines with a L-toned inalienable possessive suffix, the H tone of the root spreads one (and only one) mora to the right. If the first syllable of the resulting stem is monomoraic, the H spreads onto the suffix, deleting its L tone, as in (71) (all examples in this section take the third person singular suffix -àr for illustration).Footnote ³³

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This form involves V2 deletionn: /kúrá-àr/ $\rightarrow$ kúr-àr $\rightarrow$ kúrár.

If the first syllable is bimoraic, on the other hand, the H does not spread onto the suffix, which keeps its low tone, as in (72).

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This H tone spread can easily be analysed as the spreading of the initial H tone's TRN one mora to the right, as shown in (73) and (74).

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High Tone Spread is regular within the closed class of nouns compatible with inalienable possessive suffixes,Footnote ³⁵ and provides additional evidence for the TRN. Indeed, a subtonal feature analysis offers no advantage. One featural analysis that would capture the data consists in analysing this pattern as involving rightward [+upper] spread from the initial mora onto the following mora. Indeed, replacing the [–upper] feature of the L-toned suffix with a [+upper] specification changes it to a H tone, since both H and L are [–raised]. Both analyses are descriptively adequate, and it is impossible to find definitive evidence in favor or against either one. The fact that the [upper] feature is not involved in any active spreading/assimilative pattern elsewhere in the language (the spreading involved in the realisation of the ventive suffix is only structure-filling), and that cases of TRN spread are independently attested militate in favor of the TRN-spread analysis of High Tone Spread.

7.1. Tone-as-unit analysis

A featural analysis would be unwarranted if it could be demonstrated that an analysis resorting only to the tonal primitives H, M, and L accounts for all the facts listed in (50) above. I show in this section that such an analysis is impossible without stipulating (i.e. circularly including the descriptive generalisation in the analysis) some of the points in (50).

Instead of positing subtonal features and viewing M-lowering as resulting from [–raised] assimilation, one could analyse M-lowering as involving a L assimilation rule targeting M tones within the stem. This can be represented as spreading of L onto M followed by delinking of the M tone, as shown in (75) and (76) below. This would straightforwardly account for morphophonological M-lowering before a L-toned suffix (75), as well as morphosyntactic M-lowering, analysed as involving a floating L (rather than [–raised]) suffix (76).

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There are at least three problems with this approach. First, it does not account for morphophonological M-lowering before a H-toned suffix – unless one posits a floating L before every H-toned suffix in the language, as in (77), for which there is no independent evidence.

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Note that this floating L tone cannot be viewed as marking the presence in situ of the object of the verb, nominal or pronominal, as in example (75) and (77). Indeed, we saw that M-lowering does not apply solely before object suffixes, but before all stratum-2 suffixes, including suffixes unrelated to the presence of the object or even transitivity at large, e.g. medio-passive /-ɨ́ɲ/ and instrumental /-V́/, which we saw is compatible with intransitive verbs.

An alternative to explain why M changes to L before H would be to posit a M to L change satisfying the *MX/XM phonotactic constraint. This solution is far from satisfactory, as it consists solely in formalising the surface descriptive generalisation, i.e. stipulating the alternation rather than accounting for it. The featural analysis I propose does not stipulate M-lowering, but derives it from the properties of the subtonal features that make up the three tones H, M, and L, i.e. from simple representations not directly related to the surface pattern it purports to analyse. These representations, in turn, are not stipulated, but posited on the basis of evidence consisting of natural classes involved in an assimilation process and defined by common phonological behavior (H and L are both triggers, M is the only target, M and L merge under assimilation).

The second problem with the tone-as-unit analysis is that L spreads only onto a preceding M and never a preceding H, which does not follow from any property of the three tones H, M and L, and must be stipulated. In the subtonal approach, on the other hand, the featural makeup of each tone directly explains their different behaviors: H is immune to lowering because lowering is [–raised] assimilation, and H is already specified as [–raised]; M being [+raised], it is by necessity the only possible target of [–raised] assimilation.

Finally, the *MX/XM phonotactic constraint on stem-level tone patterns is not fully accounted for in the tone-as-unit analysis. While the absence of *ML and *LM patterns can be explained through bidirectional L spreading, the absence of *MH and *HM has to be stipulated – or explained by positing a floating L tone between H and M, which, again, is not independently motivated.

Note, also, that with the tone-as-unit approach, the ventive suffix would have to be analysed as carrying a full tone, e.g. a L tone subject to high tone spread, as suggested in §5.5 above. This is not impossible of course, in particular given that high tone spread is attested in possessive morphology. But, as discussed in §5.5, it is a morpheme specific tonal process that is unnecessary in the featural approach.

7.2. Mid as zero

The exclusivity and instability of the M tone in Laal suggests a certain weakness of the M tone compared to both H and L. This weakness is not analysed as such in the featural approach I propose, where M is weak only by virtue of being specified as [+raised], which makes it a target of [–raised] assimilation. An alternative analysis could be proposed which represents M weakness more directly, for example by analysing M as Ø within a tone-as-unit analysis. The weakness of the M tone could indeed be seen as evidence of its underlying non-existence and default status. That is, the only two underlying tones of Laal are H and L, with TBUs specified as H, L, or Ø. Ø TBUs get their tonal specification through spreading of neighboring tones, otherwise through default M insertion. This would naturally explain the static *MX/XM constraint, as well as M-lowering before a L tone, as seen in (78) and (79).Footnote ³⁶

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However, it would pose the same problem as the preceding analysis, i.e. it would still fail to account for M-lowering before a H-toned suffix without gratuitously positing a floating L tone before all such suffixes (or giving up on accounting for it and stipulating a M to L tone change instead, to avoid a violation of *MX/XM), as shown in (80).

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In general, any tone-as-unit approach runs into one fatal problem, which is that it cannot account for the fact that both H and L trigger M-lowering without stipulating all or part of the description in the analysis. That is, a tone-as-unit analysis fails to capture the natural class formed by the two non-adjacent tones H and L – which the subtonal feature approach straightforwardly accounts for, as we saw.

7.3. Tone height as one gradient feature

One final alternative I will consider is to view tone height, not as a combination of two features, but as one gradient feature.Footnote ³⁷ I do not have space here to go into details. I only give a brief sketch, and leave the full development and evaluation of this alternative to future research.

Let us represent tone height as one single gradient feature [n T-height], with n arbitrarily comprised between 0 (the lowest tone height) and 1 (the highest). This is the gradient equivalent of a multivalued feature (cf. Trubetzkoy Reference Trubetzkoy1939; Ladefoged Reference Ladefoged1971; Lindau Reference Lindau1978; Clements Reference Clements1991, Reference Clements2015). On the scale from [0 T-height] = L to [1 T-height] = H, M would occupy an intermediate position. If this position were to be defined as closer to L than to H, say [0.4 T-height], this would explain both the *MX/XM constraint and M-lowering, as I show below.

With such representations, the *MX/XM constraint can be restated as * $\Delta$ T-height¡1, i.e., within a stem, adjacent tones must be distant by at least 1 T-height level. Consequently, only HL [1-0] and LH [0-1] sequences are allowed. Any sequence involving a M tone violates this constraint since the distance is always less than 1: $\Delta$ T-height(H˜M) = .6, and $\Delta$ T-height(L˜M) = .4. The optimal repair to this violation is to change the M tone to L, because L is the closest tone in terms of T-height distance (.4, whereas the distance between M and H is .6). Changing M to L thus incurs a lesser violation of faithfulness (on the condition that violation of Ident-T-height is defined as gradient). In this alternative, M-lowering is analysed as a M to L tone change, but the tone change does not need to be stipulated: it is motivated by the proximity of M with L on the tone-height gradient.

The main challenge with such an alternative analysis is to justify the asymmetric position of M on the T-height scale. As it currently is, the theory has to stipulate it. Instrumental data are necessary to determine whether M is indeed on average realised closer to L than to H. I have not conducted this acoustic analysis. This alternative must thus remain at a tentative stage for now. It seems worth sketching it here, however, as it appears to be a potential competitor to the subtonal analysis proposed in this paper.

7.4. Alternative subtonal analysis

One anonymous reviewer suggests another account of the weakness of M, couched in the featural analysis I propose in this paper. In this analysis, M is specified as [–upper] and unspecified for [raised]. This would work for all cases of M-lowering, analysed as spreading of the [–raised] feature of the suffix onto the [raised]-deficient TRN of the root M. All suffixes (except the passive) are indeed specified as [–raised]: H, L(H) and the floating [–raised] of the transitive and genitive suffixes. This is illustrated in (82) and (81) below with H- and L-toned verbal suffixes and the floating [–raised] suffix respectively.

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One would have to posit [+raised] as the default value of [raised], assigned to [raise]-deficient TRNs in the absence of any available (i.e. spreadable) [–raised] in the stem, as illustrated in (83). Since [+raised] is never active in the tonology of Laal, this does not seem to be problematic.

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The passive suffix would have to be analysed as a replacive defective TRN: a TRN specified only as [–upper] which spreads and deletes the TRNs of the root, and then sees its missing [raised] feature filled in by default [+raised] insertion, as in (84).

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This analysis is as descriptively and explanatorily adequate as the full-specification analysis I propose in §5 above. However, I think it is slightly less satisfactory, for two reasons. First, it requires default [+raised] insertion, and the definition of a default value of [raised], which is unnecessary in the full-specification analysis.Footnote ³⁸

Secondly, it offers an unnecessarily complex representation of the contrast between L and M, which is robust in the language, despite the frequency of M-lowering. Indeed, in this approach, L and M contrast underlyingly by the specification vs. non-specification of the feature [raised]. That is, they differ not only by the fact that, on the surface, one is [–raised] and the other [+raised], but also by the timing of the assignment of the [raised] feature value. This is of course an option that is made entirely possible by the theory and is not in and of itself problematic. But I don't see any necessity to resort to this level of abstraction or complexity. In any case, this analysis can be considered a variation of the one I propose, and does not question the aptness of subtonal features for the analysis of the tonology of Laal.