2.1 Stratal Optimality Theory and the Four-Hypothesis Program

The goal of this article is to show that Kuria tone association can be captured under coherent and restrictive theoretical assumptions in a model which maintains modularity and the standard domain structure from Lexical Phonology, stems, words and phrases (utterances). Therefore, I will adopt here the most explicit recent research program along these lines, the Four-Hypothesis Program of Bermúdez-Otero (Reference Bermúdez-Otero and Trommer2012) (slightly rephrased):

Whereas the issue of Phonetic Interpretability is largely orthogonal to the problems discussed in this article, the three conditions on morphology and phonology are immediately relevant. Indirect Reference and Cyclic Locality are two of the major theoretical assumptions defended here. With Bermúdez-Otero (Reference Bermúdez-Otero, Hannahs and Bosch2018b), I assume that the latter implies a minimal version of Stratal Optimality Theory which only comprises three strata: stem, word and phrase levels (pace Kiparsky Reference Kiparsky1982). See Hyman (Reference Hyman2008) and Downing & Kadenge (Reference Downing and Kadenge2020) on overviews of the broad literature providing evidence for stems and words as phonological domains in Bantu, and Myers (Reference Myers1997), Mutaka (Reference Mutaka1994) and Hyman (Reference Hyman2017) for case studies providing detailed evidence for these domains in a three-level stratal architecture as assumed here. As shown by Bermúdez-Otero (Reference Bermúdez-Otero and Trommer2012), Morph Integrity is an important complementary assumption to Indirect Reference by prohibiting the relocation of morphologically triggered phonological rules and constraints to the morphology component, which would deprive the Indirect Reference hypothesis of most of its empirical predictions. Thus, Morph Integrity effectively commits morphology to a strictly concatenative approach: It may just add phonological structure such as segments or tones, but not alter phonological representations.

2.2 Coloured Containment Theory

The framework I will adopt here for implementing the first component of the Four-Hypothesis Program, Indirect Reference, is Coloured Containment Theory (van Oostendorp Reference van Oostendorp, Blaho, Bye and Krämer2007; Trommer Reference Trommer2011; Paschen Reference Paschen2018), since it is the only version of OT which has developed a comprehensive Indirect Reference approach to nonconcatenative morphology covering length-manipulating morphology (Zimmermann Reference Zimmermann2014), vocalic and consonantal mutation morphology (Paschen Reference Paschen2018; Trommer Reference Trommer2021), reduplication (Paschen Reference Paschen2018) and tonal morphology (Trommer Reference Trommer2022). Historically, Coloured Containment Theory is a conservative extension of the original implementation of OT in Prince & Smolensky (Reference Prince and Smolensky1993) with a more limited set of possible structural changes than Correspondence Theory – restricting them basically to insertion and marking for non-pronunciation.

3.1 Basic left-to-right association

In the simplest case, Kuria tone association instantiates a classical case of one-by-one mora-to-tone association from left to right, as predicted by standard autosegmental association conventions (Goldsmith Reference Goldsmith1976; Pulleyblank Reference Pulleyblank1986). Here, I restate these in a straightforward manner by Optimality-Theoretic constraints, which require association of tones to moras (13a) and vice versa (13b), and precedence constraints penalizing marked autosegmental structure preceding unmarked one (14): unassociated tones to the left of associated tones (14a), and unassociated moras to the left of associated ones (14b). As I will show immediately below, these constraints naturally derive left-to-right association without the formal and typological problems raised by Generalized Alignment constraints (McCarthy Reference McCarthy2003) used by Zoll (Reference Zoll2003) and Yip (Reference Yip2002). See Appendix B.1 in the Supplementary Material for a list of all constraints used in the Kuria analysis and their ranking in different strata.

That association is one-by-one in the unmarked case then follows from constraints against multiply associated moras. (15a) is basically the standard constraint against contour tones restricted to rising tones (NoContour in Yip Reference Yip2002), and (15b) a version of the *Twin constraint of McPherson (Reference McPherson2016) for Ls. Kuria systematically lacks falling tones (see Mwita Reference Mwita2008: 11), so I assume that the complement constraint to (15a) against falling tones, *, is undominated in all strata in the language.

(16) demonstrates how these constraints derive one-by-one left-to-right association in a form with more moras than tones together with standard faithfulness constraints for tones (Max/Dep $\unicode{x3C4}$ ) and association lines (Max/Dep $|$ ; see Appendix B.1 in the Supplementary Material for definitions). This effect is mostly independent from their ranking. (I will discuss effects of $\unicode{x3BC} \vartriangleright \unicode{x3C4}$ and further constraints in §3.2.) $\unicode{x3C4} \vartriangleright \unicode{x3BC}$ ensures that tones should not remain unassociated (16g), Max $\unicode{x3C4}$ blocks tone deletion (16f). * derives the fact that the melody targets the first three moras in the base, and not more rightward ones (16e) (see below for evidence that this constraint is ranked relatively low), while * and * exclude the association of multiple tones to a single mora (as in (16c) and (16d)). At the stem and word levels, there is no spreading, since Dep $|$ dominates $\unicode{x3BC} \vartriangleright \unicode{x3C4}$ (16b), and epenthesis is excluded by undominated Dep $\unicode{x3C4}$ (since epenthesis is systematically absent at these levels I will simply omit the constraint and epenthesis candidates from the tableaux. Max $|$ is omitted here because it is irrelevant in the absence of underlying association lines (input forms are included among the evaluated candidates and cross-referenced in the upper left corner of tableaux):

* becomes crucial in forms with more tones than moras, where it derives the effect that preferentially the leftmost tones associate, excluding candidates such as (17c), again closely emulating derivational left-to-right association:

As already shown in (12), the winning candidate of the stem-level evaluation is consequently transferred to the word level unchanged apart from undergoing Bracket Erasure via Monochromisation to serve as the input to the word-level evaluation. That the floating features of stem-level affixes remain ‘dormant’ until the phrase level now follows from another well-established constraint on autosegmental association, stated in (18), which requires that epenthetic association lines should not connect material belonging to the same morpheme.

Alternation has been introduced by van Oostendorp (Reference van Oostendorp, Blaho, Bye and Krämer2007) to capture what has been traditionally called Nonderived Environment Blocking, for example, the fact that featural spreading is often restricted to apply across morpheme or word boundaries. In fact, a slightly more general version of Alternation (labelled ‘Bound’) was already proposed by Myers (Reference Myers1997) in one of the foundational papers on tonal phonology in OT. Trommer (Reference Trommer2011) shows that it effectively obviates the ad hoc constraint NoTautomorphemicDocking assumed in the correspondence-theoretic literature to ensure heteromorphemic association of floating features (Wolf Reference Wolf2007). Assuming that Alt is undominated at the word level, the tonal profile of the output of (17) remains unchanged:

At the phrase level, the dormant floating tones are then free (and actually forced) to associate to the empty moras of a following word. This happens again one-by-one from left to right, excluding outputs such as (20b) and (20c), simply because the same constraints are still active. See §3.2 below on arguments for their ranking which slightly differs from stem- and word-level rankings (e.g., Alternation is ranked relatively low).

Additional support for the role of strata and Alternation in deriving left-to-right association comes from two Kuria paradigms not analysed by Reference Marlo, Mwita and PasterMMP and Reference Sande, Jenks and InkelasSJI, the hortatory imperative $_{2}$ , and the negative remote future $_{1}$ . The hortatory imperative $_{2}$ assigns a single H to the first mora of the stem for longer bases, in parallel to the past, as in (21c)–(21f). However, in forms with monomoraic stems, the H is realized on the TAM prefix instead, as in (21a) and (21b):

This follows naturally from the analysis if we assume that in contrast to other TAM markers, the TAM prefix of the hortatory imperative $_{2}$ , [ta-], is concatenated not at the word level, but already at the stem level, together with a HL-melody, where Alternation is ranked low, but above * (see below for independent evidence for the trailing L). For a stem with more than two moras, Alternation will then still enforce left-to-right association to the stem leaving the prefix toneless (with phrase-level insertion of default L; see below):

On the other hand, for a short (monomoraic) stem, obeying Alternation as in (23b) would mean that only one of the melody tones can be associated. Since $\unicode{x3C4} \vartriangleright \unicode{x3BC}$ is ranked above Alternation, violation of the latter is exceptionally tolerated here (23a):

The negative remote future $_{1}$ also shows special effects with short bases. Like the affirmative remote future, it is characterised by a H on the third mora, as in (24d) and (24e), but in contrast to the affirmative, this H ‘disappears’ in stems which have three moras or fewer (as in (24a)–(24c)). This is true even in one-mora stems, where the negative remote future $_{1}$ shows final Superlowering (see §§2 and 3.3), indicating the lack of even a floating H:

A natural explanation in the stratal analysis proposed here is that the stem-level tone morphology of this tense is identical to the pattern found in the simple $\unicode{x3BC}$ 3 remote future, introducing LLH at the stem level, but that in addition here negation is expressed by a L suffix at the word level. In fact, most tenses employing the negative prefix [ta-] also seem to exhibit the same reflexes of a final L (Mwita Reference Mwita2008: 187–188). The effect of Alternation is shown for a stem with two moras in (25). The word-level input inherits a final floating H from the stem level (25e). Since the H has effectively become a part of the stem by Monochromisation, it is blocked from associating by Alternation (25d). In contrast, the new L suffix still has a distinct colour and hence associates, to satisfy $\unicode{x3C4} \vartriangleright \unicode{x3BC}$ . * blocks overt double association to a L (25b). Deletion of melody tones is now a maybe surprising but gratuitous effect of the constraint *, blocking internal floating tones. This constraint was motivated above simply by ensuring one-by-one left-to-right association (see the discussion of (17)). In contrast, here, left-to-right association is thwarted by Alternation, and the only way to avoid internal floating tones as in (25c) is to delete them. Note also the crucial effect of ranking $\unicode{x3C4} \vartriangleright \unicode{x3BC}$ above Max $\unicode{x3C4}$ at the word level, such that it is more important to maximise tone associations, as in (25a), than to preserve the tones themselves, as in the input configuration in (25e). Since, by Containment, the phonetically inert association line of the already associated L still satisfies $\unicode{x3C4} \vartriangleright \unicode{x3BC}$ , this also loses to the affix L:

3.2 Melody-final spreading and morpheme-specific phrasal phonology

Recall that melodic Hs in all the tenses analysed by Reference Marlo, Mwita and PasterMMP systematically spread up to the penultimate mora of the stem in longer bases (see (1) in §1). This raises an apparent problem for a stratal analysis. The data in (2), where spreading extends from the rightmost mora of a verb to the (phrase-)penultimate mora of a following toneless noun, show that melody-final H-spreading must be phrasal. At the same time, melody-final spreading in verbs is co-dependent on specific morphological features of the verb. Whereas the tenses in (1) exhibit right-edge spreading of Hs, there are morphological contexts where it systematically does not apply. Thus, both the remote future and the mandatory imperative impose a H on the third stem mora, but only the remote future H spreads to the penultimate position:

Lack of spreading also obtains in the two special tense paradigms we have discussed in the last section: The negative remote future $_{1}$ , also a $\unicode{x3BC}$ 3 tense, behaves in parallel to the mandatory imperative (cf. (24)), and the hortatory imperative $_{2}$ also shows no H-spreading (e.g., [ta-káraaŋɡ-à] ‘do fry’ (21e)), which contrasts with the corresponding past forms, an otherwise similar $\unicode{x3BC}$ 1 tense which exhibits H-spreading (e.g., [] ‘we have fried’; see Appendix A.2 in the Supplementary Material for more data). Thus, melody-final spreading seems to lend further support to Reference Marlo, Mwita and PasterMMP’s claim that word-internally conditioned phonology applies in phrasal domains, which would challenge standard stratal architectures.

Again, the solution to these problems lies in the potential of autosegmental representations to remain dormant, that is, to have effects only at a later stratum. In contrast to Reference Marlo, Mwita and PasterMMP, I interpret melody-final spreading not as a process specific to Hs, but as a more general strategy in Kuria to provide toneless moras with tonal association by spreading either Hs or Ls. The only substantial departure from the original autosegmental association conventions of Goldsmith (Reference Goldsmith1976) is the assumption that, while one-to-one association of tone melodies happens at all strata in Kuria, melody-final spreading is restricted to the phrase level. In the OT implementation here, this basically follows from the fact that $\unicode{x3BC} \vartriangleright \unicode{x3C4}$ is low-ranked in the lexical strata, but undominated at the phrase level, where it enforces tonal specification of all moras to tones either by spreading or by L-epenthesis. The specifics of full-mora specification are then regulated by the additional constraints in (27).

Again, most of these constraints are basically standard constraints from the OT literature. (27a) is the well-known NonFinality constraint (Yip Reference Yip2002) restricted to Hs, and (27c) a parametric constraint determining the directionality of tone spreading equivalent, for example, to Anchor-Left in Myers (Reference Myers1997). (27b) is again a more basic OT constraint implementing one of the crucial aspects of the classical autosegmental association conventions – spreading is limited to the periphery – modulated by the crucial insight of Zoll (Reference Zoll2003) that peripheral spreading is not a property of tones per se, but of tonal melodies (i.e., sequences of tautomorphemic affix tones). (27d) derives the standard assumption from rule-based approaches to tonal underspecification that every toneless TBU is assigned a single epenthetic default tone (Pulleyblank Reference Pulleyblank1986).

For simplicity, I will omit the two undominated constraints in (27c) and (27d), and candidates violating them, from tableaux. (28) shows the phrase-level ranking of (27a) and (27b) with respect to most other constraints in the derivation of spreading in a past ( $\unicode{x3BC}$ 1) form (n-to-o-[kárááŋɡ-a] ‘we have fried’; Reference Marlo, Mwita and PasterMMP: 254). Crucially, ranking Dep $\unicode{x3C4}$ above Dep $|$ and Alternation has the effect that spreading is in principle preferred over epenthesis as in (28c). However, this preference is reined in by higher-ranked * $\acute {\unicode{x3BC}}$ ], which blocks H-spreading up to the rightmost mora as in (28b), which instead receives a L by epenthesis (28a):

The fact that melody-final spreading in this analysis is not specific to Hs, but is also predicted to apply to Ls when they are final in their morphological melody, provides a direct solution to the apparent morpheme-specific failure of right-edge spreading in the negative remote future $_{2}$ and the hortatory imperative $_{2}$ . It follows from the assumption, already introduced for independent reasons, that these tenses are lexically assigned a final L. This is illustrated in (29) for a hortatory imperative $_{2}$ form, where the tonal prefix is HL, already associated at the stem level. Spreading of the H as in (29b) is blocked by * $_{\unicode{x3BC}}$ τ $_{\unicode{x3BC}}$ τ, since it is not final in its morphological melody. Hence, the trailing L will spread automatically to phrase-final position:

3.3 Contour formation and phrase-final floating tones

Recall from the remote future ( $\unicode{x3BC}$ 3) data in (9) that under specific conditions, the final H of a verbal tone melody shows up as part of a rising contour on the last syllable of a phrase-final verb if the stem is exactly one mora too short (e.g., n-to-re-[rom-ǎ] ‘we will bite’, the Contour pattern. If the stem is even shorter, the H is lost without direct phonetic effect (e.g., n-to-re-[rj-a] ‘we will eat’, the Lost-H pattern).

Thus, the phrase level in principle allows phrase-final contours, which follows from * being ranked below Max $\unicode{x3C4}$ , and *μ…] (defined in (30)) above it.

Let us first address the Lost-H pattern. We have already seen the stem-level and word-level derivation of a monomoraic remote future stem in (17) and (19) above in §3.1. Exactly the same evaluations apply for phrase-final verbs; the two cases only diverge at the phrase level, where the verb is combined with additional syntactic material – or not. The constraint ranking established for the phrase-internal case predicts that phrase-finally the trailing Ls and Hs should remain floating. Association of the L is blocked by * (31c), association of the H across the floating L by * (31a), and deletion of the floating tones by Max $\unicode{x3C4}$ (31b):

While there is no direct pronunciation of the floating tones, they block the Superlowering process which otherwise additionally lowers L moras at phrase boundaries, as discussed in §2. If Superlowering is a phonetic implementation rule for associated phrase-final Ls, it will be correctly blocked by the persistent floating material in (31d).

The lexical evaluations for the Contour pattern are equally unremarkable. At the stem level, one-to-one left-to-right association leads to a trailing floating H (ⓁⓁⒽ +ro $_{\unicode{x3BC}}$ ma $_{\unicode{x3BC}}$ → rò $_{\unicode{x3BC}}$ mà $_{\unicode{x3BC}}$ Ⓗ), preserved at the word level due to Alternation. Again the crucial evaluation step is in the phrasal phonology. The floating H can and must associate since final contours are possible at the phrase level – in contrast to the lexical phonology, * is ranked below $\unicode{x3C4} \vartriangleright \unicode{x3BC}$ , and in contrast to the Lost-H pattern with an additional floating L, contour formation is not blocked by an intervening tone:

Thus, the Stratal OT account allows for deriving both phrase-final patterns transparently from the fully general constraints on tone association which also capture the basic familiar one-to-one left-to-right association of floating tones. This seems to be a substantial improvement over the analysis of Reference Marlo, Mwita and PasterMMP, who capture these configurations by three stipulative rules which apply in an opaque Duke-of-York derivation (phrase-final syllables are lengthened to allow for additional tone association and subsequently shortened to their original length; see §5).

Before we turn to the alleged problems for a representational account of Kuria across-word tone mapping, consider an important empirical limitation. The sources on Kuria provide only a handful of different nouns in postverbal contexts, most of which are arguably toneless, like [] ‘banana’. In all examples of across-word association provided by Mwita (Reference Mwita2008) and Marlo et al. (Reference Marlo, Mwita and Paster2012, Reference Marlo, Mwita and Paster2014, Reference Marlo, Mwita and Paster2015), verbal tone melodies target only toneless moras in following nouns. Therefore, I tentatively assume here that melodic association is limited to underlyingly toneless moras.

A further factor which might have an impact on the phrase-level realization of floating tones is syntactic category and constituency. Thus, association of verbal tones might be blocked (or more limited) if the word following the verb is not an object noun. Again, at this point, there are hardly any data of this type in the literature that would shed light on this question. Mwita (Reference Mwita2008) shows that melodic Hs can also dock on postverbal locative particles and the negation morpheme [hai], which are clitics (they can also occur preverbally or attached to non-verbal lexemes). Thus, in the negative remote future $_{2}$ , the $\unicode{x3BC}3$ H of a two-mora stem associates to [hai] as in [] neg-S3pl-tam-call neg ‘they will not bite (then)’ (Mwita Reference Mwita2008: 220).

Diercks et al. (Reference Diercks, Ranero, Paster, Kramer, Zsiga and Boyer2015: 59) further report a case of across-word association which crosses two word boundaries and affects an embedded verb across a pronoun. In (33a), the inceptive $\unicode{x3BC}4$ H of the initial matrix verb (‘expect’) shows up on the following object pronoun []. The stem domain (delimited by square brackets) starts here with the object prefix [mo-]. In (33b), [mo-] is omitted, and the first mora of the embedded subjunctive verb (‘leave’) becomes the fourth mora H after the left stem boundary of the matrix verb, and consequently hosts the inceptive H. Note that in both sentences the embedded verb also has an independent morphological $\unicode{x3BC}3$ H, which surfaces on the final vowel of the verb (see §4.1 for more discussion). However, the status of these data is somewhat unclear since the Kuria speaker who produced them, according to Diercks et al. (Reference Diercks, Ranero, Paster, Kramer, Zsiga and Boyer2015), does not apply across-word association at all in other recordings.

Theoretically, the indirect-reference approach and the Stratal OT framework adopted here predict that any blocking effect for across-word association should be linked not to specific syntactic configurations, but to the general prosodic structure of Kuria. There is some evidence from tone spreading for the assumption that Kuria verbs, as in many other languages and especially in Bantu (Cheng & Downing Reference Cheng and Downing2012), form phonological phrases with one or more following complements (Diercks et al. Reference Diercks, Ranero, Paster, Kramer, Zsiga and Boyer2015: 60). If this turns out to be correct, the Indirect Reference approach predicts that any restrictions on the association of morphological tone melodies across words should reflect the same phrase boundaries as evidenced by spreading.

4.1 The spreading problem

The major empirical argument against the assumption of Ls in Kuria verb tone raised by Reference Marlo, Mwita and PasterMMP is unbounded rightwards spreading of Hs affecting the initial portions of verb stems which exhibit morphological Hs on later moras in the same stem. This pattern is found in the negative infinitive, where the negative prefix [] has a H which spreads up to two syllables before the $\unicode{x3BC}$ 4 H of the infinitive, and in the negative remote future $_{2}$ , where the negative prefix [te-] carries a floating H which associates to the following agreement prefix, from where it spreads to the penultimate syllable before the $\unicode{x3BC}$ 3 H of the remote future. These two negative forms are illustrated in (34):

If the fourth-mora and third-mora patterns in these paradigms actually involved leading Ls, this would imply, according to Reference Marlo, Mwita and PasterMMP, that they should block spreading, counter to fact.

Here, I will show that no such problem obtains in a Stratal OT account. But before we turn to this point, we have to take a closer look at the interpretation of Kuria H-spreading more in general. Whereas Reference Marlo, Mwita and PasterMMP assume that there is a single general process of H-spreading deriving both melody-final spreading of Hs (see §3.2) and the pattern in (34), Mwita (Reference Mwita2008) argues stringently that there are several spreading processes, one which applies to the last H in a verb, and a different one applying only to a H preceding another H as in (34): Plateauing, a process well-known from the literature on Bantu tone (see Jardine Reference Jardine2016 for recent discussion and references). Whereas Plateauing applies without exceptions whenever there are two Hs separated by more than one syllable (as in (34), it typically leaves one intervening L syllable intact), we have already seen in §3.2 that there are tonal melodies applying to verb stems where Hs separated from the right word/phrase edge by several L moras do not spread. Thus, H-spreading in Plateauing contexts is exceptionless, but simple melody-final H-spreading depends on the TAM category of the verb. Additional support for this conclusion comes from the fact that H-spreading from prefixes is also blocked in specific verb forms without a H (which would trigger Plateauing). Thus, in the hortatory imperative $_{1}$ , the H of the TAM prefix [] does not undergo H-spreading, in contrast to the forms in (34).

This falls out naturally under the analysis here if the hortatory imperative $_{1}$ has a morphological tone melody at the stem level which lacks a H: it consists simply of a single L prefix (Ⓛ+βereker-a → βèrekera). Since melody-final spreading is not restricted to Hs, this L – being the rightmost underlying tone – spreads at the phrase level to provide toneless moras with tonal association (βèrekera → a-tá-βèrèkèrà). Thus, L-spreading bleeds H-spreading in parallel to the hortatory imperative $_{2}$ (see (29) in §3.2). There is no Plateauing, since the H on the prefix is not followed by another H.

Kuria Plateauing involves a number of complexities depending on the position of long vowels and the exact position of the triggering Hs in the verb which are beyond the scope of this article – and are also not addressed by Reference Marlo, Mwita and PasterMMP and Reference Sande, Jenks and InkelasSJI. The core of Plateauing is a general phrasal rightwards spreading process which extends the first of two non-adjacent Hs up to the penultimate syllable before the following H,Footnote ⁵ which I will implement by the constraints in (36). *H…H is equivalent to the constraint *Trough in Yip (Reference Yip2002: 137), and OCP to the OCP constraint in Myers (Reference Myers1997).

(37) shows the derivation for the negative infinitive form in (34a). While *H …H would favour full spreading to the penultimate syllable as in (37c), this is blocked by higher-ranked OCP. *Spr-L (*Spread-Left, (27c)) ensures that the left, not the right H spreads as in (37d). Since * is ranked above Max $|$ and Max $\unicode{x3C4}$ , the delinked tones are deleted and not maintained afloat as in (37b) (in contrast to phrase-final floating tones, which do not violate *):

Note that the differentiation of H-spreading in instances of Melody-Final Spreading and Plateauing also obviates a variant of the spreading argument against a tone-melody analysis of Kuria, raised by Rolle & Lionnet (Reference Rolle, Lionnet, Baek, Takahashi and Yeung2020). Rolle & Lionnet acknowledge the existence of morphological Ls, and argue that this is what blocks spreading in forms like the hortatory imperative $_{1}$ (as in the analysis provided here). Since, on the other hand, in forms like the negative remote future $_{2}$ (cf. (34)) there is spreading, they conclude that these must lack Ls. Just like Reference Marlo, Mwita and PasterMMP’s criticism of tone melodies, this argument is based on the premise that there is one unified process of rightwards H-spreading. However, all examples cited by Rolle & Lionnet instantiate the configuration in (38a), not the one in (38b):

Thus, the data invoked by Rolle & Lionnet actually confirm the analysis proposed here: (38a) triggers melody-final spreading, hence L-spreading, and (38b) Plateauing.

4.2 Evidence for underlying Ls

Reference Marlo, Mwita and PasterMMP claim that the assumption of underlying Ls in Cammenga’s original tone-melody approach to Kuria is problematic because the language lacks independent evidence for Ls apart from positioning Hs. This argument takes up the major line of reasoning in analyses of many Bantu languages to justify an underlying H/ $\varnothing $ contrast for languages with a surface H/L distinction, summarised in an influential paper by Hyman (Reference Hyman and Shigeki2001a). Hyman identifies as the hallmark of a privative H/ $\varnothing $ language that Ls (in contrast to Hs) do not spread, trigger dissimilation or show other similar effects: they are ‘inactive’. However, if the Kuria reanalysis provided here is on the right track, there clearly is substantial evidence for active underlying Ls in Kuria. As we have seen, the underlying Ls of tonal melodies have at least four different surface effects apart from their role in capturing the position of morphological Hs: (a) Ls spread (and prevent otherwise expected H-spreading; see the analysis of the mandatory imperative, the negative remote future $_{1}$ and the hortatory imperative $_{2}$ in §3.2); (b) they overwrite Hs (as in the negative remote future $_{1}$ ; see §3.1); (c) they surface in the formation of rising tones (in the Contour pattern; see §3.3); and (d) they intervene between Hs and their potential association targets (in the Lost-H pattern; see again §3.3).

One might interpret Reference Marlo, Mwita and PasterMMP’s argument in a broader sense presupposing a parameter model which allows only strict H/L or strict H/ $\varnothing $ languages, thus excluding an analysis where Ls are absent in verb roots but employed as inflectional tones. But there are clear examples of languages with an underlying H/L/ $\varnothing $ contrast where L and $\varnothing $ neutralise on the surface – the textbook example is Margi (Pulleyblank Reference Pulleyblank1986; Tranel Reference Tranel1992; Kenstowicz Reference Kenstowicz1994), and Hyman (Reference Hyman and Shigeki2001a) cites Kinande as a Bantu case in line with Mutaka (Reference Mutaka1994). Also, a substantial number of other Bantu languages which otherwise seem to be consistent with a H/ $\varnothing $ analysis provide evidence for underlying Ls in some minor part of their system. For example, Haya (Hyman & Byarushengo Reference Hyman, Byarushengo, Clements and Goldsmith1984) employs Ls as boundary tones postlexically. According to Hyman & Byarushengo (Reference Hyman, Byarushengo, Clements and Goldsmith1984: 66–67), Ls are also exceptionally employed in the HLH melody of specific imperative forms.

In Hyman’s analysis of Luganda, Ls are created by lexical rules, an analysis also argued for by Ebarb (Reference Ebarb2014) for Idakho and by Paster & Kim (Reference Paster and Kim2011) for Tiriki. Tiriki also provides evidence for lexically sparse underlying Ls which block H-spreading, also found in other Bantu languages such as Lumarachi (Marlo Reference Marlo2007). In sum, there does not seem to be strong support for a strict parametric distinction between underlying H/L vs. H/ $\varnothing $ languages. OT also provides a fundamental alternative to the parameter view, the principle of Richness of the Base in tandem with a mechanism of Lexicon Optimisation (Prince & Smolensky Reference Prince and Smolensky1993). By Richness of the Base, grammars have to consider in principle all possible input specifications (in our case L and $\varnothing $ ); however, the underlying forms of specific roots and affixes are computed by a ‘reverse’ application of optimisation to their surface realizations.Footnote ⁶ As shown by Inkelas (Reference Inkelas1995) for Margi, Lexicon Optimisation predicts for tonal systems underlying underspecification for lexical material which alternates, but full specification for non-alternating patterns. This seems to fit well with the situation in Kuria: Verb roots are tonally underspecified since their tonal shape varies according to tense, whereas tone melodies such as the Remote Past LLH are reliably realized in the output and should correspond to underlying Ls.

4.3 The Obligatory Contour Principle

A further objection raised by several anonymous reviewers against a tone-melody approach is that consecutive Ls violate the original version of the Obligatory Contour Principle (OCP), the ban against adjacent identical tones.

Even before the original formulation of Autosegmental Phonology in Goldsmith (Reference Goldsmith1976), the OCP was invoked by Leben (Reference Leben1973) as an inviolable universal morpheme structure constraint which restricts tonal melodies before they are mapped to segments. However, Goldsmith (Reference Goldsmith1976) himself rejects the principle because it cannot capture lexically distinctive tone association in Etung and tone melodies with multiple Hs. Thus, in Tiv, the recent past is marked by a single H mora after the root tone of L verbs (e.g., /nɡòhoro/ $\rightarrow $ [nɡòhórò] ‘accepted (rec.)’) and H verbs (e.g., /jévese/ $\rightarrow $ [jévésè] ‘fled’). In the same context, the past habitual exhibits two consecutive H moras (e.g., /nɡòhoro/ $\rightarrow $ [nɡòhóróǹ] ‘used to accept’, /jévese/ $\rightarrow $ [jévéséǹ] ‘fled’; Pulleyblank Reference Pulleyblank1986: 83, 87). Odden (Reference Odden1986), in the most thorough pre-OT study on the OCP, uncovers several hard exceptions to the predictions of the OCP from Shona, Shambala, Kikuyu, Kishambaa, Yala Ikom and Temne. Tranel (Reference Tranel1992) notes lexical exceptions to the predictions of the OCP in Margi, and Cahill (Reference Cahill2007) makes a detailed argument for input OCP violations of both Ls and Hs in Kɔnni. Hyman (Reference Hyman, Oostendorp, Ewen, Hume and Rice2011) lists additional potentially problematic cases from Dioula’Odienne and Acatlán Mixtec. Representative recent OT studies providing analyses requiring the abandonment of the OCP as an input constraint on tone melodies are provided by McCarthy et al. (Reference McCarthy, Mullin, Smith, Botma and Noske2012), McPherson (Reference McPherson2016) and Rolle (Reference Rolle2021).

In OT, the natural response to the exceptions to the OCP has been to reinterpret it as a violable constraint on output representations, which also solves the conceptual problem that Leben’s version of the constraint violates, again, Richness of the Base (Yip Reference Yip2002; McCarthy et al. Reference McCarthy, Mullin, Smith, Botma and Noske2012). Crucially, specific OT analyses also show that the original empirical insights behind the OCP for single languages can still be captured if it is understood as an output constraint on stems and/or words, not on single morphemes. This is demonstrated by Myers (Reference Myers1997) for Shona, which Kenstowicz (Reference Kenstowicz1994) cites as a prototypical case of evidence for the input OCP. Similarly, Tebay (Reference Tebay2022) shows that basic Mende tone patterns – the original data set put forth by Leben (Reference Leben1973) as evidence for the input OCP – can be captured directly by violable output constraints in OT including an output version of the OCP.

Let us now turn to the specific use of the morpheme structure version of the OCP as an argument for a Construction Phonology approach. Whereas the analyses of Reference Marlo, Mwita and PasterMMP and Reference Sande, Jenks and InkelasSJI adhere to the letter of the principle, the unrestricted use of morpheme-specific rules or constraints makes its empirical predictions virtually empty. Thus, Construction Phonology can simply emulate the effect of affixal tone melodies with multiple adjacent Hs or Ls excluded by the input OCP by assuming a morpheme-specific insertion or spreading rule as in the analysis of OCP-violating morphology in Manyika by Paster (Reference Paster2019) (see Appendix C.1 in the Supplementary Material for a more general demonstration of this point). In sum, the cross-linguistic evidence for the tonal OCP does neither provide a compelling argument against tonal input melodies which violate it nor for a Construction Phonology account which adheres to its interpretation as an inviolable morpheme structure constraint.

Kuria by morphologically sensitive ordered rules (Marlo et al. Reference Marlo, Mwita and Paster2015)

Reference Marlo, Mwita and PasterMMP’s analysis of Kuria employs ordered derivational rules as in SPE (Chomsky & Halle Reference Chomsky and Halle1968). However, unlike SPE, these rules seem not to apply cyclically, but on complete postlexical representations where word-internal morphological and prosodic structure is still fully visible. All verbal inflectional tones are introduced by morphology as single floating Hs, whereas association and spreading are triggered by phonological rules sensitive to morphological features. Thus, the $\unicode{x3BC}$ 3 pattern of the remote future is captured by (39a), the $\unicode{x3BC}$ 4 pattern of the inceptive by (39b) and H spreading for both tenses by (39c), whereas this rule would not apply to the hortatory imperative H without H spreading (the apostrophe indicates an unassociated tone).

Rules like (39a) and (39b) show the gist of Reference Marlo, Mwita and PasterMMP’s take on the morphosyntax–phonology interface: morphologically triggered rules apply in a domain whose left edge is a word-internal boundary and whose rightward extent is unlimited in the entire utterance. The full power of SPE’s rule ordering mechanism is applied in Reference Marlo, Mwita and PasterMMP’s analysis of contours in short stems (see §3.3 for discussion): A rule of final lengthening adds a mora to phrase-final vowels (e.g., /romaⒽ/ → romaaⒽ), which may then serve as the target for H-association (→ romaá) and insertion of a default L (→ romàá), feeding a further rule which removes the epenthetic mora again and reassociates the stranded H, resulting in a rising contour (→ [romǎ]).

Kuria in Cophonologies by Phase (Sande et al. Reference Sande, Jenks and Inkelas2020)

Reference Sande, Jenks and InkelasSJI reinterpret the Kuria data as evidence for the Cophonologies by Phase model (henceforth: CbP), where morphophonology is derived cyclically in Harmonic Grammar evaluations in domains defined not by stems, words and utterances, but by syntactic phases as conceived in non-lexicalist versions of Minimalist syntax. Thus, Reference Sande, Jenks and InkelasSJI posit a syntactic structure for a Kuria inceptive (4) sentence such as (2b) [to-ra-[rom-a] ] ‘we are about to bite a banana’ in which part of the morphological verb (the stem without prefixes: [rom-á]) is spelled out together in the vP, whereas the prefixes are only introduced in the CP and spelled out there.

In Reference Sande, Jenks and InkelasSJI’s approach, construction-specific phonology is achieved by vocabulary items which as part of their idiosyncratic lexical specification contain fixed amounts of weight addition (or weight subtraction) by which they modify specific constraints. The constraint weighting of an optimization cycle in a given phase P is then the default general weighting of the language modified by all weight adjustments of the VIs concatenated in P itself (thus in the CP phase the VIs for C and Tense, but not for any material in the vP, or the subject DP, which have been introduced in earlier phases). For the general phonology of Kuria, Reference Sande, Jenks and InkelasSJI stipulate that Ident-Tone outweighs the constraint requiring tone dislocation (in (40) so that in the default case underlying tones remain unmodified in the output (Reference Sande, Jenks and InkelasSJI: 1237):

The inceptive VI has a floating H and weight modifications which effectively invert the default weighting by incrementing the weights of $\unicode{x3BC}$ 4 and Spread-(H, R), and reducing the weight of Ident-Tone. The CP evaluation for our example clause is thus as in (41), where the inceptive H is shifted by four moras to the right:

Under this analysis, all mora-counting tone morphologies in Kuria have the same source – a single floating H as part of the tense prefix; they differ only in the constraints they promote. Thus, the remote future would add weight to a $\unicode{x3BC}$ 3 constraint, the past progressive to a $\unicode{x3BC}$ 2 constraint and so on.

The central theoretical significance Reference Sande, Jenks and InkelasSJI attribute to the Kuria data is that it discredits the standard stratal architecture of the morphology–syntax interface, in which word-internal phonology strictly precedes phrase-level phonology. Reference Sande, Jenks and InkelasSJI’s argument has two components. First, they claim that delaying autosegmental material originating in word-internal morphology to associating only at the phrase level leads to technical problems (‘it is unclear how to prevent morpheme-specific phonology from being realized until the post-lexical level’ (Reference Sande, Jenks and InkelasSJI: 1239)). Second, they argue that even if the first problem could be solved, an analysis using dormant tones would make less restrictive predictions on locality domains than the CbP account. A major result of the Kuria reanalysis developed in §§3 and 4 is that it provides a constructive proof that Reference Sande, Jenks and InkelasSJI’s first argument is unfounded. A stratal tone-melody analysis of Kuria is possible (see also Appendix D in the Supplementary Material for a detailed summary of technical problems in Reference Sande, Jenks and InkelasSJI’s CbP analysis). In §5.2, I will show that the second argument is also empirically problematic.

5.1 Phonological Locality

The baseline for my discussion of Phonological Locality here will be a slightly extended version of the proposal by McCarthy (Reference McCarthy2003: 6), formulated in (42). The basic intuition is that every OT constraint has an obligatory locus, the unit which actually triggers distinct constraint violations, and optionally a left and right context specification. McCarthy considers an even tighter locality version of this principle which allows only for a single context restriction, mirroring the Locality Principle of Hewitt & Prince (Reference Hewitt and Prince1989) for derivational rules, but this is obviously too narrow. Thus, since OT constraints are generally defined negatively, binarity constraints actually require a window of three elements. For example, evaluating a constraint requiring maximally two moras in a syllable means to assign violations to syllables with three (or more) moras. Independently from specific OT assumptions, tone plateauing obviously cannot be captured using a single context restriction (as argued by Jardine Reference Jardine2016; see §4.1 for discussion). Since I am not concerned with hierarchical prosodic representations here, (42) is defined for purely autosegmental representations, where a local autosegmental object is either a single autosegmental node on tier T or a planar object, that is, an object composed of an autosegmental node $N_1$ on tier $T_1$ and a second autosegmental node $N_2$ on tier $T_2$ , where $T_1$ and $T_2$ are associated (e.g., a tone associated to a mora).

Let us see how some of the constraints used in the Kuria reanalysis fit into this template. A trivial case is Max $\unicode{x3C4}$ (‘Assign $\ast $ to every tone which is marked as phonetically invisible’). The locus is a single autosegmental node (on the tonal tier) without context restrictions. In * (‘Assign $\ast $ to every $\unicode{x3BC}$ which is phonetically associated to two Ls’), we can interpret the initial structure $\unicode{x3BC} -$ L as the constraint locus and the second L as the right context (or vice versa). Finally, in the constraint inducing Plateauing, *H …H (‘Assign $\ast $ to every mora which intervenes between two Hs’), the locus is the potentially intervening mora, and both the left and the right context contain a single H each.

On the other hand, the Construction Phonology analyses of Kuria are incompatible with the Locality Principle in (42). Thus, the constraints/rules responsible for the Kuria $\unicode{x3BC}$ 2 patterns can be approximated by the formulations in (43) compatible with the three-element window imposed by the Locality Principle, but there is no way to fit in the remote future $\unicode{x3BC}$ 3 (or, a fortiori, $\unicode{x3BC}$ 4 inceptive), since the necessary window would comprise at least four independent objects:

Thus, while the Construction Phonology accounts necessarily violate the Locality Principle, the tone-melody approach can implement the Kuria facts in accordance with (42), since the $\unicode{x3BC}3$ and $\unicode{x3BC}4$ patterns follow from morphological melodies which are not subject to categorical length restrictions. An anonymous reviewer objects that this solution just shifts the problem from phonology to morphology, since it still can capture the $\unicode{x3BC}3$ and $\unicode{x3BC}4$ ‘counting’ patterns in Kuria. Crucially, the merit of the combined Stratal OT/Locality Principle approach is not simply that it can capture the morphological LLH and LLLH patterns in Kuria, but that it also – in contrast to the Construction Phonology approaches – makes restrictive typological predictions beyond Kuria. I will illustrate this with two phenomena which under Reference Sande, Jenks and InkelasSJI’s and Reference Marlo, Mwita and PasterMMP’s analyses are closely related to the Kuria data: (a) productive instances of bounded tone shifting and spreading, and (b) tonal infixation.

5.2 Cyclic Locality

Since the general predictions of a lexicalist stratal architecture based on stems, words and phrases are well-known (see, e.g., Bermúdez-Otero Reference Bermúdez-Otero, Hannahs and Bosch2018b), I will only shortly comment here on two predictions for tone.

5.3 Indirect Reference

Under Indirect Reference, phonological constraints (or their weighting/ranking) cannot be sensitive to specific morphemes. Idiosyncratic properties of a morphological tone must be strictly due to its underlying phonological representation. Whereas this allows for capturing the Kuria facts, it still substantially limits possible systems of morpheme-specificity compared to Construction approaches. I will again discuss two specific predictions of the approach adopted here for tone: (a) Generality of Association: the association of tone melodies to moras is not morpheme-specific, but determined by the general constraint ranking of the relevant stratum; and (b) Morphological Locality: the effects of a tone melody are restricted to the tone melody itself, and hence its properties do not affect other tone melodies.

Generality of Association can be illustrated with the possibility of mirroring the processes in Kuria. Recall that for MMP the behaviour of the remote future is captured by the two morphosyntactically conditioned rules in (45a) and (45b). However, in Reference Marlo, Mwita and PasterMMP’s approach, we could also imagine another morphologically conditioned tone in Kuria – let us call this the hypothetical future – which is the mirror image of the remote future: it puts a H on the third mora before the stem boundary by the rule in (45a $'$ ), which undergoes additional unbounded leftwards spreading by (45b $'$ ):

Nothing like the morpheme-specific mirroring pattern could be implemented under the Indirect Reference approach, where unbounded spreading is achieved by general constraints (and therefore has to be either leftwards or rightwards throughout the grammar), and tone melodies map uniformly. Thus, a mirror melody to the Remote Future LLH, that is, HLL, would not have the same effect as (45b), but result in association of the H to the stem-initial mora similar to the HL of the Hortatory Imperative (see §3.1).