2.1 Basic pattern

Laal is characterised by a complex anticipatory rounding harmony, which applies under very restrictive conditions. First, it is parasitic: the trigger and target vowels need to be of the same height (the ‘αheight’ condition) and frontness (the ‘βfront’ condition). Second, it is particularly unusual in requiring two triggers: a round vowel can round a preceding vowel only with the help of a labial consonant. Interestingly, the round vowel and the labial consonant – the two co-triggers – may be on either side of the target, as in (2a), or on the same side, as in (2b, c). This harmony is restricted to certain specific morphological contexts, discussed in §2.4.

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As can be seen in (3a), Laal has twelve phonemic vowels, characterised by three degrees of aperture and an opposition between [+front] and [−front] vowels, coupled with a rounding contrast among both [+front] and [−front] vowels.Footnote ³

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The examples in (4) show that all four conditions (the two triggers V₂[rd] and labC, and the two additional conditions αheight and βfront) must be met in order for rounding to occur. If any one of the four conditions is missing, as in (4a), harmony fails to apply. The examples in (b, c) show that, as expected, harmony also does not apply when more than one condition is missing.

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Additionally, the teamwork effect is necessarily driven by the association of a labial consonant and a round vowel. Two labial consonants may not team up to co-trigger rounding, as shown in (5).Footnote ⁴

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General phonotactic restrictions limit the number of potential triggers and targets of the harmony. First, since words in Laal are maximally disyllabic,Footnote ⁵ it is impossible to derive forms that would show harmony across more than one syllable. The harmony thus involves only one target, the stem-initial vowel V₁ (there are no prefixes in Laal). The trigger is always V₂, and may be part of a disyllabic stem or a suffix, as in the examples in (2).

Furthermore, the full vowel inventory in (3a) is only attested in the stem-initial syllable (V₁). In V₂ position, only seven of the twelve vowels are attested: the three front round vowels /y yo ya/, and the two low peripheral vowels /ia ua/ are never found there.Footnote ⁶ The only triggers of the harmony are thus /u/ and /o/ – the only two [+round] vowels attested in V₂ – each of which, by virtue of the αheight and βfront conditions, can only target one vowel: V₂ /u/ rounds V₁ /ɨ/ to [u], while V₂ /o/ rounds V₁ /ə/ to [o]. The properties of the doubly triggered rounding harmony are summarised in (6).

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2.2 A note on vowel harmony

The underlying forms in the examples seen so far are those resulting from application of all other phonological processes, in particular vowel raising or lowering resulting from other vowel harmonies. A brief note on these harmonies is in order at this point, to make the data presented in the remainder of this section easier to read. No fewer than four harmony processes are attested in Laal. In additional to the doubly triggered rounding harmony, a simpler rounding harmony also exists (cf. §2.5), as well as two height harmonies: perseverative [+high] harmony and anticipatory [±low] harmony, illustrated in (7).

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In what follows, the underived form of each example will be given alongside the intermediate and final derived forms.

2.3 The blocking effect of intervening /w/

The only nine (regular) exceptions to the doubly triggered rounding harmony are listed in (8a) and (b), and illustrate another intriguing property of the harmony: the blocking effect of /w/ when it intervenes between V₁ and V₂.

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Not only does an intervening /w/ not co-trigger the harmony (a), it blocks it, as clearly shown by [məwó] in (b), where word-initial /m/ fails to act as a co-trigger. Word-initial /w/, on the other hand, co-triggers the harmony like any other labial consonant, as shown in (c).Footnote ⁷ This blocking effect of intervening /w/ is rooted in an exceptionless phonotactic constraint that bans sequences of a round vowel followed by /w/ (with an optional intervening consonant): *U(C)w. This constraint is exceptionless, both in the lexicon and in morphologically derived environments (cf. (14) below).

2.4 Morphological conditioning

The harmony is only actively enforced between roots and number-marking suffixes (other types of suffixes and their effects will be presented in §2.5). Laal has 29 number-marking suffixes (10 singular, 19 plural), which combine arbitrarily with a restricted set of nouns and verbs. Out of 1150 monomorphemic nouns in my corpus, 384 combine with at least one such suffix. The most frequent (/-u/) is attested with 73 nouns, while eleven of these suffixes are attested with fewer than five nouns each. Additionally, some of these suffixes are used to derive either the plural or the singular subject form of 38 intransitive verbs, e.g. /ɲún/ ‘go (sg subj)’ vs. /ɲún-ì/ ‘go (pl subj)’.

Four number-marking suffixes contain a round vowel (henceforth ‘round suffixes’): the three plural suffixes /-u/ (73 occurrences), /-o/ (46) and /-or/ ~ /-ur/ (14), and the singular suffix /-o/ (7). /-or/ ~ /-ur/ varies between a mid and a high realisation, subject to [+high] harmony (cf. (7a) above). All three occur only on nouns in my corpus. The doubly triggered rounding harmony is thus attested as an active process only with nouns, although this is most probably accidental.

140 of the 1150 monomorphemic nouns in the lexicon are compatible with one of the four round suffixes above. Of these 140 nouns, 89 have an underlying non-round V₁. 34 of these meet the conditions for doubly triggered rounding harmony, i.e. their plural form has both a labial consonant (C₁, C₂ and/or C₃) and two vowels of identical height and frontness. These nouns obey doubly triggered rounding harmony, with only the nine (regular) exceptions with intervening /w/ in (8) above. This leaves 25 attested cases of active doubly triggered rounding harmony, some of which are given in (9a) and (b, c), where V₁ and V₂ are both high and both mid respectively.Footnote ⁸

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A few nouns have more than one possible plural form. Interestingly, two such nouns, shown in (10), have two round suffixes, and contain a labial consonant. As expected, rounding harmony applies only when both vowels are of the same height before application of the harmony, i.e. with /-ó/, but not with /-ú/.

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The limited productivity of doubly triggered rounding harmony is due to the limited productivity of the number-marking suffixes, which seem to be in the process of becoming lexicalised. In this respect, it is not different from other morphophonological alternations that phonologists regularly choose to model. However, number-marking morphology cannot be said to be entirely fossilised, since plural suffixes (including the round suffixes /-ó/ and /-ú/) sometimes occur with more or less recent loanwords, as shown in (11). Note that the first two examples illustrate the application of doubly triggered rounding harmony to words of foreign origin. Loanwords from Bagirmi and Arabic are most probably not older than 200 to 300 years, and French loanwords are definitely less than a century old.

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The doubly triggered rounding harmony is also a morpheme structure constraint: there is no word in the lexicon that does not conform to its requirements. Words like [gōbə̄r] ‘cloud’ and [gúmlí̵l] ‘round’ further show that the harmony is strictly anticipatory.

Finally, both the harmony and the *U(C)w phonotactic constraint apply only within words, and never across a word boundary, as shown in (12).

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2.5 A phonological alternation

There is evidence that the doubly triggered rounding harmony described above is a phonological process, rather than a superficial phonetic effect. Firstly, the harmony is exceptionless: it applies systematically whenever the conditions are met. The only exceptions are entirely regular, and result from an independent phonotactic restriction, *U(C)w. Furthermore, it is not sensitive to speech rate: when asked to speak slowly, or even to mark a pause between the two syllables of a word where the harmony should apply, speakers never ‘undo’ the harmony.

The most solid argument in favour of the phonological status of the harmony is its morphological conditioning: it applies as a morpheme structure constraint, and between roots and number-marking suffixes. With pronominal suffixes, on the other hand, anticipatory rounding harmony is systematic and unconditional, as illustrated in (13a) with the object suffixes /-nǔ/ ‘us (excl)’ and /-ò(n)/ ‘her’ (subject to [+high] harmony; cf. (7a) above). (13b) shows segmentally similar examples illustrating doubly triggered harmony. As can be seen, the conditions for doubly triggered harmony (labC, αheight and βfront) are irrelevant to the simple harmony.

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Simple rounding harmony also fails to apply in contexts where it would violate *U(C)w, as seen in (14).

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The two rounding harmonies are thus specific to two exclusive sets of morphological environments. Given the requirement that words be maximally disyllabic in Laal, the segmental domain of application of both harmonies is exactly the same. For all of the above reasons, we can safely conclude that the doubly triggered rounding harmony is a phonological process, and whatever drives it should consequently be accounted for in phonology.

In conclusion, the doubly triggered rounding harmony of Laal is a phonological process that has no irregular exceptions: it systematically applies whenever the conditions summarised in (15) below are met.

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3.1 Subfeatural representations: the basics

The featural system I propose is a two-tiered system: contrastive featural categories are subdivided into non-contrastive, perceptually distinct subfeatural categories arising from coarticulatory effects. This proposal is in keeping with the idea, supported by a growing body of evidence, that contrastiveness, i.e. unpredictable phonological distribution, and perceptual distinctiveness are independent criteria (Hall Reference Hall2013, Kiparsky Reference Kiparsky2013 and references therein).

The subfeatural level of representation, scalar in nature, captures differences in perceptual distinctiveness resulting from coarticulation. The featural [±round] contrast may thus coexist with a multi-level subfeatural rounding scale, as separate (but substantively related) representations of the lip-rounding continuum.Footnote ¹¹

By convention, contrastive categories correspond to full subfeatural values, i.e. [−F] and [+F] entail 〚0F〛 and 〚1F〛 respectively, unless coarticulation applies (subfeatures are given in double square brackets). On the subfeatural scale, coarticulatorily driven subphonemic distinctions may be encoded whenever relevant, with intermediate subfeatural values x (0 < x < 1). For example in Laal, the perceptual rounding scale, corresponding at the contrastive level to the binary feature [+round] vs. [−round], can be represented as a continuum between 〚0round〛 and 〚1round〛. [+round] vowels are 〚1round〛, [−round] are 〚0round〛, unless they are labialised, in which case they are 〚xround〛. The [−round] category is thus subdivided into two subfeatural categories: 〚0round〛 ([i e ia ɨ ə a], which are not rounded at all, and 〚xround〛 ([ɨ^B ə^B], which have some proportion x of the phonetic properties that characterise fully round vowels. In other words, labial coarticulation increases 〚0round〛 to 〚xround〛. The subfeatural value 〚xround〛 represents the consequences of labial coarticulation on the realisation and perception of the feature [−round]. Subfeatures are thus determined on the basis of both phonetic factors and phonological representations.

Crucially, labialised [ɨ^B] and [ə^B] are featurally [−round], but subfeaturally 〚xround〛. This explains why they behave like their non-labialised counterparts with respect to the simple rounding harmony, which refers to binary features only, and how they can also be seen as a distinct category by doubly triggered rounding harmony, which is sensitive to subfeatural distinctions, as illustrated in Fig. 1.

Figure 1 Targets of the doubly triggered and simple rounding harmonies.

3.2 Calculating subfeatural values: the Coarticulation function

Coarticulatory triggers have the property of assigning to their target a proportion of increase (or decrease) in the value of the affected subfeature 〚F〛 incurred by the coarticulatory effect of the trigger onto the target. I will call this proportion a coarticulatory coefficient, and represent it as p _{Trigger→Target,〚F〛}, or simply p. The resulting intermediate subfeatural value x of the target segment is obtained through the application of a Coarticulation function C, defined in (16), and schematised in (18) below.

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Note that the C_p function can be either additive or subtractive, depending on which endpoint of the 〚0…1F〛 scale the function starts from, and which one it tends toward. If, as in Laal, the pre-coarticulation subfeatural value of the target corresponds to the lower endpoint 〚0F〛, the function is additive: the amount of increase incurred by the target (assuming that there is only one trigger) is +p(x_end  − x_init ) = +p(1 − 0) = +p. The 〚0F〛 value of the target segment is thus increased to 〚p F〛. If, on the other hand, x_init corresponds to the full value 〚1F〛, the function is subtractive: the amount of decrease is +p(x_end  − x_init ) = +p(0 − 1) = −p, i.e. the target segment's initial 〚1F〛 value is lowered to 〚(1 − p)F〛.Footnote ¹²

The value of the binary feature that a given intermediate subfeatural value x is associated with thus depends on the initial subfeatural value of the target and the ‘direction’ of the coarticulation function. If the function is additive (i.e. property-increasing), 〚xF〛 corresponds to [−F], like the value 〚0F〛 from which it derives; if the function is subtractive (i.e. property-decreasing), 〚xF〛 corresponds to [+F], like the value 〚1F〛 from which it is derived. The only two subfeatural values that are always associated with the same featural value are 〚0F〛, which systematically corresponds to [−F], and 〚1F〛, which can only correspond to [+F]. Conversely, [+F] and [−F] can in theory correspond to any subfeatural value between 0 and 1 except 1 and 0 respectively ([−F] ↔ 〚xF〛 with 0 ≤ x < 1; [+F] ↔ 〚xF〛 with 0 < x ≤ 1). This is schematised in (17).

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Doubly triggered rounding harmony targets vowels whose increased subfeatural 〚xround〛 value is the result of the application of the additive coarticulatory function schematised in (18).Footnote ¹³

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The value of p depends on the properties of each of the segments involved and the perceptual correlate of their coarticulation. Additionally, the C_p function needs to be relativised to context, e.g. interspeaker differences, distance between the target and the trigger, relative position of trigger and target, etc. (cf. Lionnet Reference Lionnet2016). Each trigger–target interaction in each of the relevant contexts is likely to yield a different subfeatural value (e.g. [ɨ^B] / B __ ≠ [ɨ^B] / __ B ≠ [ə^B] / B __, etc.). In the interest of a clear presentation of the theory, I tentatively consider [ɨ^B] and [ə^B] to be 〚xround〛, for all speakers, irrespective of the specific environment. This simplified analysis will be refined in §4.4.3, after the presentation of the phonetic data in §4.1 to §4.3.

3.3 Illustrative analysis: Laal doubly triggered rounding harmony

With the analysis sketched in §3.1 above, doubly triggered rounding harmony can be reduced to a case of rounding harmony parasitic on height and backness, targeting only vowels that are at least 〚xround〛. Any theory of parasitic vowel harmony will presumably account for the Laal harmony if it can refer to subfeatures, whether it utilises feature spreading (e.g. Padgett Reference Padgett1997, Jurgec Reference Jurgec2011, Reference Jurgec2013), feature alignment (Kirchner Reference Kirchner1993, Smolensky Reference Smolensky1993, Kaun Reference Kaun1995), feature agreement or no-disagreement constraints (Baković Reference Bakovi«2000, Pulleyblank Reference Pulleyblank2002), Agreement by Correspondence (Hansson Reference Hansson2001, Reference Hansson2010, Rose & Walker Reference Rose and Walker2004) or Wayment's (Reference Wayment2009) Attraction Framework.

The goal of this section is not to argue in favour of one specific theory of vowel harmony, but simply to illustrate how one such theory may easily account for the Laal harmony by simply including subfeatural representations. The illustrative analysis I propose uses Hansson's (Reference Hansson2014) Agreement by Projection theory, a revision of Agreement by Correspondence, couched in Optimality Theory (Prince & Smolensky Reference Prince and Smolensky1993).Footnote ¹⁴

First, independently of the harmony pattern, I propose that subfeatural distinctions be enforced by the phonological grammar, through high-ranked markedness constraints. The default 〚0round〛 ↔ [−round] and 〚1round〛 ↔ [+round] associations are enforced through the constraints defined in (19a, b), while labial coarticulation is enforced by the constraint in (c).

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Constraints like (19c), penalising the non-application of the coarticulatory function, must be ranked higher than the two constraints in (a) and (b) if coarticulation-driven subfeatural values are to be assigned, as shown in the tableaux in (20). In this specific case, the coarticulation function being additive, (19c) need only be ranked higher than (19a), which is the only one that is violated if Cp _B→ə/ɨ applies.

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As seen in (20), the constraints pick only one of all the possible subfeatural values between 0 and 1 for each input: default 0 or 1 when there is no coarticulation (20a, b), x (and not y ≠ x, or any other intermediate value) when B-ɨ/e coarticulation is involved (c). To keep tableaux simple and legible, these three constraints will from now on be conflated into the placeholder constraint Subfeature (Subf).

I now turn to the analysis of the harmony pattern, using Hansson's (Reference Hansson2014) revision of Agreement by Correspondence (ABC). ABC is a theory of similarity-based segmental interaction that was initially developed for long-distance consonant agreement (Walker Reference Walker1998, Reference Walker2000, Reference Walker, Kirchner, Pater and Wikeley2001, Hansson Reference Hansson2001, Reference Hansson2010, Rose & Walker Reference Rose and Walker2004). It has since been extended to vowel harmony (Sasa Reference Sasa2009, Walker Reference Walker2009, Rhodes Reference Rhodes2012), long-distance consonant dissimilation (Bennett Reference Bennett2013, Reference Bennett2015) and local effects of assimilation and dissimilation (Shih Reference Shih2013, Inkelas & Shih Reference Inkelas and Shih2014, Shih & Inkelas Reference Shih, Inkelas, Kingston, Moore-Cantwell, Pater and Staubs2014, Sylak-Glassman Reference Sylak-Glassman2014).

What makes ABC particularly suited to parasitic vowel harmony is its central insight that (dis)harmony is driven by similarity threshold effects. Harmony between segments is viewed as agreement between segments in a correspondence relationship based on phonological similarity. This surface correspondence is unstable (Inkelas & Shih Reference Inkelas and Shih2014): two (or more) segments are sufficiently similar to interact (they are in correspondence), but are too uncomfortably similar to coexist within a certain distance. Two repairs are possible: harmony (more similarity) and disharmony (less similarity).

The basic mechanics of ABC theory involve two types of output–output correspondence constraints: Corr-XX establishes surface correspondence between segments X similar in a particular (set of) feature(s), while Ident-XX[F] enforces agreement in the feature [F] between segments in the correspondence set defined by Corr-XX. Both types of constraints are ranked higher than the constraints enforcing faithfulness to the assimilating feature. Based on a diagnosis of pathological properties of the division of labour between Ident-XX[F] and Corr-XX, Hansson (Reference Hansson2014) proposes to conflate the work of both constraints into a single ‘projection-based’ markedness constraint, defined in (21).

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I adopt Hansson's (Reference Hansson2014) projection-based constraints here, simply allowing them to refer to subfeatures as well as binary features. The constraint that drives the doubly triggered rounding harmony is given in (22). In order to account for the threshold effect, I propose that projection-based constraints refer to ranges of subfeatural values rather than single values.

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The constraint in (22) (henceforth *〚≥xrd〛〚1rd〛/[+syll, αheight, βfront]) drives the harmony by establishing the threshold of subphonemic rounding beyond which a labialised [ə^B] or [ɨ^B] is targeted by the harmony at 〚xround〛. This constraint stands in a markedness hierarchy that mirrors the featural similarity scale in Table II, where the similarity levels are ordered on the basis of how much they restrict the number of potential targets; the highest level of similarity is the most restrictive.Footnote ¹⁵

Table II Similarity between round and non-round vowels in Laal: tentative scale.

Each level of similarity in the scale could in theory be the threshold involved in a rounding-harmony process. Consequently, the similarity scale translates into a markedness-constraint hierarchy, shown in (23), in which the constraint defined in (22) is ranked highest.Footnote ¹⁶

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In doubly triggered rounding harmony, the similarity threshold at work is the highest level on the scale; Ident[round] must therefore be ranked right below the highest markedness constraint *〚≥xrd〛〚1rd〛/[+syll, αheight, βfront], but crucially higher than all the other constraints in the hierarchy, as shown in tableaux (24) and (25).

Undominated Subf ensures that (24a) /ɓì̵r-ú/ and (24b) /ɓə̀r-ú/ do not surface with a V₁ that is not at least 〚xround〛, since in both forms V₁ is adjacent to a labial consonant: candidates (a.i) and (b.i) are thus always suboptimal. Candidate (a.ii), [ɓì̵^Brú], violates *〚≥xrd〛 〚1rd〛/[+syll, αheight, βfront]. The fact that this constraint is ranked higher than Ident[round] favours candidate (a.iii), [ɓùrú], in which rounding harmony has applied, repairing the marked structure. On the other hand, candidate (b.ii), [ɓə̀^Brú], does not violate this constraint: it only violates constraints that are lower on the markedness hierarchy,

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and crucially ranked lower than Ident[round], which makes it the optimal output.

Finally, given the inputs /mèn-ú/ and /gí̵n-ù/ in (25), Subf strikes candidates (a.ii), [mè^Bnú], and (b.ii), [gí̵^Bnù], where labial coarticulation has overapplied ([e] is not a coarticulatory target, and [g n] are not labialisation triggers), leaving only (a.i), [mènú], and (b.i), [gí̵nù], as the optimal outputs. Indeed, the violation of Ident[round] incurred by rounding V₁ in candidates (a.iii), [myònú], and (b.iii), [gúnù], is not compensated by satisfying a higher constraint: there is no marked structure to repair.

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To complete the analysis, two undominated constraints need to be added. The first one is a positional faithfulness constraint (Beckman Reference Beckman1999), Ident[round]σ₂, which accounts for the fact that unrounding of V₂ is not a possible repair, as shown by candidate (26d). Note that the directionality of the harmony is accounted for by the combination of this positional faithfulness constraint and the markedness constraint penalising *〚≥xrd〛〚1rd〛/[+syll, αheight, βfront] (which can only correspond to a [−round][+round], not a [+round][−round], sequence): if the [+round] feature of V₂ cannot be changed, then only anticipatory rounding will fix the marked 〚≥xround〛〚1round〛 sequence.

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Additionally, we need a projection-based markedness constraint accounting for the opacity of intervening /w/, defined in (27).

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This is illustrated in (28).

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Finally, simple rounding harmony, which belongs to a separate, morphologically specific subgrammar, is driven by a projection-based constraint referring only to binary features, defined in (29).

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This constraint also stands in a markedness hierarchy, mirroring the similarity scale in Table II. In this case, however, Ident[round] is ranked below the lowest constraint of the hierarchy, i.e. the threshold for rounding is at the lowest possible point, as shown in (30).Footnote ¹⁷

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This is illustrated in (31).

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The analysis presented above is one of many possible, and illustrates one of the advantages of the subfeatural representations proposed in this paper: extending the domain of application of existing theories of vowel harmony (and more generally assimilation) to complex multiple-trigger cases involving subphonemic teamwork.

3.4 The nature of subfeatures

3.5 Enforcing and manipulating subfeatures in a constraint grammar

A crucial property of subfeatures illustrated by the analysis proposed above is that, in an OT grammar, they are not protected by faithfulness. Indeed, a faithfulness constraint referring to a subfeature, if ranked sufficiently high, would make this subfeature contrastive, contrary to the key intuition that subfeatures encode non-contrastive categories. The nature of subfeatures thus makes them invisible to faithfulness. I assume that this is because subfeatures are not present in the input.

Additionally, it is necessary to rank the markedness constraints responsible for assigning subfeatures very high in order for subfeatural distinctions to play a role in the phonological grammar. If coarticulatory effects can be seen by phonology, the markedness constraints responsible for enforcing coarticulation-driven subfeatural distinctions cannot be ranked below other constraints whose effects would undo coarticulation. An interesting consequence of the high ranking of such constraints is that they constitute the only part of the constraint grammar that can manipulate subfeatures, i.e. be satisfied by a subfeature being added to or removed from the input. All other constraints referring to subfeatures (e.g. *〚≥xrd〛〚1rd〛/[αheight, βfront] in (22) above) can in theory be satisfied by manipulating either subfeatures or binary features, but only the latter will ever be optimal, since any subfeatural change will be filtered out by the high-ranked constraints enforcing coarticulation. Subfeatural values can thus only be modified indirectly, by changing the (substantively related) featural content of the input, e.g. changing [−round] into [+round] necessarily entails a change from 〚0round〛 or 〚xround〛 to 〚1round〛. In other words, the undesirable effects of coarticulation can only be undone by modifying the phonological environment responsible for it, not by simply modifying the subfeatural values that are a representation of those effects. In that sense, subfeatures are subordinate to classical binary features.Footnote ²⁰

3.6 The architecture of the phonological grammar

Subfeatures constitute a representation of segments in context, i.e. a representation of the phonetic knowledge of how segments interact when put together. This abstract knowledge exists alongside phonology, and is what phonology uses to predict the realisation of specific inputs. In cases where this predicted realisation violates a phonotactic constraint, a phonological operation must apply to change the coarticulatory context in order to ensure that the realisation of the output conforms to the phonotactics. The phonological grammar is thus organised in a feed-back/feed-forward loop (cf. Boersma Reference Boersma1998) that constitutes a fluid and dynamic model of the phonetics/phonology interface, where phonology and phonetic knowledge are not ordered, but parallel and interactive.

The next section presents instrumental evidence in support of subfeatural categories.

4.1 Effects of the B condition

Acoustic measurements clearly show that a labial consonant has a very significant F2 lowering effect on (near-)adjacent [ə] and [ɨ].

4.1.1 Effect of the B condition on [ə]

The ə-words included in the sample for both speakers are summarised in Table III (the full list can be found in Table VI in Appendix B in the online supplementary materials). The total number of tokens within each condition includes repetitions, e.g. three separate productions of the word [p5d] ‘pass’ and one production of the word [mə̀l] ‘be straight’ constitute a total of four [Bə] tokens.

Table III ə-words sample, B and U conditions (both speakers).

Figure 2 shows the mean F1, F2 and F3 values of stem-initial [ə] in each of the B and U conditions, for both speakers. As can be seen, the two B conditions appear to have a strong lowering effect on F2. The U condition also seems to lower F2 somewhat, but to a lesser extent. F1 and F3 appear to be unaffected.Footnote ²¹ In the remainder of this section, I will concentrate on the F2 lowering effect of the B and U conditions.

Figure 2 Effect of B and U conditions on [ə]: (a) speaker AK; (b) speaker KD.

Figure 3a shows the distribution of the F2 values of non-labialised [ə] vs. [ə] / B __ and [ə] / __ B in AK's speech. As can be seen from these figures and from Tables VIII and IX in Appendix B, a neighbouring labial consonant has a strong, consistent and highly statistically significant F2 lowering effect on [ə]: [ə] / B __ is on average 1.66 ERB (288 Hz) lower in F2 than [ə] (t(20) = −5.6, p = 9.96e⁻⁶), while [ə] / __ B is 1.42 ERB (250 Hz) lower (t(22.8) = 3.9, p = 7.79e⁻⁴). Since the lowering of F2 incurred by the B __ and __ B conditions is of similar magnitude, both can be collapsed into one single category: [ə^B], which in this case is on average 1.61 ERB (279 Hz) lower in F2 than [ə] (t(18) = 5.9, p = 1.54e⁻⁵). The overall F2 lowering effect is of a similar magnitude in KD's speech, as shown in Fig. 3b, the effect of a preceding B being stronger (ΔF2 = −1.76 ERB (−311 Hz), t(24.5) = −3.7, p = 0.001) than that of a following B (ΔF2 = −0.95 ERB (−181 Hz), t(19.9) = 2.1, p = 0.049). [ə^B] is on average 1.43 ERB (256 Hz) lower in F2 than [ə] (t(21.5) = 3.4, p = 0.003).

Figure 3 Effect of /B_ and /_B conditions on F2 of [ə]: (a) speaker AK; (b) speaker KD.

The vowel plots in Fig. 4 very clearly show that the distributions of [Bə] and [ə^B] mostly overlap, and that they are distinct from both [ə] and [o]: both [Bə] and [ə^B] (= [ə^B]) are exactly between [ə] and [o] in terms of F2.Footnote ²²

Figure 4 [ə]/B_ and [ə]/_B plotted against [e], [ə] and [o]: (a) speaker AK; (b) speaker KD.

4.1.2 Effect of the B condition on [ɨ]

The coarticulatory effects on [ɨ] are congruent with, and stronger than, the effects on [ə], for both speakers, and across the two conditions B and U. The ɨ-words included in the sample are listed in Table VII in Appendix B, and summarised in Table IV.Footnote ²³

Table IV ɨ-words sample, B and U conditions (both speakers).

Note that two of the above conditions (U in [gí̵nù] ‘nets’ and ɨCB in [lì̵gmà] ‘horses’) are attested in only one word each. Each one was recorded only once, from one speaker only (AK and KD respectively). I return to these two words below.

Figure 5 presents the mean F1, F2 and F3 values of stem-initial [ɨ] in both B __ and __ B environments, for both speakers. As in Fig. 4 for [ə], only F2 seems to be affected by a preceding or following labial consonant, and it is strongly affected, for both speakers.

Figure 5 Effect of B conditions on [ɨ]: (a) speaker AK; (b) speaker KD.

As shown in Fig. 6, the F2 lowering effect of the B condition on [ɨ] is drastic, and very highly significant for both speakers. In AK's speech, F2 is on average 2.25 ERB (407 Hz) lower in [ɨ] / B __ than [ɨ] (t(79.7) = −14.6, p = 2.20e⁻¹⁶), 2.20 ERB (396 Hz) lower in [ɨ] / __ B (t(87.7) = 12.5, p = 2.20e⁻¹⁶), and overall 2.22 ERB (402 Hz) lower for labialised [ɨ^B] than for [ɨ] (t(75) = 15.4, p = 2.20e⁻¹⁶). For KD, the findings are extremely similar: 1.96 ERB (343 Hz) lower in [ɨ] / B __ (t(59.9) = −8.6, p = 5.40⁻¹²), 1.42 (257 Hz) lower in [ɨ] / __ B (t(18.1) = 4.1, p = 6.67e⁻⁴), and 1.87 ERB (328 Hz) lower overall (t(56) = 8.5, p = 1.10e⁻¹¹).

Figure 6 Effect of /B_ and /_B conditions on F2 of [ɨ]: (a) speaker AK; (b) speaker KD.

The vowel plots in Fig. 7 show that the B __ and __ B environments have virtually the same effect on a neighbouring [ɨ]. The distribution of labialised [ɨ] / B __ and [ɨ] / B (= [ɨ^B]) with respect to [ɨ] and [u] is similar to that of [ə] / B __ and [ə] / __ B (= [ə^B]) with respect to [ə] and [o]: [ɨ] and [ɨ^B] have virtually non-overlapping distributions, and [ɨ^B] seems to be exactly between [ɨ] and [u], for both speakers.

Figure 7 [ɨ]/B_ and [ɨ]/_B plotted against [i], [ɨ] and [u]: (a) speaker AK; (b) speaker KD.

As mentioned earlier, only one token illustrating the ɨCB condition could be included in the sample: the plural noun [lì̵gmà] (KD). With only one token, it is impossible to draw any generalisations. However, it is noteworthy that the mean F2 of [ɨ] in [lì̵gmà], 18.02 ERB (1407 Hz), is much closer to that of KD's [ɨ] / __ B (17.80 ERB/1378 Hz) than to that of non-labialised [ɨ] (19.22 ERB/1635 Hz), and the mean F2 difference between the [ɨ] in [lì̵gmà] and KD's non-labialised [ɨ] (ΔF2 = 1.20 ERB (227 Hz)) is very close to that between KD's [ɨ] and [ɨ] / __ B (ΔF2 = −1.42 (−257 Hz)).This suggests that the intervening non-labial consonant does not prevent labialisation of the preceding [ɨ].

4.2 Effect of the U condition

4.2.1 Effect of the U condition on [ə]

As previously noted, the charts in Fig. 2 show lowering of the mean F2 [ə] in the presence of a following round vowel for both speakers, although this lowering effect is less strong than that caused by either of the two B environments. For AK, [ə] / __ U is on average 0.57 ERB (110 Hz) lower than [ə] (Fig. 8a), and for KD 0.89 ERB (172 Hz) lower (Fig. 8b). However, this difference is not statistically significant, as shown in Appendix C (t(13.7) = 1.7, p = 0.12 for AK; t(18) = 2.0, p = 0.059 for KD).

Figure 8 Effect of U condition on F2 of [ə]: (a) speaker AK; (b) speaker KD.

This can be seen in the vowel plot in Fig. 9, where the centre of the [ə…U] ellipse is noticeably further right than that of the [ə] ellipse – indicating a substantive mean F2 difference – but the F2 range of [ə…U] is nearly entirely contained within that of the [ə] ellipse, contrary to that of the [ə^B] (= [Bə]+[əB]) ellipse, which clearly occupies an intermediate range between [ə] and [o].

Figure 9 [ə]/__…U plotted against [e], [ə], [ə^B] and [o]: (a) speaker AK; (b) speaker KD.

4.3 Cumulative effect

When more than one condition is met, the effect of each individual condition is cumulative. This can be illustrated with AK's short [ə] in the B __ B condition only. As can be seen in Fig. 10 and in Table VIII in Appendix C, the cumulative F2 lowering effect of two labial consonants (B __ B) on [ə], such as in [mə̀mlə̀l] ‘my grandchild’, is significantly greater than that of a single labial consonant. Indeed, [ə] / B __ B is 2.51 ERB (425 Hz) lower in F2 than [ə] (t(10) = 8.4, p = 7.72e⁻⁶), and 0.91 ERB (146 Hz) lower than that of short [ə^B] (t(0.7) = −4.1, p = 0.011).

Figure 10 Effect of B_B condition on F2 of [ə] (speaker AK).

4.4 Summary and discussion

4.4.3 Calculating p and x

The coarticulatory coefficient p _{B→ə/ɨ,〚rd〛} involved in the labialisation of [ə ɨ] can be calculated on the basis of the F2 measurements provided above. For example, assuming that the F2 values of [ə] (18.95 ERB) and [o] (14.31 ERB) correspond to the subfeatural values 〚0round〛 and 〚1round〛 respectively, the proportion of increase from 〚0round〛 [ə] to 〚xround〛 [ə^B] p _{B→ə,〚rd〛} in AK's speech can be calculated as the ratio between ΔF2 [ə^B]–[ə] and ΔF2 [o]–[ə], as shown in (32).

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Table V provides the value of p for all trigger–target pairs (i.e. B→[ə] and B→[ɨ]), for both speakers.

Table V Values for p _{B→ə,〚rd〛} and p _{B→əɨ,〚rd〛} for speakers AK and KD.

The subfeatural value of x for an 〚x round〛 vowel can then be determined by applying the C _p function defined in (16) above, as shown in (33).

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In other words, in AK's speech, a labial consonant increases the subfeatural 〚round〛 value of a (near-)adjacent [ə] by ≈34%, making labialised [ə^B] subfeaturally 〚0.34 round〛.

In a form like [mə̀mlə̀l], where the first [ə] is surrounded by two labial consonants, the same function applies twice (i.e. is composed with itself, cf. (16d)), as illustrated in (34).Footnote ²⁵

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This prediction almost perfectly matches the observed F2 decrease incurred by two labial consonants on [ə] (cf. Table IX in Appendix C). Indeed, the observed F2 value of [ə] / B_B (16.44 ERB) corresponds to 54% of that of 〚0round〛 [ə] (18.95 ERB), given that 〚1round〛 [o] is 14.31 ERB. Compare this with the predicted 56% in (34b).

To refine the analysis developed in §3 above, there should be as many coarticulation-enforcing constraints (i.e. *¬Cp _{B→ə/ɨ,〚rd〛}; cf. (19c)) as there are p _{Tr→Ta,〚rd〛} values. For example, for AK, we need both *¬Cp _{B→ə,〚rd〛}, setting the proportion of 〚round〛 caused by B on [ə] at 34%, and *¬Cp _{B→ɨ,〚rd〛}, setting the proportion of increase caused by B on [ɨ] at 47% (cf. Table III).

The threshold at work in doubly triggered rounding harmony can be defined as 〚≥0.34〛 for AK and 〚≥0.39〛 for KD (i.e. the lowest x-value obtained through B-ɨ/ə coarticulation). The constraint driving doubly triggered rounding harmony, defined in (22) above (as well as the other constraints in the markedness constraint hierarchy in (23)) can thus be redefined as (35).

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As we have seen, every one of the constraints referring to subfeatures exists in as many variants as there are relevant coarticulatory contexts, i.e. as there are p and x values, and of course as many as there are speakers. In this way, the theory of subfeatural representations can easily accommodate interspeaker variation.

5.1 The [labial] approach

The first possibility is to represent the coarticulatory effect of labial consonants on neighbouring central vowels with the feature [labial]: labialised [ɨ^B ə^B] are both [−round] and [labial], and doubly triggered rounding harmony targets only [labial] vowels: V_[labial] → [+round] / __ C(C)V[+round]. This supposes both that the CPlace feature [labial] and the VPlace feature [round] are phonologically different (as in VPlace theory; cf. Ní Chiosáin & Padgett Reference Ní Chiosáin and Padgett1993). This account is descriptively adequate: the feature [labial] plays exactly the same role as the 〚xround〛 subfeature advocated above, without adding any novel representations to the phonological machinery.

However, the distinction between [labial] and [round] vowels has five main problems, which are avoided in the subfeatural approach.

First, the fact that labial consonants and round vowels pattern together in the doubly triggered rounding harmony is exactly the kind of argument used elsewhere in favour of treating labial consonants and round vowels as carrying the same contrastive feature, as opposed to two substantively separate features [labial] and [round] (cf. Unified Feature Theory; Clements Reference Clements1989, Clements & Hume Reference Clements, Hume and Goldsmith1995; also Ní Chiosáin & Padgett Reference Ní Chiosáin and Padgett1993: 2).

More problematic is the fact that the [labial] account is more stipulative than the subfeatural one. Indeed, the CPlace feature [labial] seems to have properties that other binary or privative CPlace features do not have, and such properties must be stipulated. For example, it must be stipulated that [labial], despite being a CPlace feature, may be borne by a vowel.Footnote ²⁶ Additionally, in order to maintain the non-structure-preserving nature of this allophony (i.e. [ɨ ə] and [ɨ^B ə^B] do not constitute contrastive phonemes), it also has to be stipulated that [labial] is non-contrastive for vowels, and never part of any vowel's underlying representation: it may only be assigned to a vowel through coarticulation (or spreading) from a neighbouring consonant. No such stipulation is necessary in the subfeatural approach, where 〚xround〛 is not specific to consonants, but substantively related to the VPlace feature [±round], and is, like any other subfeature, defined as non-contrastive and never present underlyingly.

The third problem posed by the [labial] approach is that there is no natural relation between the [round]–[labial] featural difference and the acoustic differences observed between the two categories of vowels. Indeed, while it seems natural for a vowel that has only 34% of what constitutes a fully round vowel (as in the case of AK's [ə^B] vs. [o]) to be characterised as 〚0.34 round〛, it is not clear why a [labial] vowel (let alone a labial consonant) should be realised with 34% of the phonetic correlate of the feature [round]. It is actually not entirely clear how a [labial] vowel should be realised.

Fourth, such a convenient split between two similar features – one vocalic, the other consonantal – is not available in all cases of teamwork. Cases that involve only vocalic triggers and targets, such as the Woleaian alternation illustrated in §1, could not be accounted for in the same way (cf. Lionnet Reference Lionnet2016: 105–111).

Finally, the [labial] account seems to be mostly based on convenience, rather than explanatory adequacy, and misses an important generalisation. What the acoustic measurements show in Laal is partial F2 lowering, which is not accounted for by the feature [labial] and the mostly artificial distinction between [labial] and [round].

5.2 The backness approach

Another possibility is to consider that the doubly triggered rounding harmony is actually better characterised as [+back] harmony. Indeed, front vowels do not take part in the harmony – which we have seen involves only [−front] vowels – and rounding and backness are systematically correlated among [−front] vowels: the central vowels are always [−round], and the back ones always [+round]. There is thus a confound: the doubly triggered harmony may be regarded either as rounding harmony or as [+back] harmony.

The advantage of choosing the latter option is that it leaves the feature [+round] available to account for the labial coarticulatory effect on [ɨ] and [ə]. Non-low central vowels [ɨ ə] would thus not be analysed as partially rounded to [ɨ^B ə^B] in the vicinity of a labial consonant, but as fully rounded to [ʉ ɵ]. All that is left to do is restrict the possible targets of [+back] harmony to [−front, +round] vowels with the same height specification as the trigger vowel: [ʉ ɵ] → [u o] / __ (CC)V[+back, αheight].

This analysis, which seems to render the use of subfeatures unnecessary, would be descriptively adequate if we focused only on the doubly triggered harmony. However, it has less explanatory power than the subfeatural account, and encounters numerous problems when the simple rounding harmony described in §2.5 is considered, which seriously undermines its validity.

Firstly, it mischaracterises the doubly triggered rounding harmony, by failing to capture its most interesting property: the substantive relation that exists between the activity of the two triggers. Indeed, both the alternation and the instrumental measurements indicate that the doubly triggered rounding harmony is a single process, involving only one property: rounding – not two separate properties and processes: rounding from the labial consonant, backing from the V₂. In that sense, 〚xround〛 [ɨ^B ə^B] is a better transcription and analysis than [+round, −back] [ʉ ɵ], since it clearly indicates the degree and provenance of the partial rounding effect. The substantive relation between the partial coarticulatory effect of the labial co-trigger and the categorical effect of the round vowel is also very well represented in the two-tiered feature + subfeature system, whereas it is not at all represented in either the [labial] vs. [round] or [−back, +round] vs. [+back, +round] accounts.

But more importantly, by making the vowel inventory more complex, it severely mischaracterises simple rounding harmony as well, and unnecessarily complicates its analysis. As shown in (36), the recognition of a featural distinction between [ʉ ɵ] and [u o] requires a third feature to account for the now five-way horizontal distinction: [±front] and [±round] are no longer sufficient; [±back] is also necessary (compare the inventory in (3a) above).

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This complicates the analysis of the simple rounding harmony. If it is analysed as one single rounding harmony process, then [+front] vowels are rounded to [y yo a], as expected, but [−front] vowels are changed to central rounded vowels [ʉ ɵ ɞ].Footnote ²⁷ For the latter to be realised as [u o ua], we would further need to change these vowels into [+back] [u o ua], either through a high-ranked constraint against central rounded vowels (in parallel OT), or with a late rule ensuring that [ʉ ɵ ɞ] are unconditionally changed to [+back] on the surface (in a rule-based account). However, this option is not available, since [ʉ ɵ] (= [ɨ^B ə^B]) are attested on the surface, as shown by the phonetic measurements in §4. They are not contrastive, but are definitely part of the inventory, as conditioned allophones of /ɨ ə/, which means that there cannot be a high-ranked constraint (or a late rule) banning them from surface representations.

A second option is to analyse the [ɨ ə a] → [u o ua] change as a case of [+back] harmony (similar to the one involved in the doubly triggered harmony, but without the height and frontness conditions). What appears to be a very simple case of rounding harmony is here divided into two unrelated processes, driven by two different rules or set(s) of constraints: rounding harmony among [+front] vowels, [+back] harmony among [−front] vowels, as illustrated in (37).

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However, there is no evidence that (37a) and (37b) are distinct processes, and treating them separately goes against both the economy principle and the human instinct for pattern recognition.

In conclusion, the [labial] and [+back] accounts seem to be uninsightful and unnecessarily complicated solutions whose unique advantage is to avoid adding new representations to phonological theory. However, they only achieve this representational economy at the expense of grammatical simplicity and, more importantly, explanatory power. I contend that the new subfeatural representations proposed here offer a simpler and more explanatory account of the Laal data, a criterion I think should be ranked above representational economy in the design of a theory.