2.1 The Law of Three Consonants

In French, some morphemes alternate between a form with schwa and a form without schwa. For instance, the noun demande ‘request’ can be realized with a schwa as [dəmãd] or without schwa as [dmãd]. Determining the factors that condition the distribution of schwa-zero alternations has been a central topic in French phonology for more than a century. Table 1 provides a non-exhaustive list of the variables that have been reported to play a role in this alternation along with a non-exhaustive list of the sources that document these effects. This table builds largely but not exclusively on Bürki et al. (2011: 3982–3985).

Among these variables, the consonantal context, and in particular the number of consonants surrounding schwa, has received particular attention early on. In his influential treaty on French pronunciation, Grammont (1914: 115–116) states that a preconsonantal schwa is obligatory when preceded by two consonants (CC_C), as illustrated in (1a), but excluded when preceded by a single consonant (C_C), as illustrated in (1b). He calls this generalization the ‘loi des trois consonnes’ (Law of Three Consonants; LTC) and explains it as a strategy to avoid three-consonant clusters. In (1a), the schwa form is preferred because it makes it possible to avoid the three-consonant cluster [tdm]. In (1b), the schwa-less form is preferred in the absence of three-consonant clusters.

2.2 Not only size matters, at least at the word and phrase levels

Subsequent works on French schwa have provided a more nuanced view of the LTC. First, the LTC has been found to hold as a gradient rather than a categorical generalization: schwa is not obligatory in CC_C and excluded in C_C but more likely in CC_C overall than in C_C (Bürki et al. 2011; Racine & Andreassen 2012; Côté 2012; Hambye & Simon 2012; Hansen 2012). Second, not only the number but also the nature and order of surrounding consonants has been found to be relevant. C_C sequences with increasing sonority favor the schwa-less form (Bürki et al. 2011). In CC_C, schwa is more likely to be pronounced if the middle consonant is a stop than if it is a fricative (see Côté 2001: 119 and earlier references therein), as illustrated in (2). Also, schwa is more likely to be pronounced if its absence implies that an obstruent-liquid cluster (OL) is not directly followed by a vowel (Dell 1976; 1985; Côté 2001), as illustrated in (3).

This nuanced view of the LTC has been argued to be relevant at the phrase level (e.g. when the three-consonant cluster spans a word boundary, as illustrated in (2) and (3)) and at the word level (e.g. when the three-consonant cluster spans a boundary between a stem and an inflectional suffix). This latter case is illustrated in (4) with the inflectional future/conditional suffix -r- [ʁ]. At the boundary between a stem and this inflectional suffix, schwa is more likely to be pronounced if its absence implies that an obstruent-liquid cluster (OL) is not directly followed by a vowel (Côté 2001: 85). The situation is analogous to what happens at the phrase level (see (3)).

However, at the stem level, the LTC is still generally considered to hold as a categorical generalization in line with Grammont’s strict interpretation in (1). Three-consonant sequences (CC_C) at the stem level include sequences that are contained within a single morpheme (e.g. [ʁg_ʁ] in marguerite ‘daisy’) or span a boundary between a stem and a derivational suffix (e.g. [ʁd_-ʁ_derivational] in garde-rie ‘Kindergarten’). In this context, schwa is generally reported to be categorically pronounced and this regardless of the nature and order of surrounding consonants (Dell 1978; Côté 2001: 85, 109; Côté 2012: 258–259; but Scheer 1999: 90 with further discussion in section 2.4). For instance, schwa is reported by Dell and Côté to be obligatory in both OL_C and CO_L at the boundary between stems and derivational suffixes, as illustrated in (5a) and (5b). This contrasts with the differential treatment of OL_C and CO_L at the phrase and word levels illustrated in (3) and (4).

2.3 The hypothesis of strongly distinct phonologies across domains

The common view according to which the nature of consonants involved in CC_C sequences is relevant for schwa-zero alternations in words and phrases but not in stems implies that the phonological grammar may differ quite substantially across morphosyntactic domains. At the word and phrase levels, a set of phonotactic constraints referencing different types of three-consonant clusters (e.g. *OLC, *COL, etc.) would be active, resulting in different patterns of schwa-zero alternations for different types of three-consonant clusters, as illustrated in (2), (3), and (4). At the stem level, only a single phonotactic constraint banning three-consonant clusters would be active (*CCC),¹ resulting in a single pattern of schwa-zero alternations for all CC_C sequences, as illustrated in (5).

This paper will test the hypothesis of strongly distinct phonologies across morphosyntactic domains for French by focusing on two specific three-consonant sequences (obstruent-liquid-consonant sequences and liquid-obstruent-liquid sequences) and two specific morphosyntactic contexts (derivation and inflection). Obstruent-liquid-consonant sequences (OL_C) and liquid-obstruent-liquid sequences (LO_L) were chosen because they behave differently in some morphosyntactic domains (see (3) and (4)). Derivational suffixes (as illustrated in (5)) and inflectional suffixes (as illustrated in (4)) were chosen as examples of stem-level and word-level domains, respectively, because both involve suffixation and therefore form a minimal pair for the stem-level vs. word-level distinction. Derivational suffixes attach to stems to form complex stems, as illustrated in (6a). Inflectional suffixes attach to stems to form words, as illustrated in (6b) (Dell 1978: 7–8).

The predictions of the hypothesis of strongly distinct phonologies across domains are summarized in (7) for the two relevant consonant sequences (OL_C and LO_L) and the two relevant morphological contexts (derivation and inflection). The predictions are summarized in (7a) at the level of the data (probability distribution of schwa-zero alternations) and in (7b) at the level of the grammar (constraint set in each stratum).

In (7a), P(ə|context) refers to the conditional probability of schwa presence given a particular morphophonological context. According to the hypothesis of strongly distinct phonologies across stem and word levels, this probability varies depending on the nature of the consonants involved in the CC_C sequence at the word level (inflection) but it is constant for all CC_C sequences at the stem level (derivation).

The main features of a phonological grammar that can derive these asymmetries are summarized in (7b). Phonotactic constraints are indexed to specific morphosyntactic domains. Constraint indexation is one of the ways to derive morpheme-specific phonology (Pater 2007). At the stem level, a single *CCC_derivation constraint penalizes any three-consonant cluster that spans a boundary between a stem and a derivational suffix. Hence it penalizes equally OLC clusters (e.g. [ɡlm] in règle-ment [ʁɛɡl-mã] ‘regulation’ in (5a)) and LOL clusters (e.g. [ʁdʁ] in garde-rie [ɡaʁd-ʁi] ‘Kindergarten’ in (5b)). At the word level, different consonant clusters are penalized by different constraints. *OLC_inflection penalizes an obstruent-liquid-consonant cluster that spans a boundary between a stem and an inflectional suffix (e.g. [ɡlʁ] in règle-ra [ʁɛɡl-ʁa] ‘adjust-fut.3sg’; see (4a)). *LOL_inflection penalizes a liquid-obstruent-liquid cluster that spans a boundary between a stem and an inflectional suffix (e.g. [ʁdʁ] in garde-ra [ɡaʁd-ʁa] ‘keep.fut.3sg’; see (4b)).

Table 2 shows how a grammar with the properties in (7b) can in principle derive the type of probability distribution hypothesized in (7a) for schwa-zero alternations. Each of the four relevant morphophonological contexts are shown in the first column. The second column shows the schwa and schwa-less variants for each context. Columns 3 to 6 show how each variant is evaluated by the four constraints in the analysis (1 indicates that the candidate in the corresponding row violates the constraint in the corresponding column). In addition to the three constraints in (7b), a faithfulness constraint Dep(ə) penalizing the epenthesis of schwa was added. This analysis assumes that the schwa-less variant is the underlying form and the schwa variant is derived through epenthesis. This is the classic analysis of French schwa at morpheme boundaries (Dell 1985).² To materialize the relative importance of constraints, weights (w) are used. The constraint weights in Table 2 were chosen for illustration purposes only. The harmony of a candidate (column 7) corresponds to the weighted sum of its constraint violations, as in Harmonic Grammar (Smolensky & Legendre 2006). Probabilities (last column) are calculated from those harmonies using the MaxEnt framework (Goldwater & Johnson 2003; Hayes & Wilson 2008).

The probabilities in Table 2 follow the predictions in (7a): the probability of using the schwa form (in bold characters) is constant at the stem level (derivation) regardless of the consonants involved in the CC_C sequence whereas this probability varies depending on the nature of the consonants involved at the word level (inflection). Moreover, if the weight of the constraint banning three-consonant clusters at the stem level (derivation) is sufficiently high relative to the weight of the faithfulness constraint penalizing schwa (here the ratio of the corresponding weights is 7/1), then it is possible to derive a near categorical behavior for schwa-zero alternations in this context, with schwa being nearly obligatory (the probability is equal to 1.00 due to rounding). More variability can be derived at the word level (inflection) if the weights for the relevant constraints are not as far apart (here the ratios for the corresponding weights are 2/1 and 1/1).

The hypothesis of strongly distinct phonologies across stem and word levels seems to be generally assumed in the literature, at least by Dell (1985) and Côté (2001). One exception is Scheer (1999: 90), who reports differential treatments for three-consonant clusters even in stems for some speakers. However he does not provide direct empirical evidence for this claim. To the author’s knowledge, the only study which tested the Law of Three Consonants in stems is Côté (2012): in a corpus study of Quebec French, she found no exception to the LTC under its categorical version (Côté 2012: 258). However, as will be further discussed in section 3.1.1, the corpus used in this study is probably too small to draw strong conclusions regarding the categorical nature of the LTC.

2.4 The hypothesis of weakly distinct phonologies across domains

Alternatively, schwa-zero alternations could be gradient and sensitive to the nature of consonants across levels but closer to categorical at the stem level, at least for some speakers (e.g. Scheer 1999). According to this view, the same phonotactic constraints against various types of three-consonant clusters would be active across levels but their effects would be potentially more subtle at the stem level. The predictions of this hypothesis are summarized in (8), with (8a) focusing on the predictions at the level of the data and (8b) on the predictions at the level of the grammar. The grammar in (8b) uses the same phonotactic constraints at the stem and word levels (contrary to the grammar in (7b)). This means that the probability of the schwa form can vary by consonant cluster both at the stem and word levels, as shown in (8a). But it does not need to vary at both levels if the relevant constraints have the same weights for some speakers.

Table 3 shows how a grammar with the properties in (8b) and an additional Dep(ə) constraint can predict differential treatments of different CC_C sequences at both word and stem levels, as hypothesized in (8a).

The probabilities in Table 3 follow the predictions in (8a): the probability of using the schwa form (in bold characters) varies both at the stem level (derivation) and at the word level (inflection). Moreover, if the weights of the constraint banning OLC clusters (*OLC) and LOL clusters (*LOL) at the stem level are sufficiently high relative to the weight of the faithfulness constraint penalizing schwa (here the ratios of the corresponding weights are 5/1 and 4/1, respectively), then it is possible to derive near categorical behaviors for schwa-zero alternations in these contexts, with schwa being nearly obligatory (probabilities are equal to 0.98 and 0.95, respectively). However the two morphophonological contexts (OL-C_derivation, LO-L_derivation) are still predicted to behave slightly differently with respect to schwa-zero alternations (the probabilities of the schwa form are distinct although close; 0.98 vs. 0.95), due to the weights of the two relevant phonotactic constraints being different (5 vs. 4). Moreover, the effects of phonotactic constraints are predicted to be more salient at the word level (inflection) if their weights are not as large relatively to the weight of the faithfulness constraint. Here the ratios for the corresponding weights are 2/1 and 1/1, to be compared to the larger ratios at the stem level (5/1 and 4/1).

A grammar with the property in (8b) can also derive uniform and near-categorical treatments for OL_C and LO_L sequences at the stem level if the two relevant constraints (*OLC_derivation and *LOL_derivation) have the same weights and these weights are high (the resulting grammar then behaves like the grammar in Table 2).

In other words, this analysis shows that it is theoretically possible to predict more subtle and closer to categorical effects of phonotactic constraints at the stem level than at the word level while still assuming the same phonotactic constraints in both morphosyntactic domains. This type of asymmetries in the effect of phonotactic constraints is actually predicted by current models of probabilistic constraint-based grammars such as MaxEnt. This type of models are indeed known to produce floor and ceiling effects, due to the sigmoid relationship they imply between harmony and probability (Zuraw & Hayes 2017: 506–510). Moreover, the same analysis can derive uniform treatments of CC_C sequences at the stem level if the relevant constraints have the same weight for some speakers.

The difference between the hypotheses of strongly vs. weakly distinct phonologies across stem and word levels ultimately hinges on whether some French speakers allow for differential treatments of CC_C sequences at the stem level. Indeed, both hypotheses can derive uniform treatments of CC_C sequences at the stem level. But only the latter hypothesis (weakly distinct phonologies) can derive differential treatments of CC_C sequences at the stem level.

2.5 Implications for phonetically based theories of phonotactic constraints

The main goal of this paper is to tease apart the two versions of the stem-level vs. word-level divide presented in sections 2.3 and 2.4 for French. This question also has theoretical implications beyond French. As anticipated in Section 1, phonetically based theories of phonotactics hold that phonotactic asymmetries ultimately reflect perceptual and articulatory asymmetries (Ohala 1990; 1992; Steriade 1997; Flemming 2002; Storme 2019). According to these theories, the same phonotactic asymmetries should be reflected across the grammar’s morphosyntactic domains if the same phonetic asymmetries among segments hold across these domains. Under the default assumption that segmental properties are largely independent from morphosyntactic context, these theories of phonotactics are more directly compatible with the hypothesis of weakly distinct phonologies across domains in (8).

This point can be illustrated more concretely by considering explanations that have been proposed for asymmetries among three-consonant clusters in French. The phonotactic constraints that drive French schwa-zero alternations in three-consonant sequences have been argued to ultimately have phonetic motivations (Côté 2001: 137–152). For instance, Côté proposed that schwa is more likely to appear after a medial stop (CS_C) than after a medial fricative (CF_C), as illustrated in (2), because stops have weaker perceptual cues than fricatives to signal place of articulation (Wright 2004; Jun 2004) and therefore are more in need of vocalic support. She also proposed that schwa is more likely to occur in OL_C than in CO_L, as illustrated in (3) and (4), because, in the absence of schwa, OL_C features a local sonority peak (the medial liquid) that does not correspond to a syllable peak (French does not allow syllabic liquids), in violation of the sonority sequencing principle (Clements 1990). This problem is solved if schwa is pronounced in OL_C. By contrast, CO_L already satisfies the sonority sequencing principle in the absence of schwa and therefore schwa presence is not as crucial. In both cases (CF_C vs. CS_C and OL_C vs. CO_L), the explanation refers to phonetically based asymmetries among segments. Because these segmental asymmetries are expected to hold across the grammar’s morphosyntactic domains (e.g. a stop should have weaker internal cues than a fricative regardless of morphosyntactic context), then the same phonotactic asymmetries among clusters should be observed across strata, in line with the weak version of the divide between stem-level and word-level phonologies in (8).

2.6 Further hypotheses to be tested

In addition to the strong and weak versions of the stem-level vs. word-level divide, four further hypotheses will be tested in this paper.

3.2 Results

3.2.2 Description of results

Figure 2 shows the posterior distribution (mean and 95% CI) of each response category (1, 2, …, 6, 7) for all cells in the factorial design. This posterior distribution was calculated using Equation 5 in Bürkner & Vuorre (2019: 79). This equation expresses the probability of each response category k as a function of the predictors, their corresponding regression coefficients, and the thresholds τ_k and τ_k-1 inferred along the latent continuous variable.

Figure 2

Posterior distribution (mean and 95% CI) of each of the seven response categories as a function of Morphology, Cluster, and Origin.

Differences between clusters in derived words. Participants were found to rate schwa absence as more likely in LO_L than in OL_C in derivation and there is compelling evidence for this difference for participants from both France (𝔼(μFrench, _{LO_L}, _der — μ_{French, OL_C, der}) = 0.54, CI = [0.15,0.93], P(Δ > 0) = 1) and Switzerland (𝔼 (μ_{Swiss, LO_L, der} — μ_{Swiss, OL_C, der}) = 0.65, CI = [0.25,1.08], P(Δ > 0) = 1). ⁸ Participants were found to rate schwa absence as more likely in C_C than in LO_L in derivation and there is compelling evidence for this difference for participants from both France (𝔼(μ_{French, C_C, der}-μ_{French, LO_L, der}) = 2.49, CI = [2.02,2.99], P(Δ > 0) = 1) and Switzerland (𝔼(μ_{Swiss, C_C, der}-μ_{Swiss, LO_L, der}) = 2.28, CI = [1.74,2.85], P(Δ > 0) = 1).

Controlling for individual differences in the treatment of three-consonant sequences in derived words. As discussed in section 2.4, only some speakers might be driving the general asymmetry between OL_C and LO_L in derived words (stem level). Figure 3 shows how each individual participant in Study 1 treats OL_C and LO_L in derived words. The results confirm the hypothesis of individual variation at the stem level: some participants are more likely to delete schwa in LO_L than in OL_C (participants on the left side of the figure) whereas some participants do not treat the two sequences differently (participants on the right side of the figure).

Figure 3

Posterior distribution (mean and 95% CI) of the difference between LO_L and OL_C in derived words (stem level) by participant. A positive value means that schwa deletion is more likely in LO_L than in OL_C.

Differences between clusters in inflected words. Participants were also found to rate schwa absence as more likely in LO_L than in OL_C in inflection and there is compelling evidence for this difference for participants from both France (𝔼(μ_{French, LO_L, inf}-μ_{French, OL_C, inf}) = 1.37, CI = [0.92, 1.78], P(Δ > 0) = 1) and Switzerland (𝔼(μ_{Swiss, LO_L, inf}-μ_{Swiss, CO_L, inf}) = 1.11, CI = [0.63, 1.57], P(Δ > 0) = 1). Participants were found to rate schwa absence as more likely in C_C than in LO_L in inflected words and there is compelling evidence for this difference for participants from both France (𝔼(μ_{French, C_C, inf}-μ_{French, LO_L, inf}) = 1.10, CI = [0.74, 1.45], P(Δ > 0) = 1) and Switzerland (𝔼(μ_{Swiss, C_C, inf}-μ_{Swiss, LO_, inf}) = 1.07, CI = [0.67, 1.48], P(Δ > 0) = 1).

It can be concluded that there is sufficient evidence to support the hypothesis that the number and nature of surrounding consonants are revelant in both derived and inflected words, with OL_C being judged overall as more likely to feature schwa than LO_L and LO_L more likely to feature schwa than C_C in both derived and inflected words. However there is individual variation at the stem level, as some speakers do not treat OL_C and LO_L differently in this context.

Differences between derivation and inflection. For OL_C clusters, participants were found to rate schwa absence as more likely in inflection than in derivation, but there is compelling evidence for this difference for participants from Switzerland (𝔼(μ_{Swiss, OL_C, inf}-μ_{Swiss, OL_C, der}) = 0.40, CI = [0.05, 0.74], P(Δ > 0) = 0.99) but not for participants from France (𝔼(μ_{French, OL_C, inf}-μ_{French, OL_C, der}) = 0.05, CI = [–0.29, 0.39], P(Δ > 0) = 0.62). For LO_L clusters, participants were found to rate schwa absence as more likely in inflection than in derivation, and there is compelling for this difference for participants from both France (𝔼(μ_{French, LO_L, inf}-μ_{French, LO_L, der}) = 0.88, CI = [0.48, 1.28], P(Δ > 0) = 1) and Switzerland (𝔼(μ_{Swiss, OL_C, inf}-μ_{Swiss, OL_C, der}) = 0.86, CI = [0.43, 1.30], P(Δ > 0) = 1). An unexpected result was obtained for C_C clusters. In this context, participants were found to rate schwa absence as less likely in inflection than in derivation, with compelling evidence from participants from both France (𝔼(μ_{French, C_C, inf}-μ_{French, C_C, der}) = –0.51, CI = [–0.81, –0.19], P(Δ > 0) = 0) and Switzerland (𝔼 (μ_{Swiss, C_C, inf}-μ_{Swiss, C_C, der}) = –0.35, CI = [–0.69, 0.01], P(Δ > 0) = 0.03). See section 3.3 for further discussion.

Differences between speakers from France and Switzerland. Speakers from Switzerland systematically rate the schwa-less variant higher than speakers from France, and this holds across all six morphophonological contexts: for OL_C sequences in derived words (𝔼(μ_{Swiss, OL_C, der}-μ_{French, OL_C, der}) = 1.22, CI = [0.62, 1.84], P(Δ > 0) = 1), for LO_L sequences in derived words (𝔼(μ_{Swiss, LO_L, der}-μ_{French, LO_L, der}) = 1.33, CI = [0.71, 1.93], P(Δ > 0) = 1), for C_C sequences in derived words (𝔼(μ_{Swiss, C_C, der}-μ_{French, C_C, der}) = 1.11, CI = [0.40, 1.91], P(Δ > 0) = 1), for OL_C sequences in inflected words (𝔼(μ_{Swiss, OL_C, inf}-μ_{French, OL_C, inf}) = 1.57, CI = [0.96, 2.25], P(Δ > 0) = 1), for LO_L sequences in inflected words (𝔼(μ_{Swiss, LO_L, inf}-μ_{French, LO_L, inf}) = 1.31, CI = [0.57, 2.00], P(Δ > 0) = 1), and for C_C sequences in inflected words (𝔼(μ_{Swiss, C_C, inf}-μ_{French, C_C, inf}) = 1.27, CI = [0.51, 2.08], P(Δ > 0) = 1).

3.3 Discussion

The results of Study 1 are summarized in Table 5 for the six morphophonological contexts, with > indicating a greater estimated likelihood of the schwa variant.

Table 5

Summary of Study 1 results: probability of the schwa variant as a function of Cluster, Morphology, and Origin (France vs. Switzerland).

The results of Study 1 support the hypothesis that phonologies are weakly distinct across stem and word levels (see section 2.4) against the hypothesis that they differ strongly (see section 2.3). At the stem level (derivation), not only the number but also the nature of surrounding consonants matters for schwa-zero alternations, at least for some speakers from both France and Switzerland. This means that Grammont’s Law of Three Consonants should be relaxed not only at the word level but also at the stem level. At the grammatical level, the fact that some speakers show sensitivity to the nature of consonants involved in the CC_C sequence in derived words is problematic for the view that only a single *CCC constraint is active at the stem level (see the modeling study in section 5 for further confirmation). By contrast, the absence of effect for other speakers is not particularly problematic for the view that different phonotactic constraints (e.g. *OLC, *LOL) are active at the stem level: indeed, the relevant constraints could have the same (or very similar) weights for these speakers.

Furthermore, the relative markedness of clusters was found to be the same in both derived and inflected words, with OLC being more strongly avoided than LOL and LOL being more strongly avoided than CC. This is in line with the hypotheses presented in section 2.6.2. This is also consistent with phonetically based theories of phonotactic constraints that hold that asymmetries between phonotactic constraints ultimately derive from perceptual/articulatory or sonority asymmetries and therefore predict that these phonotactic asymmetries should be consistent across domains.

Three-consonant clusters were found to be more strongly avoided in derived than in inflected words, in line with the hypothesis that phonotactic restrictions are stronger in lower than in higher morphosyntactic domains (see section 2.6.1). This is consistent with the claim that there are genuine effects of morphosyntactic domains on schwa-zero alternations below the word level (Dell 1977).

However, this result did not extend to two-consonant clusters: two-consonant clusters were unexpectedly found to be more strongly avoided in inflected than in derived words, and for both speakers from France and Switzerland. This result is unexpected in two ways. The literature on French indeed does not report any asymmetry between inflection and derivation in schwa likelihood for two-consonant clusters (e.g. Côté 2001: 85). Moreover, if any asymmetry was to be observed, one would expect it to go in the opposite direction, with derivation favoring schwa presence more than inflection. Indeed, this is what has been observed for three-consonant clusters in the present study and this is also what is expected under the general hypothesis that schwa is more likely at the boundary of lower morphosyntactic domains (Dell 1977; Côté 2001). A follow-up analysis was run to test whether this could be due to uncontrolled differences in sonority in the stimuli (sonority-increasing C_C sequences favor schwa deletion). But the same results were found.

One possibility to explore in further research would be that derived words are more likely to be analyzed as morphologically simple than inflected words, and even more when the cluster at the stem-suffix boundary is simple (C_C). Derived words often have less transparent semantics than inflected words, making their morphological structure less salient (Haspelmath & Sims 2010). The presence of a simple consonant cluster (C_C) at the stem-suffix boundary could make the morpheme boundary even less salient, therefore favoring even further a non-decompositional analysis of derived words (Hay 2003). As a result, morpheme-boundary schwas could end up being reanalyzed as being morpheme-internal in (some) derived words. Contrary to morpheme-boundary schwas, morpheme-internal schwas have to be analyzed as underlying, because their distribution is not entirely predictable (e.g. pelouse [p(ə)luz] ‘lawn’ vs. plus [p(*ə)lys] ‘more’). If schwas are sufficiently unlikely in derived words with C_C sequences at the stem-suffix boundary, speakers could then tend to reanalyze these words as featuring a morpheme-internal CC sequence (without any underlying schwa). If a faithfulness constraint specifically penalizes schwa epenthesis in morpheme-internal consonant clusters (e.g. contiguity) and has a larger weight than the general constraint penalizing schwa epenthesis, then schwa could end up being more likely in inflected words with C_C at the stem-suffix boundary than in derived words reanalyzed as featuring a morpheme-internal CC sequence, despite clusters being generally more marked at the stem level than at the word level. Exploring the detailed predictions of this account (in particular whether derived words with C_C are more likely to be analyzed as morphologically simple than inflected words) is left for further research.

The finding that Swiss French speakers are systematically more likely to accept the schwa-less variant than French speakers from France is in line with the conclusions reached by Racine (2007; 2008) based on judgment data and by Racine et al. (2016) (among others) based on production data. Despite these systematic differences, participants from France and Switzerland behaved remarkably similarly with respect to the hypotheses studied in this paper, except for the treatment of OL_C in derived vs. inflected words (see Table 5). This similarity between the two groups of participants is line with Racine (2007)’s observation that speakers from France and Switzerland differ in their baseline rates of schwa production but otherwise follow the same general principles for schwa-zero alternations.

4.2 Results

4.2.2 Description of results

Figure 4 shows the posterior distribution (mean and 95% CI) of each response category (1, 2, …, 6, 7) for all cells in the factorial design.

Figure 4

Posterior distribution (mean and 95% CI) of each of the seven response categories as a function of Morphology, Cluster, and Stem Length.

Differences between clusters in derived words. Participants were found to rate schwa absence as more likely in LO_L than in OL_C in derivation and there is compelling evidence for this difference both in monosyllabic stems (𝔼(μ_{monosyll, LO_L, der}-μ_{monosyll, OL_C, der}) = 0.39, CI = [0.01, 0.75], P(Δ > 0) = 0.98) and disyllabic stems (𝔼(μ_{disyll, LO_L, der}-μ_{disyll, OL_C, der}) = 0.79, CI = [0.41, 1.17], P(Δ > 0) = 1).

Controlling for individual differences in the treatment of three-consonant sequences in derived words. As discussed in section 2.4 and as found in Study 1, only some speakers might be driving the general asymmetry between OL_C and LO_L in derived words (stem level). Figure 5 shows how each individual participant in Study 2 treats OL_C and LO_L in derived words with monosyllabic and disyllabic stems. The results confirm the hypothesis of individual variation at the stem level. Some participants are more likely to delete schwa in LO_L than in OL_C whereas some participants do not treat the two sequences differently. Generally, participants are more likely to treat the two clusters differently with disyllabic stems than with monosyllabic stems. There is also one outlier who is more likely to delete schwa in OL_C than in LO_L (Participant 33).

Figure 5

Posterior distribution (mean and 95% CI) of the difference between LO_L and OL_C in derived words (stem level) by participant and stem length (monosyllabic, disyllabic). A positive value means that schwa deletion is more likely in LO_L than in OL_C.

Differences between clusters in inflected words. Participants were also found to rate schwa absence as more likely in LO_L than in OL_C in inflection and there is compelling evidence for this difference both in monosyllabic stems (𝔼(μ_{monosyll, LO_L, inf}-μ_{monosyll, OL_C, inf}) = 1.29, CI = [0.88, 1.73], P(Δ > 0) = 1) and in disyllabic stems (𝔼(μ_{disyll, LO_L, inf}-μ_{disyll, CO_L, inf}) = 1.34, CI = [0.90, 1.82], P(Δ > 0) = 1).

It can be concluded that there is sufficient evidence to support the hypothesis that the number and nature of surrounding consonants are revelant in both derived and inflected words, with OL_C being judged overall as more likely to feature schwa than LO_L in both derived and inflected words. However there is individual variation at the stem level, as some speakers do not treat OL_C and LO_L differently in this context, in particular in monosyllabic stems.

Differences between derivation and inflection. For OL_C clusters, participants were not found to rate schwa absence as more likely in inflection than in derivation, neither in monosyllabic stems (𝔼(μ_{monosyll, OL_C, inf}-μ_{monosyll, OL_C, der}) = –0.21, CI = [–0.55, 0.16], P(Δ > 0) = 0.12) nor in disyllabic stems (𝔼(μ_{disyll, OL_C, inf}-μ_{monosyll, OL_C, der}) = –0.02, CI = [–0.38, 0.32], P(Δ > 0) = 0.47). For LO_L clusters, participants were found to rate schwa absence as more likely in inflection than in derivation, and there is compelling for this difference in both monosyllabic stems (𝔼(μ_{monosyll, LO_L, inf}-μ_{monosyll, LO_L, der}) = 0.68, CI = [0.31, 1.04], P(Δ > 0) = 1) and disyllabic stems (𝔼(μ_{Swiss, OL_C, inf}-μ_{Swiss, OL_C, der}) = 0.53, CI = [0.17, 0.89], P(Δ > 0) = 1).

Differences between monosyllabic stems and disyllabic stems. Participants generally rated the schwa-less variant higher in disyllabic stems than in monosyllabic stems. For OL_C clusters in derived words, there is no compelling evidence for this asymmetry (𝔼(μ_{monosyll, OL_C, der}-μ_{disyll, OL_C, der}) = 0.11, CI = [–0.21, 0.44], P(Δ > 0) = 0.75). However, disyllabic stems were found to favor schwa absence in the three other contexts: in inflected words with OL_C clusters (𝔼(μ_{monosyll, OL_C, inf}-μ_{disyll, OL_C, inf}) = 0.31, CI = [0.00, 0.66], P(Δ > 0) = 0.97), in derived words with LO_L clusters (𝔼(μ_{monosyll, LO_L, der}-μ_{disyll, LO_L, der}) = 0.51, CI = [0.17, 0.86], P(Δ > 0) = 1), and in inflected words with LO_L clusters (𝔼(μ_{monosyll, LO_L, inf}-μ_{disyll, LO_L, inf}) = 0.36, CI = [0.03, 0.70], P(Δ > 0) = 0.98).

4.3 Discussion

The results of Study 2 are summarized in Table 7 for the eight morphophonological contexts, with > indicating a greater estimated likelihood of the schwa variant.

Table 7

Summary of Study 2 results: probability of the schwa variant as a function of Cluster, Morphology, and Stem Length.

Study 2 mainly replicates the results of Study 1. The results indeed support the hypothesis that phonologies are weakly distinct across stem and word levels (see section 2.4) against the hypothesis that they differ strongly (see section 2.3). At the stem level (derivation), not only the number but also the nature of surrounding consonants matters for schwa-zero alternations, at least for some speakers. This further supports the claim that Grammont’s Law of Three Consonants should be relaxed not only at the word level but also at the stem level.

Furthermore, the relative markedness of clusters was found to be the same in both derived and inflected words, with OLC being more strongly avoided than LOL, in line with the hypotheses presented in section 2.6.2 and with the results of Study 1. LOL clusters were found to be more strongly avoided in derived than in inflected words, in line with the hypothesis that phonotactic restrictions are stronger in lower than in higher morphosyntactic domains (see section 2.6.1) and with the results of Study 1. This is consistent with the claim that there are genuine effects of morphosyntactic domains on schwa-zero alternations below the word level (Dell 1977). No effect was observed for OLC clusters though. This might be interpreted as a ceiling effect, as the likelihood of schwa presence was high in this context.

The finding that monosyllabic stems are more likely to feature a schwa at the stem-suffix boundary than disyllabic stems is also consistent with the results of earlier studies showing an avoidance of adjacent prosodically prominent syllables in French (see section 2.6.3).

5.2 Results for Study 1

The posterior distributions for the constraint weights are shown in Table 8a and 8b for the grammar that distinguishes three-consonant clusters in derived words and for the grammar that does not, respectively. Figure 6 shows the frequencies that each grammar predicts for the schwa variant in the 12 contexts (6 morphophonological contexts × 2 varieties) against the frequencies attested in Study 1. The grammar with the same phonotactic constraints across word and stem levels (Table 8a, Figure 6a) was found to have a smaller deviation information criterion (Δ = –18.02) than the grammar with distinct phonotactic constraints in the two levels (Table 8b, Figure 6b), indicating that the increase in goodness of fit is worth the added complexity in the grammar. In other words, the data provide evidence for constraints referencing the nature of consonants in CCC clusters even at the stem level.

Figure 6

Data vs. predictions for the two grammars. (a) Grammar with *OL_C_der and *LO_L_der. (b) Grammar with *CCC_der.

Moreover, most of the grammatical hypotheses presented in section 2.6 are supported by the results of the modeling study. As expected under the hypothesis that *OLC is more marked than *LOL and *LOL more marked than *CC (see section 2.6.2), *OLC was found to have a greater weight than *LOL and *LOL a greater weight than *CC at both stem and word levels, as shown in Table 8a. As expected under the hypothesis that phonotactic constraints are more strongly enforced at the stem level than at the word level (see section 2.6.1), *OLC and *LOL were found to have greater weights in derived than in inflected words. The unexpected result found in section 3.2.2 was replicated at the grammatical level: the weight of *CC_inf is larger than the weight of *CC_der, meaning that phonotactic constraints referring to two-consonant clusters are more strongly enforced at the word level (see section 3.3 for a potential explanation for this unexpected effect). Finally, as expected (see section 2.6.4), French speakers from Switzerland were found to weigh Dep(ə) higher than French speakers from France.

5.3 Results for Study 2

The posterior distributions for the constraint weights are shown in Table 9a and 9b for the grammar that distinguishes three-consonant clusters in derived words and for the grammar that does not, respectively. Figure 7 shows the frequencies that each grammar predicts for the schwa variant in the 8 contexts (2 morphological contexts × 2 stem lengths × 2 three-consonant clusters) against the frequencies attested in Study 2. The grammar with the same phonotactic constraints across word and stem levels (Table 9a, Figure 7a) was found to have a smaller deviation information criterion (Δ = –77.36) than the grammar with distinct phonotactic constraints in the two levels (Table 9b, Figure 7b), indicating that the increase in goodness of fit is worth the added complexity in the grammar. In other words, the data provide evidence for constraints referencing the nature of consonants in CCC clusters even at the stem level.

Figure 7

Data vs. predictions for the two grammars. (a) Grammar with *OL_C_der and *LO_L_der. (b) Grammar with *CCC_der.

Moreover, most of the grammatical hypotheses presented in section 2.6 are supported by the results of the modeling study. *OLC was found to have a greater weight than *LOL, as shown in Table 9a. As expected under the hypothesis that phonotactic constraints are more strongly enforced at the stem level than at the word level (see section 2.6.1), *OLC and *LOL were found to have greater weights in derived than in inflected words. Finally, *Clash was found to have a non-zero weight, meaning that the language does avoid sequences of stressed syllables, as expected (see section 2.6.4).