1.1. Cluster overlap and rapidity

In the past three decades, a number of parameters have been identified to affect inter-segmental overlap in C1C2 clusters. These include cluster position within a word (Hardcastle, 1985; Byrd, 1996; Chitoran, Goldstein, & Byrd, 2002), place order of the involved segments (Chitoran, Goldstein, & Byrd, 2002; Gafos, Hoole, Roon & Zeroual, 2010), C1 voicing (Hoole, Bombien, Kühnert, & Mooshammer, 2009; Bombien & Hoole, 2013; Gibson, Sotiropoulou, Tobin, & Gafos, 2017, 2019; Pouplier, Pastätter, Hoole, Marin, Chitoran, Lentz, & Kochetov, 2022), C1 place (Yanagawa, 2006; Bombien & Hoole, 2013; Gibson et al., 2017, 2019; Pouplier et al., 2022), C2 manner (Gibson et al., 2017, 2019), vowel identity following the cluster (Lialiou, Sotiropoulou, & Gafos, 2021), speech rate (Byrd, 1994; Luo, 2017), age (Mücke, Hermes, & Tilsen, 2020), intonational or phrasal boundaries (Byrd & Saltzman, 1998; Hoole et al., 2009; Byrd & Choi, 2010; Cho, Lee, & Kim, 2014; Cho, 2016) and language-specific timing patterns (Yanagawa, 2006; Hoole et al., 2009; Shaw, Gafos, Hoole, & Zeroual, 2009; Gafos et al., 2010; Marin & Pouplier, 2010; Tilsen, Zec, Bjorndahl, Butler, L’Experance, Fisher, Heimisdottir, Renwick, & Sanker, 2012; Bombien & Hoole, 2013; Hermes, Mücke, & Grice, 2013; Marin, 2013; Pastätter & Pouplier, 2013; Brunner, Geng, Sotiropoulou, & Gafos, 2014; Hermes, Mücke, & Auris, 2017; Pastätter & Pouplier, 2017; Gibson et al., 2017, 2019; Sotiropoulou, Gibson, & Gafos, 2020 among others). However, little attention has been paid to the potential role of parameters in the underlying dynamics assumed to control the articulatory gestures (comprising these C1C2 clusters). Most notable among these parameters is stiffness, whose modulations directly affect durational aspects of the unfolding of gestures. Specifically, higher stiffness results in increased peak velocity to movement amplitude ratios and shorter movement durations. It seems intuitive, yet largely still unexplored, that overlap in C1C2 clusters would be directly affected by these ‘rapidity’ aspects of stiffness-controlled kinematics.

Browman and Goldstein (1990a) first pointed to the possibility that different degrees of overlap may be related to some notion of rapidity of the different oral articulators implicated in the consonants of the cluster. This suggestion was based on early work by Brown (1977) and Gimson (1962) who observed that the most common cases of place assimilation in English typically involve alveolar consonants assimilating to labials or velars, rather than the other way around. Browman and Goldstein (1990a) suggested that this propensity for assimilation might result from some gestures being more easily overlapped or “hidden” by other gestures due to differences in rapidity. Specifically, they postulated that a slower gesture, such as that implicated in a labial or a velar constriction, “might prove more difficult to hide” than a faster one as in a coronal, since the tongue tip enjoys a greater flexibility than the lips or more posterior parts of the tongue such as the tongue body implicated in velars (Browman & Goldstein, 1990a, p. 18).

The conjectured link between overlap and some notion of rapidity by Browman and Goldstein (1990a) was taken up by Jun (1995, 2004) in a proposal aimed at accounting for patterns of place assimilation. In his typological study, Jun observed that coronals are the most likely to be targeted by place assimilation, but the least likely to be the trigger of place assimilation compared to non-coronals (Jun, 2004, p. 64). To explain such propensities in place assimilation, Jun proposes that in a C1C2 consonant cluster, when the rapidity of C2 is held constant, a more rapid C1 articulatory movement (Figure 1A) would result in more overlap between the gestures of C1 and C2 than a slower C1 (Figure 1B). This in turn would render the acoustic place cues of C1 more easily hidden by those of the overlapping C2 and thus perceptually less salient and more prone to assimilate in place to C2. Conversely, when the rapidity of C1 is held constant, a slower C2 (Figure 1D) would lead to more overlap between the gestures of C1 and C2 than a faster C2 (Figure 1C), as the C2 gesture would “intrude” into the unfolding of the C1 gesture. This would also have the effect of C2 obscuring C1 place cues acoustically, with C1 more likely to assimilate in place to C2 as a consequence. The propensity of (presumed more rapid) coronals to more frequently assimilate (than other consonants) to a following non-coronal corresponds to, according to the overlap schemes of Jun, the scenario described in Figure 1A (compared to Figure 1B). Likewise, the propensity of non-coronals to less frequently assimilate to a following coronal corresponds to the scenario laid out in Figure 1C (compared to Figure 1D). In short, Jun posits that the rapidities of both C1 and C2 should exert effects on the amount of overlap. Specifically, overlap should increase as the rapidity of C1 increases and that of C2 decreases; conversely, as the rapidity of C1 decreases and that of C2 increases, overlap should decrease.

Figure 1

Schematic representation of Jun’s proposal about the relationship between rapidity and overlap (recreated from Jun, 2004 (5) and (6); same as Figure 1 in Roon et al., 2021). In panels A and B, as the rapidity of C2 is held constant, a rapid C1 (A) results in more overlap than a slow C1 (B). Similarly, in panels C and D, as the rapidity of C1 is held constant, a slow C2 (D) results in more overlap than a rapid C2 (C).

Schematic representation of Jun’s proposal about the relationship between rapidity and overlap (recreated from Jun, 2004 (5) and (6); same as Figure 1 in Roon et al., 2021). In panels A and B, as the rapidity of C2 is held constant, a rapid C1 (A) results in more overlap than a slow C1 (B). Similarly, in panels C and D, as the rapidity of C1 is held constant, a slow C2 (D) results in more overlap than a rapid C2 (C)

Recently, Roon et al. (2021) tested Jun’s proposal about the relationship between rapidity and overlap using electromagnetic articulography (EMA) data from Moroccan Arabic word-medial stop-stop clusters. Specifically, Roon et al. (2021) tested two predictions related to Jun’s proposal. The first concerns an ordering of rapidities determined by the place of articulation as shown in (1). In Jun’s proposal, asymmetries in assimilation reflect different degrees of saliency in place transition cues, which in turn are related to the rapidity of the gestures being targeted in assimilation. For Jun, propensities in place assimilation are to be derived from the saliency of place cues which is in turn, at least in part, determined by the articulatory rapidity of the gestures whose execution gives rise to these cues. Specifically, rapid gestures, such as those implicated in coronals (cor), are proposed to have brief and thus less salient place cues, whereas sluggish gestures, such as those implicated in non-coronals, are proposed to have more salient place cues.¹ Within the non-coronals, Jun reviews evidence pointing to velars (vel) having more salient cues than labials (lab) (Jun, 2004, pp. 63–65). Assuming that this notion of saliency has its basis in the rapidity of the gestures of these consonants (Roon et al., 2021),² this leads to the ordering of rapidity shown in (1).

Secondly, the rapidity ordering in (1) yields a further prediction in the form of a partial ordering in overlap between different cluster types shown in (2): COR-VEL > COR-LAB, LAB-VEL > LAB-COR, VEL-LAB > VEL-COR (Roon et al., 2021). The table in (2) illustrates how to derive this partial ordering from Jun’s proposals in Figure 1. In the table in (2), for any given column, going from top to bottom, C1 rapidity increases (from VEL to LAB to COR) while C2 remains fixed, thus leading to increasingly more overlap among the cluster types in any given column of the table; this is because, as illustrated in Figure 1, panels A and B, in a C1C2 cluster, as the rapidity of C2 is held constant, a slow C1 (Figure 1B) results in more overlap than a fast C1 (Figure 1A). For example, looking at the leftmost column of the table in (2), the rapidity-based prediction is that the VEL-COR cluster /gl/ should be less overlapped than the LAB-COR cluster /bl/. Note that in (2) we leave cells that correspond to combinations of the same effector (e.g., VEL-VEL) empty, because C1, C2 individual rapidity measures cannot be reliable extracted in such combinations due to their homorganicity. Similarly, on the basis of the table in (2), we can project predictions by moving horizontally, from left to right. That is, looking now within each row of the table, C2 rapidity decreases (from COR to LAB to VEL), while C1 remains fixed, thus leading to increasingly more overlap among the cluster types in any given row of the table; this is because, as illustrated in Figure 1, panels C and D, in a C1C2 cluster, as the rapidity of C1 is held constant, a slow C2 (Figure 1D) results in more overlap than a faster C2 (Figure 1C). Overall, the closer a cluster type is located towards the upper left corner of the resulting table, the less overlapped it is, with VEL-COR predicted to be the least overlapped cluster type; the closer a cluster type is located towards the bottom right corner of the table, the more overlapped it is, with COR-VEL predicted to be the most overlapped cluster type. The predicted overlap patterns can thus be expressed in a partial ordering as in: COR-VEL > COR-LAB, LAB-VEL > LAB-COR, VEL-LAB > VEL-COR (where a comma separates cluster types for which no rapidity-based overlap prediction is made).

Roon et al. (2021) argued that Moroccan Arabic offers an ideal case for assessing these predictions because all place of articulation combinations ([bd, bt, bg, bk, dg, dk, tg, tk, db, gb, gd, gt, kb, kd, kt, tb]) are permitted in this language. Rapidity was quantified in Roon et al. (2021) in two ways. The first way operationalizes the notion of rapidity with the peak velocity of the closing phase movement for any given consonant. The second way employed instead the amplitude-normalized peak velocity, a measure that is assumed to index the parameter of “stiffness” in the underlying dynamics of gestures.

In assessing the effects of either of these two operationalizations of rapidity on overlap, Roon et al. (2021) quantified overlap in two different ways. The first measure of overlap was calculated as the ratio of the unfolding of C2 closing phase movement to the duration of C1 gestural plateau and termed as relative overlap. A second measure of overlap was quantified by the temporal interval between the initiation of C1 and C2 gestures, termed as onset lag (see §2.4.2 for reasons). In their results, Roon et al. (2021) found no systematic differences in rapidity based on articulator, regardless of whether rapidity was indexed by peak velocity or stiffness. Furthermore, the findings on overlap did not conform to the predicted partial ordering of overlap listed under (2), since LAB-VEL and LAB -COR were found to be significantly more overlapped than the other clusters, while the difference between COR-VEL and COR- LAB clusters was not reliable. Although neither of these two predictions was borne out in the empirical data, Roon et al. (2021) did find a strong correlation between overlap and the difference between C1 and C2 stiffness. In other words, they found that overlap increases as the stiffness of C2 decreases with respect to the stiffness of C1 independent of the identities of the involved oral articulators. Crucially, this lawful relationship between overlap and rapidity was only significant when rapidity was indexed by stiffness and not by peak velocity. Therefore, they concluded that stiffness, not peak velocity, modulates overlap in C1C2 clusters.

Even though Roon et al. (2021) identified stiffness as a systematic determinant of overlap in consonant clusters, their “results should be interpreted with some caution, since they come from one language” (Roon et al., 2021, p. 19). Hence, evidence from languages other than Moroccan Arabic, in particular those involving different coordination relations between consonantal gestures, is needed to solidify or, should contradictory evidence be found, rebut the conclusions drawn by Roon et al. (2021). Another potential drawback in the study of Roon et al. (2021) lies in their choice of the stiffness difference and the peak velocity difference of articulations as an alternative to Jun’s original articulator-specific proposal. On the one hand, this choice, as the authors intended, indeed strips off the component of “inherent velocity” associated with different articulators in Jun’s proposal, which did not find support in the empirical data, but maintained the spirit of Jun’s idea that the rapidities of C1 and C2 both contribute to variances in overlap. On the other hand, this approach lumps C1 and C2 rapidities together into a single parameter quantified by either stiffness difference or peak velocity difference between C1 and C2. This prevents observation of any differential effects of the individual consonants on overlap (recall that Jun’s original proposal predicts that both C1 and C2 rapidities modulate overlap, a hypothesis which is yet to be assessed with empirical data). Granted, modelling C1 and C2 rapidity as separate effects potentially risks ignoring within-token factors and variability across tokens, but this can be partially compensated by allowing by-cluster variance in the statistical models. Overall, it is worth exploring the rapidity effects of each consonant in a C1C2 cluster individually from the perspective of hypothesis testing. It is precisely the aforementioned two points which extend the work of Roon et al. (2021) that this present study aims to address.

Finally, whereas much of the literature on consonantal overlap tends to retain an articulatory perspective, there is evidence that the generalizations at play may have a perceptuomotor rather than a purely articulatory basis (see, for instance, the proposed basis for the place order effect in Gafos et al., 2010). We similarly seek here, once the patterns in our findings are identified, to relate our results to other results in motor control that have a basis in the coupling between action and perception.

1.2. Hypotheses tested

Here, we present the two broad hypotheses this work intends to assess. The first broad hypothesis posits that the observations and conclusions drawn by Roon et al. (2021) from the Moroccan Arabic data can be extended to typologically different languages. In the present study, articulatory data from German, English, and Spanish stop-lateral clusters were analyzed to enable a cross-language comparison. In more specific terms, this first hypothesis has three components, corresponding to H-J1, H-J2, H-J3 (mistakenly written as H-3) in Roon et al. (2021) and stated in (3) below. The first and second components aim at the predictions of Jun (2004) on articulatory-specific inherent velocity and the projected partial ordering of overlap in clusters based on the presumed rapidity differences. Thus, the first component under (3) concerns the presence of consistent differences in rapidity among coronal, labial, and velar consonants. The second component under (3) aims at the predicted difference in overlap between velar-lateral (/kl/, /gl/) and labial-lateral clusters (/pl/, /bl/); as illustrated in (2), the former is predicted to be less overlapped than the latter, a prediction that was not verified in the Roon et al. (2021) results. The third component under (3) concerns the replicability of the relation between relative rapidity and overlap in Roon et al. (2021). Specifically, if the finding from Roon et al. (2021) is indeed valid across languages, then a robust (meaning significant across different overlap measures) correlation is expected between overlap and stiffness difference, but not between overlap and peak velocity difference.

Our second hypothesis aims to tease apart the separate contributions of C1 and C2 individual stiffness values on overlap. This hypothesis, stated in (4) below, was not assessed in Roon et al. (2021).

If Jun’s schemas about the relations between the rapidities of C1 and C2 (interpreted in the present work by using stiffness rather than peak velocity) and overlap (that overlap increases as C1 rapidity increases and C2 rapidity decreases; see Figure 1) comply with the data, then we should expect to see significant effects of both C1 and C2 stiffness on overlap. Crucially, the directions of the individual stiffness effects are expected to be opposite to each other: Higher rapidity, more overlap for C1 stiffness and higher rapidity, less overlap for C2 stiffness.

Note that the approach in Jun (1995, 2004), to which the above hypotheses relate, comprises a link between rapidity and overlap and another link between overlap and phonological patterns of assimilation. We hasten to point out that the hypotheses evaluated in the present work only concern the first link in Jun’s proposal, the one regarding whether overlap between the gestures of the consonants in a C1C2 cluster is modulated by rapidity measures such as peak velocity and stiffness. Our work does not address the second link, that is, the issue of what drives assimilation. We return to this point in the discussion as well.

3.1. Hypothesis 1: Validity across datasets

Our aim here is to assess whether the findings of Roon et al. (2021) can be extended to the three languages in the present study. If this is indeed the case, then we should find no evidence for a consistent ordering of articulator-specific inherent velocities and no effect of peak velocity on overlap. Instead, an effect of relative rapidity indexed specifically by stiffness difference is expected on overlap.

First, we looked at whether the notion of inherent velocity finds any basis in our data and specifically whether inherent velocities follow the order in (1), COR > LAB > VEL, from most rapid to less rapid. Figure 4A displays the peak velocity for velars (VEL), labials (LAB), and coronals (COR). The results for COR are shown separately for each context as defined by C1 place, with separate violin plots for (VEL-)COR and (LAB-)COR. Figure 4B does the same for stiffness across German, English, and Spanish. In our datasets, LAB seems to have both higher peak velocity and higher stiffness than COR, with the difference between the two being the largest in Spanish when rapidity is indexed by peak velocity (rightmost panel in Figure 4A). COR generally has lower peak velocity than VEL and LAB, but the differences are mitigated when rapidity is measured by stiffness.

Figure 4

Peak velocity (A) and stiffness (B) values, by primary articulator and cluster position in our German, English and Spanish datasets.⁶

Peak velocity (A) and stiffness (B) values, by primary articulator and cluster position in our German, English and Spanish datasets

To determine which differences shown in the figures were significant, two linear mixed-effects models (Baayen, Davidson, & Bates, 2008; Gelman & Hill, 2007) were fit to each individual language using the LME4 package (Bates, 2005; Bates et al., 2020) for R (R Development Core Team, 2018). One model had peak velocity as the dependent variable and the other had stiffness as the dependent value. Articulator was modeled as the fixed effect. SPEAKER was modeled as random effect allowing varying intercepts and varying slopes for the effect of articulator by speaker. Omnibus test statistics for the fixed effects were determined using a type III analysis of variance with Satterthwaite’s method from the ANOVA function of the stats package (R Development Core Team, 2018) in R. The results of the statistical models are listed in Table 5.

There were significant effects of articulator across languages for peak velocity and significant effects of articulator in English and Spanish for stiffness. Post-hoc differences in articulator pairs within language were assessed using estimated marginal means (Searle, Speed, & Milliken, 1980) provided by the EMMEANS package (Lenth, Singmann, Love, Buerkner, & Herve, 2019) for R. Table 6 shows the results, where pairs with a Tukey-adjusted p-value < 0.05 were considered reliable and are shown in bold.

In German, LAB had a significantly higher peak velocity than both VEL and COR (independent of C1 place). The differences between the same two sets of articulators when stiffness is used as the index of rapidity were however not significant. The same goes for English: although VEL had significantly lower stiffness than both LAB and COR (independent of C1 place), and LAB had significantly higher peak velocity than COR (independent of C1 place), their differences in the other rapidity measure were not significant (except for the difference between VEL and (VEL-)COR, which was significant across both rapidity measures). Similarly, Spanish VEL had significantly lower peak velocity than both LAB and COR (independent of C1 place). However, the differences were not significant in stiffness (except for the difference between VEL and (VEL-)COR, which was significant across both rapidity measures). Finally, C1 place had no effect on the rapidity of COR at all regardless of which rapidity measures were used as the index. In general, even though there are some significant differences in rapidity measures between certain articulators for each language, the majority of those differences was not consistent across both rapidity measures and also not consistent across languages. More importantly, they did not conform to the rapidity ordering (COR > LAB > VEL) derived from Jun’s proposal, regardless of rapidity index or language. Hence, we conclude that, similar to the findings in Roon et al. (2021), there is no reliable evidence for the concept of inherent velocity and its ordering as in Prediction 1 in the current data (Component 1, Hypothesis 1).

Next, we inspected whether there were robust differences in overlap between LAB-COR and VEL-COR clusters for the three languages. Specifically, LAB-COR was expected to show more overlap than VEL-COR as per (2). Given that support for an ordering of articulator-specific inherent velocity was not obtained for the current data, there was no rapidity-difference basis on which to expect LAB-COR and VEL-COR clusters to differ significantly in overlap. Thus, we predicted that either no reliable differences or differences in the non-expected direction exist in overlap between LAB-COR and VEL-COR across languages (that is, VEL-COR has more overlap than LAB-COR). Figure 5A shows relative overlap by cluster for each language, Figure 5B does the same for onset lag, and Figure 5C for absolute overlap. Across languages, clusters with voiced C1 (/bl, gl/) show more overlap than their voiceless counterparts, especially for English and Spanish. Additionally, English and Spanish clusters show a potential effect of C1 place, whereby LAB-COR clusters (/bl/, /pl/) appear to be more overlapped than VEL-COR clusters (/gl/, /kl/).

Figure 5

Relative overlap (A), onset lag (B) and absolute overlap (C) by cluster (i.e., /bl/, /gl/, /pl/, /kl/) in our German, English and Spanish datasets.

Relative overlap (A), onset lag (B) and absolute overlap (C) by cluster (i.e., /bl/, /gl/, /pl/, /kl/) in our German, English and Spanish datasets

Three linear mixed-effects models were fit to the dataset of each language individually with either relative overlap or onset lag as the dependent variable to determine the reliability of the differences. Cluster type and C1 voicing were modeled as fixed effects for all models with LAB-COR cluster and voiced C1 as the reference level. Random intercepts and slopes for both fixed effects were included for. For German and Spanish, an additional interaction between the fixed effects was also included in each model (English data do not allow this since /gl/ is lacking). Table 7 shows that there was no reliable difference between the two cluster types in German and English regardless of whether overlap was indexed by relative overlap, onset lag or absolute overlap, but in Spanish the same difference was significant across all three overlap measures. C1 voicing revealed a consistently significant effect on all overlap measures across languages, such that clusters with voiced C1 show more overlap than their voiceless counterparts. In addition, Spanish clusters showed a significant interaction between cluster type and C1 voicing across overlap indices. Ad-hoc pairwise comparisons confirmed that the significant interaction in Spanish was due to Spanish /bl/ being significant more overlapped than all the other three clusters across overlap indices.

Lastly but most importantly, we turned to the effects of relative rapidity, where Roon et al. (2021) found the stiffness difference, rather than the peak velocity difference, between C1 and C2 to be a reliable predictor of overlap. Figure 6 shows the relationship between relative rapidity and overlap by cluster type (horizontally) and language (vertically). Figure 6A plots peak velocity difference in the two cluster types (left two columns) and stiffness difference in the two cluster types (right two columns) against relative overlap, Figure 6B does the same for onset lag, and Figure 6C for absolute overlap. A colored regression line was overlayed for every speaker on each subplot.

Figure 6

Relationship between within-token C1-C2 relative rapidity and relative overlap (A), onset lag (B) and absolute overlap (C) across our German, English and Spanish datasets. In the left two columns of each plot (LAB-COR and VEL-COR respectively), relative rapidity is indexed by C1-C2 peak velocity difference, whereas in the right two columns (LAB-COR and VEL-COR respectively) it is indexed by C1-C2 stiffness difference. Colored regression lines correspond to speakers.⁷

Relationship between within-token C1-C2 relative rapidity and relative overlap (A), onset lag (B) and absolute overlap (C) across our German, English and Spanish datasets. In the left two columns of each plot (LAB-COR and VEL-COR respectively), relative rapidity is indexed by C1-C2 peak velocity difference, whereas in the right two columns (LAB-COR and VEL-COR respectively) it is indexed by C1-C2 stiffness difference. Colored regression lines correspond to speakers

Across languages, cluster types, and speakers, stiffness difference mostly showed a positive correlation with the three overlap indices (right two columns in Figure 6A, 6B, 6C) with the exception of Spanish VEL-COR clusters (the subplot in the bottom right corner of Figure 6A, 6B, 6C) and the VEL-COR clusters of one English speaker (the last subplots in the second rows of Figure 6A, 6C). The correlation between peak velocity difference and overlap was much less uniform compared to the former relation and showed substantial individual variability across speakers within each language (left two columns in Figure 6A, 6B, 6C). Six linear mixed models (three overlap measures by two relative rapidity measures) were fit to the data for each language (for a total of 18 linear mixed models). Peak velocity difference or stiffness difference (both continuous), cluster type, and their interaction were modelled as fixed effects. LAB-COR was designated as the base level of cluster type. Random intercepts were allowed for both speaker and stimulus. Speaker-specific random slopes for cluster type were also included. The results of all models are listed in Table 8.

The statistical results confirmed that effects of stiffness difference on the three overlap indices were all significant across all three languages and both cluster types (LAB-COR, VEL-COR) assessed here.⁸ This was not true for peak velocity difference, which had significant effects only in German LAB-COR clusters when using relative overlap and onset lag, but not absolute overlap, in English LAB-COR clusters when using absolute overlap, but not relative overlap and onset lag, and in Spanish VEL-COR clusters when using absolute overlap, but not relative overlap and onset lag, based on post-hoc analyses. Therefore, the effect of peak velocity difference on overlap was not robust across languages, clusters and overlap measures.

Overall, stiffness difference does appear as a more robust predictor of overlap than peak velocity difference across languages, consistent with the findings of Roon et al. (2021) in Moroccan Arabic (Component 3, Hypothesis 1).

3.2. Hypothesis 2: Individual consonant stiffness effects

While Roon et al. (2021) first established a robust effect of stiffness difference on overlap, a result we replicated and extended here to new languages, their measure (the difference between the two stiffness values of the two consonants) yokes the stiffness values of the two consonants in one independent variable. As such, this measure cannot address whether both C1 and C2 stiffness, individually, contribute to overlap in a way predicted by Jun (2004). It is this prediction we take up next. Specifically, the proposal in Jun (2004) predicts that an increase in overlap should be accompanied by increasing C1 stiffness and/or decreasing C2 stiffness. To test this hypothesis, we modelled both C1 and C2 stiffnesses and their interactions with cluster type as fixed effects. Relative overlap, onset lag and absolute overlap remained as dependent variables. Speaker and stimulus were included as random effects enabling varying intercepts. Random slopes of cluster type by speaker were allowed as well. Figure 7 displays the relations between C1 or C2 stiffness with relative overlap (A), onset lag (B) and absolute overlap (C) respectively divided by cluster types (horizontally) and languages (vertically). Colored regressions lines were added for speakers. As seen in Figure 7, while C2 stiffness shows a consistent negative correlation with all overlap measures across languages and speakers except for some in Spanish VEL-COR (right two columns in Figure 7A, 7B, 7C), C1 stiffness only shows a relatively clear relation with onset lag (left two columns in Figure 7B) and even here not without inconsistency among speakers in German and Spanish VEL-COR. Results of the statistical analyses are shown in Table 9.

Figure 7

Relationship between C1 or C2 stiffness and relative overlap (A), onset lag (B) and absolute overlap (C) across our German, English and Spanish datasets. C1 stiffness is shown in the left two columns of each plot (LAB-COR and VEL-COR respectively) and C2 stiffness is shown in the right two columns (LAB-COR and VEL-COR respectively). Colored regression lines correspond to speakers.

Relationship between C1 or C2 stiffness and relative overlap (A), onset lag (B) and absolute overlap (C) across our German, English and Spanish datasets. C1 stiffness is shown in the left two columns of each plot (LAB-COR and VEL-COR respectively) and C2 stiffness is shown in the right two columns (LAB-COR and VEL-COR respectively). Colored regression lines correspond to speakers

Statistical results provide evidence for C2 stiffness as a robust predictor of overlap, as its effect on overlap was significant across languages, cluster types, and overlap indices. The only exception was Spanish VEL-COR clusters when overlap was indexed by one of the three overlap measures, that of onset lag. Post-hoc analysis done on Spanish VEL-COR clusters alone revealed that the effect of C2 stiffness on onset lag approached statistical significance (p-value = 0.064). Crucially, in all cases the correlation between C2 stiffness and the three overlap measures was negative for both cluster types across all three languages, confirming the prediction of Jun’s proposal regarding the effect of C2 rapidity on overlap (Hypothesis 2). On the other hand, C1 stiffness was positively associated with overlap only for onset lag but not for relative overlap and absolute overlap across languages. Apart from onset lag, the only cases where C1 stiffness also showed a significant effect were German LAB-COR clusters (relative overlap) and English LAB-COR clusters (absolute overlap). For the last two cases, the effect of C1 stiffness in the corresponding VEL-COR clusters not only did not reach significance, but also had opposite signs compared to its effect in LAB-COR clusters. Specifically, in German and English LAB-COR clusters, C1 stiffness was positively associated with relative overlap and absolute overlap respectively, whereas in VEL-COR clusters of the two languages it was negatively associated with overlap.

In short, C2 stiffness is a more robust predictor of overlap compared to C1 stiffness for two reasons. Firstly, it has a significant effect on overlap across the three overlap measures and the three languages (only one exception out of 18 cluster type-and-overlap combinations). Secondly, the prediction of Hypothesis 2 on the effect direction of C2 stiffness (negative) was validated by the empirical results across languages and overlap indices, whereas that of C1 stiffness was not, given that significant effects of C1 stiffness had different effect directions for the LAB-COR clusters in German and English when relative overlap and absolute overlap were used as the overlap index respectively.