1.1 General background

It has long been known that how two adjacent consonantal gestures are coordinated differs considerably across languages. Given a [tk] sequence, for example, some languages show a clear audible release for [t] whereas other languages do not. As such, such coordination patterns are a part of what speakers actively control, and hence they constitute an important part of linguistic knowledge (Gafos et al., 2020; Shaw, 2022). However, precisely pinning down the nature of coordination relations has been a difficult issue, partly because it is not always possible to infer coordination relations from impressionistic observations of speech or even from acoustic signals. The development of research methods which have allowed us to directly observe articulatory movement with high temporal resolution has made this a tractable problem. Recent work by Shaw and colleagues has demonstrated, through a number of case studies, that coordination relations between gestures can be revealed by studying the structure of temporal variation in articulatory kinematic data (e.g., Gafos et al., 2014; Shaw, 2022; Shaw & Gafos, 2015; Shaw & Kawahara, 2018b; Shaw et al., 2021; see also Durvasula et al., 2021; Lialiou et al., 2021; Sotiropoulou & Gafos, 2022). A topic that is nevertheless still under-explored is how consonant clusters created via vowel deletion are coordinated, a gap that the current paper attempts to address. Specifically, in this paper we study the coordination of consonant clusters resulting from high vowel deletion in Tokyo Japanese.

Apparent deletion of a segment can follow from a phonological process—a wholesale deletion of a phonological category—or certain patterns of gestural overlap, i.e., “gestural hiding.” Extreme theoretical poles posit that all cases of apparent deletion follow from one of these sources. For example, Browman & Goldstein (1990) develop the gestural overlap hypothesis of segmental “deletion”, showing how numerous cases of apparent deletion, insertion and allophony can be derived from the timing and magnitude of gestures, without necessitating symbolic transformations, including deletion. At the other end of the theoretical spectrum, allophony has been treated as transformations between linearly ordered segments. On this view, the /pǝt/ → [pt] mapping, as in ‘potato,’ can only be seen as deletion, and not as gestural overlap (Chomsky & Halle, 1968; Kaisse & Shaw, 1985) (cf. Davidson, 2006). By now, enough empirical evidence has been amassed to make it clear that both theoretical accounts—gestural hiding and categorical deletion—have to be retained. That is, some cases of apparent deletion, such as the /t/ in ‘perfec/t/ memory’ at fast speech are clearly present in the articulation, even though they can be masked by the overlapping lip closure (Browman & Goldstein, 1990), making them inaudible. Other cases of apparent deletion are clearly attributable to categorical deletion, even though they might plausibly have been due to overlap (Ellis & Hardcastle, 2002; Kochetov & Pouplier, 2008) (cf. Nolan, 1992; see also Zsiga, 2020). Studies on this topic for the last three decades have shown that without careful examination of articulatory data, it is difficult to ascertain the true source of ‘apparent’ deletions. The empirical necessity to integrate theoretical perspectives raises interesting and hitherto under-researched questions. When categorical deletion does occur, what happens to the coordination of the remaining gestures? We address this question in the current study.

To investigate this issue, it is necessary to first establish that a segment is categorically deleted using articulatory data. Only then is it possible to evaluate the coordination patterns of the resulting gestures. Tokyo Japanese presents an ideal case to investigate how vowel deletion impacts gestural coordination, because recent studies have established that devoiced vowels in this language are variably and categorically deleted (Shaw & Kawahara, 2018b, 2021). This is ideal because we can investigate coordination patterns in the same words with and without a vowel. Vowel deletion can be determined by looking at whether the tongue dorsum moves towards a target for the vowel. The timing of consonants produced with different articulators, e.g., the tongue front and the lips, can then be compared in tokens with and without a vowel, as determined by tongue dorsum movement. This is what we do in the current paper.

In the remainder of the Introduction, we summarize past work on vowel deletion in Japanese (Section 1.2), discuss expectations for how coordination might be impacted by vowel deletion (Section 1.3), and illustrate specific predictions for different coordination relations, which can be tested in kinematic data (Section 1.4).

1.2 Vowel deletion in Japanese

A traditional description of high vowel devoicing in Japanese is that high vowels are devoiced between two voiceless obstruents and after a voiceless obstruent word-finally. Sometimes the environment between two voiceless obstruents is further sub-divided into ‘typical’ and ‘atypical’ devoicing environments. The ‘typical’ devoicing environment is either (1) between two voiceless stops or (2) between one voiceless fricative and one voicless stop. The ‘atypical’ devoicing environment is between two voiceless fricatives (Fujimoto, 2015). Devoicing is found in both environments but it is more common (and more nearly categorical) in the ‘typical’ environments than in the ‘atypical’ environment (Maekawa & Kikuchi, 2005). There has been a long debate about the deletion status of devoiced high vowels in Japanese, with arguments that they are phonologically deleted (Beckman, 1982; Beckman & Shoji, 1984; Kondo, 2001) and also that they are merely devoiced due to overlap of the glottal abduction gestures associated with the flanking consonants (Faber & Vance, 2010; Jun & Beckman, 1993) (though see Fujimoto et al., 2002); see Fujimoto (2015) for a summary of the studies that express each point of view.

Shaw & Kawahara (2018b) contribute to this debate by conducting an experiment using EMA (Electromagnetic Articulography) and showing, in a sample of six speakers, that many tokens of devoiced [u] were produced without any tongue dorsum raising gesture, which they interpreted as vowel absence. A follow-up study replicated the result with a larger number of items and more systematic control of the surrounding consonant environment (Shaw & Kawahara, 2021).¹ In that study as well, there were numerous tokens which showed no evidence of a tongue dorsum raising gesture, and were better characterized as interpolation between surrounding vowels than as controlled movement towards a separate vowel target. Importantly, the vocalic gestures for /u/ in these tokens were not just simply reduced or undershot due to temporal constraints; the tongue dorsum trajectory showed a high probability of linear interpolation between flanking targets even at slow speech rates, hence supporting the categorical deletion view (Shaw & Kawahara, 2018b, 2021).² In this paper, we build on that result. To diagnose whether categorical deletion impacts how the resulting consonant clusters are coordinated, we analyze coordination in tokens that were classified as either having a vowel or lacking one.

1.3 Theoretical landscape: What happens to coordination when a vowel deletes?

Since there is little or no empirical data showing directly what happens to consonant coordination when a vowel deletes, we discuss possible expectations for our study based on theoretical considerations and other types of empirical data.

Perhaps the most straight-forward assumption about gestural coordination is that coordination is local (Gafos, 1999). On this assumption, the deletion of a vowel in CVC would leave the remaining two consonantal gestures, CC, locally adjacent. While the consonants may be coordinated with the vowel in CVC, they would have to be coordinated with each other in CC. On this assumption, deletion of a vowel would require a new coordination relation (i.e., gesture reorganization) because the two consonants would be coordinated with each other in CC but not in CVC (see also the schemata in Figure 2). We take this to be the standard assumption, but we also recognize that there are in fact a range of additional theoretical possibilities.

The alternative to the standard assumption would be that the coordination of gestures in CVC actually persists in CC, even in the absence of the vowel. A conceptual antecedent for this hypothesis can be found in phonological patterns. There are numerous cases in which segment deletion does not necessarily trigger additional phonological re-organization; for example, Kawahara & Shaw (2018) list a number of examples in which vowel deletion does not trigger resyllabification (see also Shaw et al., 2020). Additionally, deletion of a segment (vowel or consonant) is often incomplete in that the timing slot associated with the deleted segment persists, sometimes lengthening adjacent segments, i.e., phenomena falling under the label of “compensatory lengthening” (e.g., Kavitskaya, 2002).

Other phonological patterns have been analyzed in terms of ghost segments (Zimmermann, 2019), where a ghost segment is present for the purpose of conditioning phonological patterns but does not necessarily shape the phonetic signal directly. Related proposals consider gradient degrees of segment presence, which may improve the account of variable phonological patterns, such as French Liaison (Smolensky & Goldrick, 2016). Whether ghost segments, or gradiently activated segments, influence coordination is still unknown (though see Goldrick & Chu, 2014 and Pouplier & Goldstein, 2014 for some discussion of intra-gestural duration). On the other hand, there is some evidence that gestural coordination patterns can change even when the vowel is not deleted (e.g., Davidson, 2006). This observation suggests that gestural coordination and segmental deletion may be somewhat independent.

Possibly, “deleted” vowels, i.e., vowels that lack any surface phonetic manifestation, can persist as ghost segments or ghost gestures, i.e., zero magnitude gestures, which may influence the coordination of other gestures without driving articulatory movement. Geissler (2021) raises this possibility to account for variation in gesture coordination across speakers of Diaspora Tibetan. In the sample of speakers analyzed, some had contrastive tone and others did not, but all speakers showed the coordination pattern that is characteristic of a tone gesture, i.e., all behaved as if a tonal gesture is present, even when their linguistic system lacks contrastive tones.

Besides ghost gestures, there are other theoretical hypotheses that might predict that coordination is unaffected by surface deletion of a vowel. Gestural coordination might not be strictly local. It might instead be organized according to a higher level clock, or cycle (e.g. Barbosa, 2007; O’Dell & Nieminen, 2019). In this case, the surface timing of consonants in CC and CVC could be identical because they stand in the same relation relative to a higher level triggering clock. For concreteness, consider a syllable-sized clock which triggers gestures according to a syllable cycle. In CVC, the first C could start at the beginning of the cycle, the V in the middle, and the second C towards the end. The consonants of CC could start at the beginning and towards the end of an abstract syllable cycle regardless of whether there is also a vowel timed to the middle of the cycle. This mechanism is no longer local, since gestures are not timed directly to each other but to an extrinsic timing mechanism.

Yet another theoretical hypothesis motivating no change in coordination following vowel deletion comes from Selection-Coordination Theory (Tilsen, 2016). In this theory, gestures that compose selection sets (which are assumed to be linguistically relevant units, such as syllables) are locally coordinated. However, gestures of different selection sets cannot be directly coordinated. This means, for example, that in a language where selection sets are syllables, vowels in adjacent syllables cannot be directly coordinated, (c.f. Smith, 1995 for V-V coordination). Variable vowel deletion could be implemented in this framework as the competition between selection sets with and without a vowel, e.g., CVC vs. CC. However, if vowel deletion comes at a syllable boundary, as in CV.C → C.C, then the competition for the first selection set is between CV and C. Regardless of whether C or CV is selected in the first selection set, the gestures cannot be directly coordinated with the next C gesture, because the next C gesture is in a different selection set. Since coordination does not happen across selection sets in either case, there is no real difference in coordination when the vowel is absent.

To provide a summary of the literature reviewed above, there are two broad hypotheses that emerge from theoretical and empirical considerations. Vowel deletion may or may not trigger reorganization of gestural coordination. If vowel deletion does trigger gestural reorganization, it may be the case that reorganization occurs only in certain contexts but not others.

In the strictly local coordination scenario, we expect vowel deletion in CVC (yielding CC) to result in C-C coordination, where the remaining consonants are coordinated with each other. In this case, the consonant gestures would be subject to (language-specific) constraints on C-C coordination. For example, in Moroccan Arabic, homoorganic consonant clusters have different C-C coordination than hetero-organic consonant clusters (Gafos, 2002; Gafos et al., 2010a). In Georgian, C-C coordination depends on the place of articulation of the consonants—if the first consonant is anterior to the second, there is greater overlap than if the first consonant is posterior to the second (Chitoran et al., 2002; Crouch et al., 2020). The Georgian pattern—the so-called “place-order effect”—has also been documented in other languages, particularly at faster speech rates (Gafos et al., 2010a).

As illustrated by the examples above, the nature of C-C coordination may interact with the identity of the consonants or the relation between them. It is also possible that certain consonant combinations may be more or less likely to enter into a C-C coordination relation. Cross-linguistically, fricative-stop clusters are more common across a syllable boundary than fricative-fricative clusters (Gouskova, 2004; Murray & Vennemann, 1983; Vennemann, 1988). Possibly, this is related to the relative ease of producing and perceiving these sequences (Ohala & Kawasaki-Fukumori, 1997). From this standpoint, we might expect fricative-stop clusters to reorganize to C-C coordination more readily than fricative-fricative clusters.

Specifically for Tokyo Japanese, deletion of devoiced vowels in CVC is equally likely when the vowel is flanked by two fricatives, e.g., [ϕus], as when it is flanked by a fricative and a stop, e.g., [ϕut] (Shaw & Kawahara, 2021). Moreover, in both cases, there is evidence that the initial consonant is not re-syllabified as a complex onset (Kawahara & Shaw, 2018). Rather, the initial consonant still appears to contribute a mora and syllable to the phonological representation.³ However, it is still possible that changes in coordination are more likely for some consonant sequences than others. There may be several relevant considerations for predicting which clusters are more likely reorganize than others (cf. Gafos et al., 2020; Lialiou et al., 2021). Since, in the case at hand, we are dealing with consonants that cross a syllable boundary, e.g., [ϕ.so] vs.[ϕ.ta] syllable contact constraints are one consideration (Gouskova, 2004; Murray & Vennemann, 1983; Vennemann, 1988). According to syllable contact laws, falling sonority, as in fricative-stop, is preferred to a sonority plateau, as in fricative-fricative, which may contribute to a tendency for fricative-stop (but not fricative-fricative) to reorganize.

Another difference between fricative-fricative and fricative-stop sequences has been found in Japanese text-setting, the process of aligning musical notes to song lyrics. Devoiced vowels between fricative-fricative consonants are more likely to be aligned to two separate musical notes than devoiced vowels between fricative-stop clusters (Starr & Shih, 2017). The devoiced vowel in FF can carry its own note, possibly because it maintains the timing of CVC instead of reorganizing. The difference in type-setting between FF and FS cannot be attributed to a difference in vowel deletion, given that there is variable vowel deletion in both environments (Shaw & Kawahara, 2021), but it might be due to a difference in how the resulting consonants are coordinated. We note as well that devoicing itself is less common in fricative-fricative contexts than in stop-fricative contexts (see discussion of ‘typical’ vs. ‘atypical’ devoicing environments in Section 1.2), which may also be related.

To summarize, we take the standard view to be that vowel deletion triggers gesture re-organization. This is consistent with the assumption that gestural coordination is local. However, we also presented a number of theoretical reasons to expect the opposite, that coordination patterns will persist even in the absence of the vowel. Moreover, these two possible behaviors may differ according to the specific consonants involved. As motivation for this third alternative we considered several possibly related patterns in which FF and FS sequences differ. The current study aims to identify which of these three empirical possibilities is actually attested in Japanese.

1.4 Assessing changes in coordination

In order to evaluate the three possible outcomes described above, it is necessary to evaluate coordination relations in the data. Recent studies have demonstrated that language-specific coordination relations between articulatory gestures can be reliably identified in the speech signal because of how they structure temporal variability (e.g. Gafos et al., 2014; Shaw, 2022; Shaw et al., 2011). We illustrate this strategy with a simple model of gestural coordination for CC and CVC sequences. The framework for specifying the model builds on the articulatory representations proposed and deployed by various work (Gafos, 2002; Gafos et al., 2020; Shaw & Gafos, 2015), shown in Figure 1. We assume that a small number of gestural landmarks are available for coordination. In this case, the relevant landmarks are the gesture start, target, release, and end. The gesture start is the onset of movement associated with the gesture. The gesture target is the assumed goal of the movement. The gesture release is the onset of movement away from the assumed goal. The gesture end is the offset of controlled movement.

Figure 1

Four gestural landmarks posited by Gafos (2002) and subsequent work: The “start” of the gesture, sometimes also referred to as the “onset,” the (achievement of) “target,” abbreviated “tar,” the release (from constriction), abbreviated “rel,” and the “end” (of controlled movement), sometimes also referred to as “offset.”

In specifying stochastic models of gestural coordination, we define both inter- and intra-gestural timing as relationships between gestural landmarks (Shaw, 2022). The temporal precedence of intra-gestural landmarks is fixed: start → target → release → end. However, because we assume that gestures can temporally overlap, the inter-gestural relationship is not fixed. Rather, it depends on specification of inter-gestural coordination relations, which are often language specific. For example, consider a CV sequence. Within the set of gestural landmarks defined above, we could specify that the start of the vowel is coordinated with the start of the consonant. Alternatively, we could specify that the start of the vowel is coordinated with the target of the consonant, the release, or the offset. Alternatively, in this framework we could also specify that it is the target of the vowel (as opposed to the start) that is coordinated with the preceding consonant (see, e.g., Gafos et al., 2020; Roon et al., 2021; Shaw & Chen, 2019). In some cases, coordination relations are known to map isomorphically to aspects of phonological structure, such as syllabic organization, making it possible to deduce higher level phonological structure from patterns of phonetic variability (e.g. Durvasula et al., 2021; Goldstein et al., 2007; Hermes et al., 2013, 2017; Shaw et al., 2009). Our focus here is on the relationship between coordination relations and kinematics. We build on the recent observation that different coordination relations (made available by the assumptions above) structure phonetic variability in different ways.

To illustrate this observation, we consider two different patterns of coordination, one for CC sequences and one for CVC sequences. An algorithm for generating gestural landmarks for each type of sequence is shown in Figure 2. The top shows a CC sequence in which the target of C₂ is timed directly to the release of C₁, shown in red. The phonetic constant, k^ipi, which could be zero, dictates how long after the release of C₁ the target of C₂ will occur, on average. The bottom panel shows a CVC sequence in which the target of C₂ is timed to the end of the vowel (c.f., the release of C₁), shown in red. The other aspects of the coordination patterns are the same. In both examples, the target of C₁ is generated from a distribution defined by a constant, k^p (the p stands for plateau duration) and normally distributed error, and the release landmark, rel, is sampled from a normal distribution, N, defined by mean, μ, and variance, σ².

Figure 2

Two coordination patterns, one for CC sequences and one for CVC sequences. A crucial difference involves the specification of inter-gestural coordination. For the CC sequence, the target of C₂ is timed to the release of C₁ (shown in red); for CVC, the target of C₂ is timed to the end of the vowel (shown in red); see text for complete description.

The result of the simulations are presented in Figure 3, which shows simulation results under very low levels of random noise, and Figure 4, which shows simulation results under levels of random noise typical of kinematic data.

Figure 3

The simulated correlations between ICI and C₁ duration for the two coordination patterns in Figure 2 at low noise levels.

Figure 4

The simulated correlations between ICI and C₁ duration for the two coordination patterns in Figure 2 at noise levels typical of kinematic data.

Of interest is how variation in k^p differentially influences the interval between the release of C₁ to the target of C₂ (henceforth, ICI, for inter-consonantal interval). As k^p increases in CVC, ICI decreases. In contrast, for CC sequences in the bottom panel of Figure 2, variation in k^p has no effect on ICI. Thus, a negative correlation between C₁ plateau duration and ICI is only consistent with the topology for the CVC sequence. This is regardless of the level of noise in the data. Figure 3 shows the same trend as Figure 4. The relation between C₁ duration and ICI is conditioned by the coordination relations between gestures, regardless of the degree of random variation added to the model. Since these two patterns of coordination make different predictions (Figures 3 and 4)—i.e., they structure variability in different ways—they can be diagnosed in the data.

The different coordination topologies in Figure 2 make different predictions about the covariation between C₁ duration and the inter-consonantal interval (ICI), defined as the interval from the release of C₁ to the achievement of target of C₂ (Shaw & Kawahara, 2018b). When the vowel is present (Figure 2, top), increases in C₁ duration will, all else equal, decrease ICI, because ICI is fixed in this coordination pattern. Thus, there should be a negative correlation between these intervals (C₁ duration and ICI) when the vowel is present. When the vowel is absent (Figure 2, bottom), on the other hand, variation in C₁ duration is not predicted to impact ICI, because the onset of C₂ is coordinated with the offset of C₁, i.e., C₂ onset can covary with C₁ offset. The rich theoretical landscape described above (Section 1.3) notwithstanding, these predictions follow what we take to be the standard view that gestural coordination is local and gesture duration triggers gestural reorganization.

Shaw & Kawahara (2018b) demonstrate that the different covariation patterns illustrated in Figure 2 indeed hold in their dataset, implying that consonant clusters resulting from high vowel deletion are coordinated with each other. However, the dataset that was analyzed by Shaw & Kawahara (2018b) was somewhat limited, as the consonantal environments surrounding the devoiced/deleted vowels, which can crucially affect gestural reorganization, were not controlled in that experiment. Given that a larger and more controlled data set is available (Shaw & Kawahara, 2021), we aim to reexamine this question of how consonant clusters are organized after the intervening vowel is deleted.

3.1 Data processing

The wav files recorded in the experiment were submitted to forced alignment, using FAVE.⁵ Textgrids from forced alignment were hand-corrected and, during this process, the target vowels were coded for voicing. Many vowels in devoicing environments were in fact devoiced, as evident from visual inspection of the spectrogram and waveform (see Shaw & Kawahara, 2021). However, some tokens in the devoicing environment retained clear signs of glottal vibration. These vowels were coded as voiced, and excluded from further analysis. There were a total 240 vowels (12% of the data) in voiceless environments produced with some voicing; most of these 184/240 (77%) came from the FF condition but there were also 56/240 (23%) in the FS condition.

Articulatory data corresponding to each token were extracted based on the textgrids. To eliminate high frequency noise in the EMA recording, the kinematic data were smoothed using the robust smoothing algorithm (Garcia, 2010) and, subsequently, visualized in MVIEW, a Matlab-based program to analyze articulatory data (Tiede, 2005). Within MVIEW, gestural landmarks were parsed using the findgest algorithm. Findgest identifies gesture landmarks semi-automatically based upon the velocity signal in the movement toward and away from constrictions. The algorithm is semi-automatic in that it requires the user to identify the constriction of interest in one of the articulator movement trajectories. We identified gesture constrictions based on the primary oral articulator for each consonant: For the alveolar stops, /t/ and /d/, we used the tongue tip sensor; for the bilabial fricative, we used the lower lip sensor; for the alveolo-palatal fricative (shown in Table 1 as [∫]), we used the tongue blade sensor.

Whether to compute velocity signals based on movement in a single dimension, i.e., a component velocity, such as the vertical movement of the lower lip, or to instead refer to tangential velocity, a velocity signal that incorporates movement in all three available dimensions: Vertical (up ↔ down), longitudinal (front ↔ back), and lateral (left ↔ right) is a researcher degree of freedom. Within the literature on kinematic analysis of speech movements, both approaches are common. Tangential velocity is preferable when the achievement of a speech production goal is distributed across dimensions: For example, a tongue tip movement to the alveolar ridge may involve both raising (vertical dimension) and also fronting (longitudinal dimension) of the tongue tip. If movements in both dimensions are in the service of achieving a single gestural goal, parsing the gesture based on just one dimension of movement may under-estimate movement velocity, which can impact gestural landmarks based on velocity-referential heuristics. On the other hand, there are cases in which a controlled movement can be better isolated by picking out a single movement dimension. Consider the case in which vertical movement is driven by one gesture while movement in the longitudinal dimension is driven by a temporally overlapped but distinct gesture. In this case, landmarks for each gesture would be better estimated by component velocities than by tangential velocities.

In our data it was generally appropriate to use tangential velocities, incorporating movement in three-dimensions into the gesture parse (below we discuss exceptions to this trend). Generally, there was very little movement in the lateral (left ↔ right) dimension, so tangential velocities were dictated primarily by movement in the vertical and longitudinal dimensions. An example of a gesture parse of a bilabial fricative based on tangential velocity is provided in Figure 6. The top three panels show movement of the lower lip (LL) in the: (from top to bottom) longitudinal, vertical, and lateral dimensions. The bottom panel (red trajectory) shows the tangential velocity. The greatest displacement of the lower lip is in the vertical dimension, a movement magnitude of around eight mm. However, there is also movement in the longitudinal dimension, i.e., lip protrusion, of about three mm and a small displacement, about one mm, in the lateral dimension. The bottom panel shows a sequence of four gestural landmarks, identified with reference to the tangential velocity signal, following, e.g., Shaw et al. (2009, 2011), Shaw et al. (2021), Shaw (2022): The “start” of the gesture, the achievement of “target,” the “release” from constriction and the “end” of the gesture. Following past work, these landmarks were labeled with reference to the tangential velocity signal. The “start” landmark is when the velocity of the movement towards the constriction reaches 20% of peak velocity. The “target” landmark is labeled when velocity again lowers from its peak value to 20% of its peak value. Thus, the “start” and “target” landmarks are found on each side of the velocity peak. The “release” and “end” landmarks are identified with reference to the velocity peak in the movement away from constriction. The “release” landmark is labeled before the velocity peak, when velocity reaches 20% of its peak value. Finally, the “end” of the gesture is identified after the velocity peak in the movement away from constriction, at the time when velocity falls below 20% of its peak value. Gesture landmarks identified with reference to thresholds of peak velocity, as opposed to, e.g., velocity extrema (maximum and minimum), have the advantage of being generally more robust to small variations in spatial position than velocity minima and maxima (see, e.g., Blackwood Ximenes et al., 2017 for discussion).

Figure 6

A sample articulatory trajectory and how the articulatory landmarks were identified using findgest.

Since we labelled tokens one at a time, we could observe when the application of the Findgest algorithm yielded an unrealistic gesture parse. There were two main reasons for this. Some tokens had velocity peaks that were not large enough to clearly parse out movement related to the consonants. If the local velocity peaks for either consonant were too small to detect gestural landmarks, we excluded the token from further analysis. A total of 239 tokens (13% of the data), 142 (7.8%) from the FS condition, and 97 (5.3%) from the FF condition, were excluded for this reason. The resulting data set consisted of 1,579 tokens for analysis, which had clearly distinguishable consonantal gestures flanking the target vowel. Additionally, in some cases it was clear that the tangential velocity was inappropriately summing over multiple gestures. This was typically because a movement associated with C₂ overlapped with C₁. In these cases, we reverted to using component velocities instead of tangential velocities so as to disentangle the influence of overlapping gestures on the kinematics. For example, movement towards C₂ in one dimension, such as anterior movement of the tongue for /t/ in /∫utaisei/ sometimes overlapped in time with movement in another dimension associated with C₁, such as lowering of the tongue for /∫/. For this kind of case, we were able to isolate distinct velocity peaks for C₁ and C₂ by focusing on the primary spatial dimension of movement for each gesture: e.g., tongue lowering for /∫/ and tongue fronting toward the target for /t/. This approach is suggested in Guidelines for using MVIEW (Gafos et al., 2010b) and allowed us to consider a greater number of tokens for analysis. Instead of excluding tokens for which tangential velocities inappropriately summed movement components across distinct gestures, we instead parsed gestural landmarks in these cases using component velocities. For labial C₁, we used tangential velocity for 747 out of 783 tokens (95%); for coronal C₁, we used tangential velocity for 517 out of 796 tokens (65%).

The gestural landmarks parsed from the signal were used to define key measurements for further analysis. The inter-consonantal interval (ICI) was defined as the interval from the release of C₁ to the target of C₂ (see also Section 1.4). We defined C₁ plateau duration as the interval from target to release. Figure 7 illustrates the intervals on a representative token. These intervals allow us to test the key prediction laid out in Section 1.4 that the presence of a vowel conditions a negative correlation between them. Before conducting any analysis we removed outliers more than 2.5 standard deviations from the mean for these two key variables, C₁ plateau duration and ICI.

Figure 7

Illustrations of critical intervals. C₁ duration and C₂ duration are defined as the interval from target to release. ICI (Inter-consonantal Interval) is from the release of C₁ to the target of C₂.

3.2 Assessing the probability of vowel deletion

The data that we are working with has already been classified for vowel presence/absense on the basis of the tongue dorsum trajectory, results reported in Shaw & Kawahara (2021) (for method, see also Shaw & Kawahara, 2018a). For completeness, we briefly summarize the method here.

The temporal interval spanning from the start of movement of C₁, the consonant preceding the target vowel, and the end of movement of C₂, the consonant following the target vowel, was used to determine the probability of vowel deletion. We applied Discrete Cosine Transform (DCT) to represent the kinematic signal as the sum of four DCT components. Gaussian distributions over the DCT components for voiced vowel tokens were used to define a stochastic generator of vowel-present trajectories. We also setup a stochastic generator for the vowel-absent case. For each token of a devoiced item, we fit DCT components to the straight line connecting the position of the tongue dorsum at the onset and offset of the analysis window. The average of these DCT components (fit to the linear interpolation) defines the mean of the probability distribution for the “target absent” hypothesis. The standard deviation of the distributions is computed from the devoiced trajectories in the same manner as for the voiced items. Consequently, the probability distributions that characterize the “target absent” hypothesis are defined by linear interpolation and the variability around each DCT component in the data. We then used these two stochastically defined hypotheses—for target present and target absent trajectories—to classify the trajectories of devoiced items.

As the final step of the computational analysis, for each devoiced token, we determined the posterior probability of a vowel target, based on Bayesian classification of the tongue dorsum trajectory. The classifier was trained on the distributions described above for voiced tokens, which unambiguously contain a vowel target, and a noisy null hypothesis, defined as linear interpolation across the target interval. We do not force a categorical decision, but instead interpret the posterior probability of target absence for each token.