2.1 L2 learning of complex onsets

It has been previously observed that an individual’s L1 can have profound effects on the acquisition of an L2. Generally speaking, if a structure/contrast is present in L2 but lacks a correspondent in L1, it can be difficult to learn. This is referred to as transfer effects (e.g., Lado, 1957; Eckman et al., 2003; Zampini & Edwards, 2008). One example of transfer effects is the influence of phonotactic restrictions in L1 on L2 acquisition. If L1 disallows a certain phonotactic structure, second language learners will often transfer this restriction to L2, even if the structure is permitted under L2. Thus, in order to become a competent speaker of L2, speakers must learn to “undo” these L1 constraints in their L2.

A specific instance of this kind of phonotactic transfer effect comes from the acquisition of complex onsets in L2. Many languages differ with respect to the types of onsets they permit. English, Spanish, and Farsi, for example, all have the sounds /p s l/. They differ, however, in how these sounds can be sequenced into onsets. In English, the legal complex onsets that can be generated from this set are /sp/ (as in ‘speech’), /sl/ (as in ‘sleek’), and /pl/ (as in ‘please’). Spanish is more restrictive, allowing /pl/ (as in ‘playa’), but not */sp/ or */sl/. Farsi is even more restrictive, allowing no complex onsets at all. When a native Spanish or Farsi speaker learns a more phonotactically permissive language like English, they will often struggle specifically with those onsets that violate syllable structure constraints present in their L1.

In both L1 and L2 phonology, a common strategy for dealing with illicit onsets is to repair them via insertion, deletion, or other mechanisms, such that a licit sequence is formed. The focus of this paper will be on the use of vowel epenthesis as a repair strategy, since this is the most observed repair strategy for our population of interest, L1 Farsi/L2 English speakers. Vowel epenthesis is defined as the insertion of a vowel that is not present underlyingly (e.g., Hall, 2011). The outcome of epenthesis is such that an illicit complex onset will be split over two syllables into simple onsets or codas. For example, the onset in a word like /flɑp/ ‘flop’ might be repaired to [fe.lɑp],² restructuring the complex onset into two simple onsets in separate syllables. Epenthesis has been claimed to be a significantly more common repair strategy than deletion of segments in the onset during L2 acquisition (Brasington, 1981).

2.2 Asymmetries in epenthesis location in complex onset repair

The placement of the epenthetic vowel within a word often varies systematically based on the segments in the onset, resulting in an asymmetric patterning. A majority of languages that display this asymmetry make a distinction between ST onsets and all other onsets. ST onsets tend to be repaired via pre-epenthesis (also known as prothesis; e.g., /spuk/ ‘spook’ → [es.puk]), while other onsets are repaired with medial epenthesis (also known as anaptyxis; /brɪŋ/ ‘bring’ → [be.rɪŋ]; e.g., Broselow, 1983; Fleischhacker, 2001; Shademan, 2002; Hall, 2011; Goad, 2012).

To account for this asymmetric patterning of epenthesis, Broselow (1992) claims that ST onsets are structurally represented as a single complex segment, which prevents them from being split in repair. One source of evidence used in this argument is that these clusters are notable exceptions to the Sonority Sequencing Principle (SSP; Selkirk, 1984), which dictates that languages prefer syllable onsets that rise in sonority as they move away from the syllable-initial position. Sonority is defined, roughly, as the resonance or loudness of a sound (see e.g., Clements, 2009), and the concept has been widely used in analyses of syllable structure and certain phonological processes. Sonority is often thought of as a scalar value, as shown in Figure 1.

Figure 1

A scalar sonority hierarchy, showing that stops are considered less sonorous than fricatives, which are less sonorous than nasals, and so on.

Onsets consisting of a non-sibilant obstruent followed by a sonorant (henceforth, OR onsets) like /bl/, /fɹ/, and /tw/, satisfy the SSP because they rise in sonority: Their second sound is more sonorous than their first. ST onsets fall in sonority, violating the SSP, and should therefore be dispreferred. The fact that they are cross-linguistically common motivates their treatment as representationally distinct from other complex onsets. Other special representations for SC onsets have been proposed as well (for an overview, see Goad, 2012), but these all share the basic claim that SC onsets are somehow structurally different from other onset types.

Gouskova (2001, 2004) argues that, although this depiction of ST onsets does offer an explanation for their lack of “splittability” in interlanguage phonology, it does not sufficiently explain why an epenthetic vowel would be needed in the first place. In other words, if ST onsets comprise a single segment, then they should not violate L1 phonotactic constraints against complex onsets and should therefore not trigger epenthesis at all. Fleischhacker (2001, 2005) also argues that the single-segment account is unmotivated for several reasons (including some not repeated here). First, it does not explain the fact that some languages repair other types of sibilant-initial clusters (not just ST onsets), using pre-epenthesis as well (see also Krämer, 2021). Second, there is no obvious difference in markedness between ST clusters and OR clusters, despite the former’s purported higher degree of structural complexity. Both cluster types are commonly attested, and there is none of the implicational relationships that we often see between less marked and more marked structures.

We will not consider the single-segment account further in this paper, but we note that it is generally incompatible with our results, which show that Farsi speakers repair all SC onsets except for /sw/ with pre-epenthesis, not just ST onsets as Broselow’s theory might predict.

Other theories have been proposed to account for the epenthesis asymmetry phenomenon across languages based on the sonority of the individual sounds (e.g., Singh, 1985). Gouskova (2001, 2004) proposes that the asymmetric patterning is due to an innate dispreference against rises in sonority across syllable boundaries. This is referred to as the Syllable Contact Law (SCL; Hooper, 1976; Murray & Vennemann, 1983; Vennemann, 1988; Seo, 2011). In these analyses, researchers similarly make use of a scalar sonority hierarchy (e.g., Figure 1) to represent the relative sonority levels of different types of segments (e.g., Hooper, 1976; Murray & Vennemann, 1983; Vennemann, 1988; Clements, 1990; and for an overview, see Parker, 2002).

Gouskova (2001, 2004) suggests that the SCL, along with a preference towards pre-epenthesis, account for the epenthesis asymmetry between SC and OR onsets. In an OR onset like in /pliz/, repair using pre-epenthesis to [ep.liz] results in a violation of the SCL, since [p] at the end of the first syllable has a lower sonority than [l] at the beginning of the second. Medial epenthesis to [pe.liz] results in no violation of the SCP and so is preferred. In an SC onset like in /stɑp/, neither pre-epenthesis to [es.tɑp] nor medial epenthesis to *[se.tɑp] results in an SCL violation. Gouskova motivates the preference for [es.tɑp] as reflecting a bias against medial epenthesis. In other words, pre-epenthesis is preferred unless doing so would violate the SCL, in which case medial epenthesis is used.

Farsi poses a problem for this analysis because it repairs almost all SC onsets using pre-epenthesis (see Fleischhacker, 2001, 2005; Krämer, 2021). For example, the SCL-based analysis predicts that Farsi speakers should repair /slæb/ ‘slab’ to [se.læb], since [es.læb] produces an SCL violation. Despite this, [es.lab] is the preferred repair strategy among Farsi speakers, suggesting that avoidance of SCL violations is not the mechanism driving epenthesis asymmetries in Farsi. Krämer confirms this empirically by asking Iranian Farsi speakers to produce attested loanwords and wug words with complex onsets of varying sonority profiles, including many not attested in English. Although he observes a high amount of variability between participants, Krämer finds several robustly attested epenthesis patterns that are not predicted by the SCL, casting further doubt on its ability to account for these epenthesis asymmetries.³

Farsi is not exceptional in how it repairs SC onsets. Fleischhacker (2001, 2005) points out that variability in the treatment of SL (sibilant + liquid) and SN (sibilant + nasal) clusters has also been displayed in Hindi (Bharati, 1994), as well as in Russian loanwords produced in Kazakh (Sulejmanova, 1965), among other languages. With this in mind, Fleischhacker (2001, 2005) proposes that epenthesis repair asymmetries emerge from pressures to minimize perceptual distance from the unepenthesized form. In a series of studies, she observes that English speakers find medial epenthesis to be more perceptually disruptive than pre-epenthesis into ST clusters, while in other clusters, including SR (sibilant + sonorant) and OR clusters, medial epenthesis was judged to be less disruptive. Based on these results, she proposes that complex onsets across languages are repaired in such a way as to minimize perceptual distance from the unepenthesized form. The perceptual perspective is supported by independent evidence showing that L1 speakers of Spanish, which does not allow ST onsets and repairs them using pre-epenthesis, commonly perceive pre-epenthesized vowels in such clusters, even when they are not present (e.g., Cuetos et al., 2011; Gibson, 2012; Carlson, 2019). Thus, not only is pre-epenthesis into SC clusters less perceptually disruptive than medial epenthesis, it also aligns with a common misperception of these clusters by speakers whose languages do not allow them.

The phonological modeling study in Section 4 will directly compare the SCL analysis (Gouskova, 2001, 2004) and the perception-based analysis (Fleischhacker, 2001, 2005). We will discuss the formalization of these analyses in more detail in that section.

2.3 The acquisition and articulation of complex onsets

In addition to the differences in their preferred epenthesis locations, SC onsets appear to behave differently from OR onsets in terms of their acquisition and their articulation.

Given the marked status that the SSP ascribes to ST clusters, one might expect them to be acquired more slowly than other clusters in both L1 and L2. The evidence for this is equivocal. In L1, there is some evidence that SC onsets are indeed acquired later than other types of clusters, in the sense of being repaired more frequently by children (e.g., Barlow, 2001; Yavaş, et al. 2008), though other studies have failed to find this difference or found that SC onsets were acquired earlier (e.g., Smit, 1993; Gierut, 1999; Yavaş & Core, 2006). It has also been shown that generalization (i.e., the learning of one complex onset facilitating the learning of another) occurs within the SC and OR classes but not between them (e.g., Gierut, 1999, 2001). Finally, in both SC and OR onsets, the greater the difference in sonority between the first and second elements in the cluster (the better it abides by the SSP), the less likely learners are to repair that cluster (e.g., Jarosz, 2017).

Similarly, conflicting results have been found for L2 speakers. Epenthesis rates in general have been shown to decrease as L2 proficiency increases (Boudaoud & Cardoso, 2009, Yazawa et al., 2015). Some studies have found that L2 learners repair SC onsets more frequently than OR onsets (e.g., Carlisle, 2001; Yildiz, 2005), but other papers have failed to find such an effect (Sherwin, 1999; Tessier et al., 2013). As well, within the classes of SC and OR onsets, learners are generally less likely to repair onsets with greater sonority differences between the first and second segments (Carlisle 2001; Cardoso, 2007; Boudaoud & Cardoso, 2009).

Studies investigating articulatory timing have also found differences between the articulation of SC clusters and OR clusters. Pouplier et al. (2022) show that across seven languages, sibilant-initial clusters exhibit greater articulatory overlap between the two segments and decreased variability in timing when compared to stop-initial onsets. With regards to temporal organization, SC onsets appear to display a more robust “c-center” effect (Browman & Goldstein, 2000) in comparison to singleton onsets (Pastätter & Pouplier, 2014), as well as coda /s/ clusters (Marin, 2013). This does not seem to be the case with stop-initial clusters. Although this heightened articulatory coupling between the segments in SC onsets is generally consistent with the notion that they constitute a single complex segment, the relationship between these results and the sonority and perceptual accounts of SC cluster behavior is less clear. We will return to this question in the discussion at the end of the paper.

2.4 The current study

In the remainder of the paper, we analyze epenthesis asymmetry patterns in native Farsi speakers who have learned English as their L2. As noted above, we choose this population because Farsi has no complex onsets, allowing us to compare SC and OR onsets directly and because Farsi speakers have been shown to repair a majority of SC onsets using pre-epenthesis, which poses a challenge for several of the theoretical analyses described above. We also seek to provide additional clarity on whether the cross-linguistic asymmetry in repair that has been displayed between SC and OR onsets corresponds to an asymmetry in acquisition as well.

Section 3 presents the results of an experimental study looking at the production of English complex onsets by L1 Farsi/L2 English speakers of varying abilities. Section 4 presents a phonological analysis and modeling study of the experimental data. Section 5 discusses the implications of these results and speculates on how a perceptual account of SC clusters can unify some of their heterogeneous properties.

3.1 Methods

We recruited 20 native Farsi speakers living in Orange County, California who learned English as a second language (14 male; 36–80 years old⁴) and tasked them with producing 78 English target words with complex onsets. Thirty-seven of these target words contained SC onsets, while the other 41 contained OR onsets. Note that all SC onsets were /s/-initial, given the marginal status of /ʃ/-initial complex onsets in English. Participants were recruited by word of mouth. After providing consent, they were asked to fill out a language background questionnaire (described in the following section). Participants were then asked to read three passages containing the target words (see Appendix A). Finally, participants were asked to read each target word in the context of a carrier phrase (‘__ is a good word’). The orders of the three passages and the carrier sentences were varied for each participant.

Audio recordings were made for 13 of the participants using a Rode Lavalier Go microphone and Focusrite Scarlet 2i2 USB audio interface. Due to technical issues, the remaining seven participants were recorded using the integrated microphone on a 2017 Macbook Pro. Although this resulted in decreased audio quality for these participants, recordings were only used qualitatively to identify the presence of epenthesis, and the quality of these recordings was sufficient for this purpose. In both cases, the recordings were made with a sampling rate of 44.1 kHz and a bit depth of 16. Recordings were made in quiet rooms at participants’ homes or places of work.

Due to variable English reading ability among our participants, four were only able to read the carrier phrases and not the passage. In addition, two participants declined to read the carrier phrases after reading the passages. One participant was entirely excluded due to poor audio quality, and two participants’ carrier phrase productions were excluded for the same reason. This left a total of 19 participants, with four having read only the carrier phrases, four only the passages, and eleven both. Words that participants were unable to read or that were read incorrectly were omitted, leaving a total of 2,129 tokens. See Appendix B for a full list of onset types and their production counts.

For each target word, epenthesis type (pre-epenthesis, medial epenthesis, or no epenthesis) was recorded. The presence of an epenthetic vowel was confirmed by examination of the waveform and spectrogram for each token, with the criteria that epenthetic vowels must display clear formant structure in the expected location (i.e., either before the onset or within the onset) and differences in amplitude sufficient to distinguish them from surrounding context.

Figure 2 shows productions of the word /floɹ/ “floor” by two different participants. The image on the left shows a production with medial epenthesis, with the epenthetic vowel indicated by *. The presence of this vowel is reflected in the spectrogram by increased amplitude and distinct formant structure from both the initial /f/ and the following /l/. The image on the right shows a production without epenthesis.

Figure 2

Tokens of the word /flor/ ‘floor/ produced with medial epenthesis (left) and without medial epenthesis (right).

Given the structure of the passages that participants were prompted to read, some of the onsets were preceded by a word-final vowel. For example, “the stove.” Though we expect such configurations to reduce rates of epenthesis, since the initial segment of the complex onset can be syllabified as the coda of the preceding syllable (e.g., Boudaoud & Cardoso, 2009), these configurations pose a challenge for detecting pre-epenthesis: cases where there is word-final vowel followed by pre-epenthesis (e.g., “the estove”) could be difficult to distinguish from cases without epenthesis. In cases of pre-epenthesis, we observed that there was often a glottal stop between the offset of the word-final vowel and the epenthetic vowel. In other cases, this juncture was less apparent. In these more ambiguous cases, we relied on F2 transitions to determine whether the preceding material constituted a single vowel (“the stove”) or a pair of adjacent vowels (“the estove”). Figure 3 provides an example of the latter case, with the epenthetic vowel indicated using “*”. Here we can see differences in the formants between the underlying and epenthetic vowel. The glottal pulses in the epenthetic vowel are also slower and less periodic, indicating weak glottalization, which is also consistent with an epenthetic vowel. In our dataset of roughly 2,100 tokens, there were only 18 cases where a word-final vowel preceded a pre-epenthesized onset.

Figure 3

An example of pre-epenthesis in a post-vocalic context in the phrase “he sniffs.”

3.2 Scalar measurement of L2 proficiency

Before reading the passages and carrier phrases, participants completed the LEAP-Q (Marian et al., 2007), an experimentally-validated questionnaire measuring the language profiles of multilingual speakers. To create a scalar measure of language proficiency suitable for both the statistical model described here and the phonological analyses presented in the next section, we retained only the LEAP-Q questions with numeric responses and conducted a Principal Components Analysis to reduce these responses to a single dimension (for a similar approach, see Danielson, 2012). In each case described below, we used the first Principal Component (PC1) as the measure of interest. This component always displayed a strong positive correlation with Farsi ability and exposure. In order to ease interpretation of this value, we negated it so that higher positive values represent greater L2 English proficiency. We refer to this negated score as Relative English Dominance (RED).

Following Marian et al. (2007), who advise against running a PCA on the entirety of the LEAP-Q data, we classified the numeric questions in the questionnaire into one of three categories based on the primary question categories described in the paper and ran separate PCA’s on each of these bins, as well as on the full set of numeric questions. This produced four different versions of RED:

1. RED_acquisition: based on questions related to age of L2 acquisition and L1/L2 exposure

2. RED_immersion: based on questions related to L1/L2 immersion

3. RED_self-report: based on questions related to self-reported L1/L2 proficiency

4. RED_full: based on all numeric questions combined

The specific questions from the LEAP-Q that were categorized into each of these bins are provided in Appendix C.

In order to determine which implementation of RED best predicts epenthesis patterns, we fit nine instantiations of our statistical model (specific details of this model are given in the following section). Eight of these had as fixed effects each possible combination of RED_acquisition, RED_immersion, and RED_self-report, while the final used only RED_full.

We compared these models using the Bayesian Information Criterion (BIC; Schwarz, 1978; Raferty, 1995), which rewards model fit and penalizes model complexity, with lower scores being better. The results of this analysis showed that the model containing only RED_acquisition performed the best. Accordingly, the results we report below come from the model that uses this score to characterize English proficiency, which we will simply abbreviate as RED going forward. The full details of the model comparison can be found in Appendix D, and Appendix E presents the loadings of the RED_acquisition principal component.

3.3 Results

Figure 4 shows the proportion of each response type (no epenthesis, medial epenthesis, or pre-epenthesis) broken down by onset type. The total number of tokens for each response type are given above each bar. Most tokens were produced without epenthesis. In cases of epenthesis, all SC onsets are repaired with pre-epenthesis, except for /sw/, which is repaired with medial epenthesis, and all OR onsets are repaired with medial epenthesis. Overall epenthesis rates are greater for SC onsets than OR onsets. Figure 5 shows epenthesis rates broken down by individual onsets (e.g., /st/, /pl/ /br/ etc.).

Figure 4

Proportion of each epenthesis outcome for SC onsets and OR onsets. Error bars indicate standard error.

Figure 5

Mean epenthesis rates for each onset in the experimental study. Error bars indicate standard error.

Figure 6 shows how overall epenthesis rates and the proportion of pre- vs. medial epenthesis correlate with RED. A higher RED score is associated with lower overall rates of epenthesis and with a higher rate of pre-epenthesis repair relative to medial epenthesis repair.

Figure 6

(Left) Epenthesis rate by RED_acquistion. (Right) Pre-epenthesis rates by RED.

Epenthesis rate is calculated as the proportion of complex onsets in our dataset that are produced with an epenthesized vowel, and pre-epenthesis rate is calculated as the proportion of cases of epenthesis where pre-epenthesis is used. There is an inverse relationship between English dominance and overall epenthesis rates (Figure 6, left). However, as proficiency rises, speakers’ repaired productions show a greater proportion of pre-epenthesis relative to medial epenthesis (Figure 6, right).

We fit a mixed-effects logistic regression model using the lme4 package in R to provide quantitative support for these observations. Because epenthesis location was almost perfectly predicted by onset type (with /sw/ the exception), we binned tokens of pre-epenthesis and medial epenthesis together, such that the dependent variable was whether epenthesis occurred (1) or not (0). The independent variables were whether the onset was preceded by a vowel, onset type (SC or OR), context (passage or carrier phrase), RED (scaled and centered), as well as an interaction between RED and onset type. The model also included random intercepts for both speaker and word.

The details of the fitted model are shown in Table 1. The results indicate that the presence of a preceding vowel is not a significant predictor of epenthesis (β = 0.297, p = 0.47). We also see that SC onsets are more likely to be epenthesized than OR onsets (β = 4.21, p < 0.001), and a complex onset is more likely to be repaired in a passage than in a carrier sentence (β = 1.287, p < 0.001). The model also suggests that a higher RED is associated with lower overall rates of epenthesis (β = –4.33, p < 0.001). The interaction between RED and Onset Type (β = 2.15, p < 0.001) shows that the effect of RED is modulated by onset type: increases in RED cause the probability of epenthesis into OR clusters to decline more quickly than for SC clusters.

3.4 Intermediate summary

The results⁵ of the experiment presented above indicate that:

1. L1 Farsi/L2 English speakers repair OR onsets using medial epenthesis, and SC onsets using pre-epenthesis. The exception to this is /sw/, which was repaired using medial epenthesis.

2. SC onsets displayed overall higher rates of repair than OR onsets.

3. Overall epenthesis rates decreased as English proficiency increased, as measured using the RED score calculated from the LEAP-Q survey.

4. More proficient English speakers showed higher rates of pre-epenthesis relative to medial epenthesis.

These results corroborate the asymmetries in epenthesis location found in previous research on Farsi speakers and support the claim that SC onsets are more difficult and slower to acquire than OR onsets. In the following section, we will use these experimental results to test the predictions of two phonological accounts of epenthesis asymmetries.

4.1 The Syllable Contact analysis

As discussed above in Section 2, Gouskova (2001, 2004) accounts for epenthesis asymmetries by proposing that pre-epenthesis is the default strategy cross-linguistically but that medial epenthesis is used to avoid repairs that would violate the Syllable Contact Law (SCL), which penalizes sonority rises across syllable boundaries. This process is demonstrated in the pseudo-tableau in Table 2, in which the word /pliz/ ‘please’ is repaired with either medial epenthesis or pre-epenthesis. Δ_sonority refers to the difference in sonority between the first segment of the second syllable, and the final segment of the first syllable, using the scale in Figure 1:

If ‘please’ were to be repaired using pre-epenthesis (/pliz/ → [ep.liz]), there would be a rise in sonority (Δ_sonority = +3) across the new syllable boundary, violating the Syllable Contact Law. On the other hand, if ‘please’ were to be repaired with medial epenthesis (/pliz/ → [pe.liz]), the output would have a fall in sonority across syllable boundaries (Δ_sonority = –2), which does not violate this law. Thus, the latter strategy emerges as the preferred choice. Conversely, Table 3 shows a pseudo-tableau for the word ‘steep’ repaired by either medial or pre-epenthesis.

Here, if ‘steep’ were repaired using pre-epenthesis (/stip/ → [es.tip]), there would be a fall in sonority across the resulting syllable boundary (Δ_sonority = –1). Medial-epenthesis (/stip/ → [se.tip]) would also yield a fall in sonority (Δ_sonority = –5). From the perspective of the SCL, therefore, both forms are acceptable. Because [es.tip] emerges as the winner, Gouskova takes this as evidence for pre-epenthesis as the default repair strategy, with medial epenthesis only used when pre-epenthesis would result in an SCL violation, as in Table 2.

Gouskova implements this analysis using the following constraints:

SyllableContact: Sonority must not rise across a syllable boundary.

*Complex: No tautosyllabic consonant sequences.

Dep: Don’t epenthesize.

Contiguity: Elements adjacent in the input must be adjacent in the output.

Tables 4 and 5 showcase two tableaux demonstrating the ranking proposed in Gouskova (2001, 2004). Table 4 shows that the analysis predicts medial epenthesis for OR onsets.

The high-ranked *Complex constraint rules out the unepenthesized candidate 4c. Although Candidate 4b satisfies the Contiguity constraint, it does so at the cost of producing a violation of SyllableContact because of the sonority rise from [f] to [r] across the syllable boundary. Candidate 4a is accordingly chosen as the winner, despite its violation of Contiguity.

Table 5 below shows that the analysis predicts pre-epenthesis for ST clusters. Candidate 5c is again ruled out because of its violation of *Complex. In contrast to the pre-epenthesized candidate in the previous tableau, Candidate 5b in this tableau does not violate the SCL, because there is a sonority drop from [s] to [p] across the syllable boundary. Although Candidate 5b also satisfies the SCL, its violation of Contiguity casts the deciding vote against it, and the pre-epenthesized candidate 5b comes out as the winner.

We will refer to the analysis above as the Simple Syllable Contact analysis. This constraint hierarchy is structured such that, in the absence of a SyllableContact violation (i.e., neither pre- nor medial epenthesis results in a rise in sonority across syllable boundaries), Contiguity will ensure that the pre-epenthesized form is chosen. In other words, this analysis predicts that all onsets with flat or falling sonority should be repaired by pre-epenthesis (ST onsets) and all others with medial epenthesis (OR and SR onsets).

Gouskova (2001, 2004) also presents an extension of this analysis that divides the SyllableContact constraint into separate constraints for each degree of sonority rise/fall across syllables. She argues that these constraints are intrinsically ranked, such that higher sonority rises are always penalized more than lower sonority rises.

SyllableContact_Δ4 >> SyllableContact_Δ3 >> … >> SyllableContact_Δ-4 >> SyllableContact_Δ-5

This hierarchy can be interspersed with other markedness or faithfulness constraints, such that the degree of sonority rise tolerated and the repair strategy used for different sonority rises can differ. We will refer to this analysis as the Complex Syllable Contact analysis.

As mentioned previously, the major issue with the Syllable Contact analysis is that it fails to account for the behavior of subtypes of SC onsets, such as SR (sibilant + sonorant) onsets in certain languages (Krämer, 2021; Fleischhacker, 2001, 2005). This phenomenon is evident in Farsi, which repairs SN (/s/ + nasal) and SL (/s/ + liquid) onsets using pre-epenthesis, despite this resulting in a violation of the SCL. Table 6 shows an example of how the Syllable Contact analysis predicts SR clusters should behave.

Table 6

A tableau showing that medial epenthesis of SN clusters is predicted under the Syllable Contact analysis. The sad face indicates the candidate who should have won but did not, while the bomb indicates the candidate that should not have won, but did.

/snɪf/	*Complex	Dep	SyllableContact	Contiguity
a.    se.nɪf		*		*
b.    es.nɪf		*	*! (s.n)
c. snɪf	*!

Here, the Syllable Contact analysis predicts that SN onsets will be repaired with medial epenthesis, since pre-epenthesis produces a violation of the SCL. The same outcome is also predicted for SL onsets. Though some languages are known to repair SR onsets using medial epenthesis, the Syllable Contact Law does not predict Farsi speakers’ repair of these onsets with pre-epenthesis (Fleischhacker, 2001, 2005; Krämer, 2021). These issues persist even in the Complex Syllable Contact analysis (see Section 4.7 for discussion as to why).

4.2 The Perceptual Cost analysis

An alternative account of epenthesis asymmetries is presented by Fleischhacker (2001, 2005), who argues that these patterns are the results of pressure to maximize perceptual similarity between the epenthesized and unepenthesized forms.

Fleischhacker provides experimental evidence to show that the perceptual cost of splitting an ST onset with medial epenthesis is greater than that of splitting an SR (sibilant + sonorant) or OR onset. In her experiments, Fleischhacker presented English-speaking participants with words that began with initial ST, SN (sibilant + nasal), SL (sibilant + liquid), SW (sibilant + glide), and OR onsets. These words were modified with either pre-epenthesis or medial epenthesis. Participants were then asked which modified form of the word sounded more like the unepenthesized word. The results demonstrate that speakers found pre-epenthesis less disruptive than medial epenthesis for SC onsets, while medial epenthesis was generally preferred for other onset types. Subsequent studies have corroborated aspects of this proposal (e.g., Davidson & Shaw, 2012). Based on these experimental results, as well as typological considerations, Fleischhacker proposes the following ranking of different onset types based on how perceptually disruptive medial epenthesis is:

In other words, the perceptual difference between inserting and not inserting a vowel in the context S_T (e.g., medial epenthesis in a word like ‘stop’ [se.tɑp]) is greater than the perceptual difference between inserting and not inserting a vowel in the context S_N (e.g., medial epenthesis in a word like ‘snap’ [se.næp]), and so on. The pressure to maximize perceptual similarity between epenthesized and non-epenthesized forms means that onsets that are higher in this ranking should be more likely to be repaired via pre-epenthesis, since it results in a relatively smaller degree of perceptual disruption than medial epenthesis.

The core constraints of this analysis are implemented using P-Map (perceptual map) constraints (Steriade, 2000, 2001; Zuraw, 2007, 2013), which penalize candidates based on the perceptual distance between underlying and surface forms.⁶ These constraints typically penalize greater perceptual deviations more strongly than smaller ones (though this effect may be modulated by language exposure).

We follow Fleischhacker in using contextual Dep constraints of the form Dep-V/X_Y. These constraints are violated when a vowel is inserted into the context X_Y, where X and Y refer to segmental classes. We adopt the following specific constraints:

Dep-V/S_T: Do not insert a vowel between a sibilant and a stop.

Dep-V/S_N: Do not insert a vowel between a sibilant and a nasal.

Dep-V/S_L: Do not insert a vowel between a sibilant and a liquid.

Dep-V/S_W: Do not insert a vowel between a sibilant and a glide.

Dep-V/O_R: Do not insert a vowel between a non-sibilant obstruent and a sonorant.⁷

Fleischhacker suggests that these constraints are ranked in a hierarchy in accordance with the scale of perceptual disruptiveness presented above.

Dep-V/S_T > > Dep-V/S_N > > Dep-V/S_L > > Dep-V/S_W > > Dep-V/O_R

This hierarchy requires that the cost of insertion into an ST cluster is higher than into an SN cluster, which is higher than into an SL cluster, and so on. In other words, epenthesis into a cluster is penalized proportionally to how perceptually distant the resulting epenthesized form is from the unepenthesized or underlying form.

Fleischhacker also uses the following additional constraints, some of which are shared with Gouskova’s (2001, 2004) analysis:

*Complex: No tautosyllabic consonant sequences.

C/V: No consonant sequences at all.

Contiguity: Elements adjacent in the input must be adjacent in the output.

L-Anchor: Elements on the left edge of the input must be on the left edge of the output.

Example tableaux based on Zuraw (2013) are shown below. In the first tableau (Table 7), the faithful realization of /frut/ (candidate 7c) is ruled out because it violates *Complex. Candidate 7b satisfies *Complex, but violates L-Anchor because the /f/ at the left edge of the input is no longer at the left edge in the output. The medial epenthesized form (candidate 7a) is chosen because it satisfies *Complex while also avoiding a violation of L-Anchor.

In the second tableau (Table 8), the pre-epenthesized form (candidate 8b) is chosen because it avoids a violation of Dep-V/S_T, which strongly penalizes epenthesis into ST clusters because of its perceptual disruptiveness.

In general, any structures whose corresponding contextual Dep constraint is ranked below L-Anchor will be repaired by medial epenthesis, while those whose Dep constraint is ranked above L-Anchor will be repaired by pre-epenthesis. In our data, both Dep-V/S_W and Dep-V/O_R must be ranked lower than L-Anchor, since /sw/ and OR onsets are always repaired using medial epenthesis.

In the following section we will describe the MaxEnt framework, which we will use to implement variants of these two analyses.

4.3 Maximum entropy constraint grammars

MaxEnt is a variant of Harmonic Grammar (Legendre et al., 1990: Prince & Smolensky, 1993/2004; Pater 2009), which is a generalization of Optimality Theory (OT; Prince & Smolensky, 1993/2004) where constraints are assigned numeric weights instead of being ranked. Higher weights indicate stronger constraints. Given some input /x/, each output candidate [y] is assigned a harmony score H based on its constraint violations:

$H(x,y) \text{=} {\displaystyle {\sum }_{i\text{=}1}^K{w}_i{C}_i(x,y),}$

where K is the number of constraints, w_i is the weight of the i^th constraint, and C_i(x,y) is the number of times the mapping /x/ → [y] violates the i^th constraint. A candidate that violates no constraints has a harmony score of 0, and a more positive score indicates a less preferred candidate.

For an input /x/, MaxEnt calculates a probability distribution over all possible output candidates y ∈ Gen(x) as follows:

$P(y|x;w) \text{=}\frac{e^{–H(x,y)}}{{\Sigma }_{z \in \mathit{\text{Gen}}(x)}\hspace{0.17em}{e}^{–H(x,z)}} .$

In other words, the probability of a candidate is proportional to its (exponentiated) negative harmony. This means that candidates that violate more constraints, or constraints with higher weights, are assigned lower probabilities.

Because MaxEnt assigns a probability to each observed form, we can use MaxEnt models to calculate a conditional log likelihood for a data set by summing the log probabilities of each of the N tokens in the data set:

$L{L}_w(D)\hspace{0.17em}\text{=} {\displaystyle \sum _{i\text{=}1}^N}ln P(y_i|x_i;w)$

A model that perfectly predicts a data set will assign it a conditional log likelihood of 0. As the predictive accuracy of the model decreases, the conditional log likelihood will become increasingly negative.

Given a set of constraints and a data set consisting of input-output pairs with violation profiles, the weights that optimally predict the data (i.e., that maximize the conditional log likelihood) can be learned using gradient descent (see Hayes & Wilson, 2008). This means the model weights can be fit directly to the experimental data rather than determined manually.

4.4 Enforcing constraint hierarchies

Both the Complex Syllable Contact and the Perceptual Cost analyses contain constraint hierarchies, which put certain constraints into a fixed relative ranking. The hierarchy in the Complex Syllable Contact analysis requires that constraints penalizing greater sonority rises across syllable boundaries should be ranked higher than those targeting smaller sonority rises. Similarly, the hierarchy in the Perceptual Cost analysis requires that the contextual Dep constraints be ranked in accordance with the relative perceptual disruptiveness of epenthesis into each context.

In order to enforce these hierarchies in MaxEnt models, we implement them as stringency relationships (e.g., de Lacy, 2004, 2006). Under such a relationship, if a constraint in the hierarchy is violated, then every constraint below it in the hierarchy is also violated. This is shown in the tableau below.

Because of the strict constraint ranking used in classical OT, the stringency relationship shown in Table 9 does not seem to do much for us: So long as we keep the constraints in the ranking shown above, violations of lower ranked constraints by candidates that also violate higher ranked ones do not affect the outcome. In the context of the numeric constraint weights used in MaxEnt, however, the usefulness of a stringency relationship becomes apparent: It allows constraint weights to be fit freely (so long as they are positive), while still imposing the restriction that forms that violate higher ranked constraints in the hierarchy cannot be penalized less than forms that violate only lower ranked constraints. An example MaxEnt tableau with toy weights is shown below in Table 10 to illustrate this. Constraint weights are given under each constraint name. The numbers in the cells below are the number of times the corresponding candidate violates each constraint (once in all cases here).

Under a stringency relationship with weighted constraints, Candidate 10d (for example), with medial epenthesis between a sibilant and a glide, must receive a harmony score that is either equal to the harmony of Candidate 10e (if the weight of Dep-V/S_W is 0) or greater than the harmony of 10e (if the weight of Dep-V/S_W > 0). In other words, the stringency relationship requires that epenthesis into SW clusters will always be penalized to an equal or greater extent than epenthesis into OR clusters, and so on up the hierarchy, regardless of how the constraints are weighted. Were this hierarchy not in place, arbitrary constraint weights could be used to generate typologically bizarre predictions. The weight of the lowest weighted constraint reflects the penalty assigned to violating that constraint (in this case, epenthesis into an OR onset), while the weights of every higher ranked constraint reflect the difference in penalty between violating that constraint and violating the next-lowest ranked constraint in the hierarchy. Note, crucially, that the stringency relationship is not meant to claim that epenthesis into an SW cluster as in 10d somehow also constitutes epenthesis into an OR cluster, despite the violation of Dep-V/O_R: Rather, the stringency relationship between these two Dep constraints mandates that forms that violate Dep-V/S_W must be penalized at least as much as forms that violate Dep-V/O_R.

4.5 Analysis variants

In addition to comparing the two Syllable Contact analyses and the Perceptual Cost analysis described above, we also compare several variants of each that differ in (a) whether *Complex constraint weights are scaled by English dominance; (b) whether *Complex can have different weights for SC vs. OR onsets; and (c) whether the relationship between English dominance and the weight of *Complex differs for SC vs. OR onsets. These variants are described in the following sections.

4.6 Model comparison

All MaxEnt models were fit to the experimental data set using the maxent.ot R package (Mayer et al., 2024). Constraint weights were fit to the data using gradient descent with a weak Gaussian prior of μ = 0 and σ = 1000. This implements a soft preference for lower constraint weights (see Mayer et al., 2024, for more detail). Optimal ρ or ρ_SC/ρ_OR was then calculated using grid search over the range [0.1, 1] in increments of 0.1. Model comparison was done using BIC, which, again, rewards model fit to the data while penalizing model complexity. When evaluating models based on BIC, it is the relative difference in BIC scores that is important, not their particular values. Lower BIC scores are preferred. A rule of thumb, proposed in Raftery (1995), is that a difference in BIC scores of 0 to 2 is weak positive evidence for the model with the lower score; a difference of 2 to 6 is positive evidence; a difference 6 to 10 is strong positive evidence; and a difference of 10 or more is very strong evidence.

This should be Table 11 below shows the conditional log likelihood, number of parameters (reflecting model complexity), and BIC score for each model we tested. The BIC scores of each model are also presented graphically in Figure 7.

Figure 7

BIC scores for each model type. The x-axis represents the base model type, and the colored points and lines correspond to the variations on each model described in the previous section.

These results demonstrate several things. First, scaling *Complex by speaker RED scores substantially improves model fit across the board. Second, splitting *Complex into SC- and OR-specific variants also improves model fit across the board, with the exception of the Simple Syllable Contact model with no scaling: Though Fleischhacker (2005) justified this split primarily on typological grounds, this provides additional evidence for its necessity. Finally, introducing separate scaling rates for SC and OR onsets results in a modest increase in model fit across the board. These results provide further support for the claims from the previous sections about the production and acquisition of complex onsets and demonstrate that the innovations to these models presented here (scaling and splitting *Complex) are useful mechanisms for modeling these factors.

Additionally, and most importantly, these results provide broad support for the Perceptual Cost model over the Syllable Contact model in accounting for patterns of repair in the experimental data. In every variant of the model where either *Complex is split by onset type or the weight of *Complex is scaled by speakers’ English dominance, the Perceptual Cost model achieves the best performance, followed by the Complex Syllable Contact model and the Simple Syllable Contact model. Only in the model that does not account for interspeaker and inter-onset differences does the Complex Syllable Contact model outperform the Perceptual Cost model. This underscores the importance of controlling for these factors in our model comparison.

4.7 Why does the Perceptual Cost model succeed?

We can gain some insight into the success of the Perceptual Cost model by plotting the mean errors made by the three best performing models in each class. These errors are shown in Figure 8. The bar corresponding to errors on tokens without epenthesis is negative for all models, indicating that all models underpredict epenthesis rates. The difference between the models becomes apparent when looking at their predictions for pre- vs. medial epenthesis. The Perceptual Cost model successfully predicts that SC onsets (with the exception of /sw/ onsets) should be repaired by pre-epenthesis and OR onsets should be repaired by medial epenthesis. On the other hand, both Syllable Contact models predict that SC onsets should sometimes be repaired by medial epenthesis (which is unattested in our data except for a small number of /sw/ tokens) and that OR onsets should sometimes be repaired by pre-epenthesis (which is completely unattested in our data). Thus, both Syllable Contact models are unable to capture the clear separation of repair strategies by onset type.

Figure 8

Error rates from each model, broken down by onset type (SC vs. OR) and epenthesis type (none vs. pre-epenthesis vs. medial epenthesis).

Why do the Syllable Contact models predict unattested repair strategies? This issue arises because some OR and SR onsets have identical sonority deltas, such as /fl/ and /sl/ where son(/f/) = son(/s/) = 1 and son(/l/) = 4. Because the Syllable Contact models cannot distinguish between onsets with the same sonority delta, the model necessarily predicts that these onsets should display equivalent behavior. An example of this is shown for the words ‘fly’ and ‘sleep’ in the following two tableaux, which uses the unscaled constraint weights from the best performing Simple Syllable Contact model.

In Table 12, Candidate 12c violates *Complex_OR due to its OR onset, but it is still the most probable candidate due to the low weight of this constraint. Although both the repaired forms 12a and 12b violate two constraints each (Dep plus Contiguity or SyllableContact respectively), Candidate 12a is predicted to be more probable because the violation of Contiguity is less costly than the violation of SyllableContact.

The situation is essentially identical in Table 13, except that Candidate 13c is expected to be relatively more probable than Candidate 12c (and, accordingly, Candidates 13a and 13b relatively less probable than Candidates 12a and 12b) due to the lower weight of *ComplexSC. Crucially, however, the Harmony of the two repaired candidates a and b is the same in both cases due to their common sonority profile. This means that their relative frequency of occurrence remains the same under any weighting of these constraints. Decreasing the weight of Contiguity or increasing the weight of SyllableContact to increase the rate of medial epenthesis for /fl/ onsets will have the same effect on /sl/ onsets, and vice versa. The same issue occurs for the Complex Syllable Contact model and for other pairs of onsets with identical sonority deltas such as /sw/ and /pl/.

In the Perceptual Cost model, on the other hand, different repair strategies are predicted due to differences in the violations of the contextual Dep-V constraints. This is illustrated in Tables 14 and 15, again using the unscaled weights of the *Complex constraints.

In Table 14, Candidate 14b receives a probability of zero due to its violation of the highly-weighted L-Anchor constraint. The relatively low weight of *Complex_OR leads to 14c being the most probable outcome, while 14a, the form repaired by medial epenthesis, receives the remainder of the probability mass.

In Table 15, the unepenthesized form 15c again receives the majority of the probability, but now the only predicted repair strategy is pre-epenthesis, in 15b. This shift is due to the additional violations 15a incurs for the constraints Dep-V/S_L and Dep-V/S_W. The violations of these two constraints are collectively costlier than Candidate 15b’s violation of L-Anchor, and so only pre-epenthesis repairs are predicted in this case.

An additional difference between the Syllable Contact and Perceptual models is in their weightings and scalings of the *Complex constraints. These values from the most successful model of each type are shown in Table 16.

Note that although all models have a higher learning rate for OR onsets than for SC onsets, the two Syllable Contact models assign lower weights to *Complex_SC than to *Complex_OR. Weights in a MaxEnt model represent the relative strength of each constraint, such that violations of constraints with higher weights are more strongly penalized. Concretely, because the probability of a candidate is inversely proportional to its harmony score, and because the harmony score is the sum of all the weights of the constraints the candidate violates, violating a constraint with a higher weight will lower the probability of a candidate more than a violation of a lower weighted constraint. Both Syllable Contact models predict that (all else being equal) forms with SC onsets should be more likely to surface without repair than forms with OR onsets, while the Perceptual Cost model predicts the opposite. Thus, the optimal weights for the Syllable Contact models fail to directly encode the observation that SC onsets are more difficult than OR onsets, while the Perceptual Cost model succeeds.

5.1 Relating acquisition, articulation, and perception

A question that emerges from the current study as well as past research is how to reconcile the idiosyncratic phonological behavior of SC onsets with their articulatory and acquisitional properties. In other words, SC onsets tend to be repaired using pre-epenthesis while other onsets use medial epenthesis. Does this relate at all to the fact that SC onsets display greater articulatory coupling between the component sounds (see Section 2.3), are more difficult to produce and are slower to acquire?

Although it is not as apparent, we will speculate here on a possible connection between the Perceptual Cost account of epenthesis asymmetries and the other properties of SC onsets. Hall (2006) demonstrates that an “intrusive” vowel may be perceived between the segments of a complex onset as the result of a mistiming of their articulatory gestures. This mistiming increases the amount of time between the offset of the initial consonant and the onset of the second consonant, resulting in a (possibly voiceless) vowel-like transition in between them. This observation, combined with Fleischhacker’s claim (2001, 2005) that vowel insertion into SC clusters is generally more perceptually disruptive than into other cluster types, suggests that the perceptual consequences of mistiming an SC cluster are greater than those of mistiming an OR cluster.

The articulatory differences between SC and OR clusters follow from this hypothesis: SC clusters are articulated more precisely because the perceptual consequences of mistiming are greater. This idea can be clarified by thinking of it from the perspective of “good variance” vs. “bad variance,” a dichotomy proposed in the motor control literature (see, e.g., Latash, 2012). The production of any task-oriented movement, speech included, is subject to variability in its execution. Some of this variability is “bad” because it interferes with the goals of the task (e.g., I articulate a word in a way that differs from my intended perceptual target), while some of it is “good” because it does not (e.g., I may articulate a word in different ways, but all variants meet the perceptual target). Researchers have found that skilled performers exhibit high degrees of good variability and low degrees of bad variability; for an example from speech, see Kang et al., (2019). The maximization of good variability, which is irrelevant to task outcomes, imparts flexibility and allows the same movement goals to be achieved under different conditions; the minimization of bad variability ensures that the task goals are consistently achieved.

Skilled production of an SC onset requires minimization of variability in the relative timing of the two component segments because excrescent vowels arising from mistiming are particularly salient. That is, for an SC onset, variability in relative timing is (mostly) bad variability. OR onsets, on the other hand, can tolerate more slop: The production of an excrescent vowel is less likely (relative to an SC onset) to be perceptually disruptive. In this sense, at least some of the variability in the relative timing of OR onset can be seen as good variability, in that it allows flexibility in articulation while still achieving perceptual goals. The slower acquisition of SC onsets could then be a consequence of their more demanding timing requirements. Although we do not provide direct evidence for this connection in the current paper, we believe it is a useful perspective to explore to provide a more holistic account of SC vs. OR onsets. This account is also broadly consistent with the idea that ST onsets (and perhaps other SC onsets to varying extents) constitute single, complex segments (e.g., Broselow, 1992; Goad, 2012), in that they exhibit a higher degree of articulatory coupling between their component segments.

The connection between the Syllable Contact account of epenthesis asymmetries and the other properties of SC clusters is less clear. Because the driving force is the avoidance of sonority rises across syllables, the composition of an onset is unimportant except for the sonority values of its component segments. Under such an account, it is difficult to see how the articulatory and acquisitional differences between SC clusters and other clusters can be explained as anything more than a coincidence.

5.2 Prospects for scalar analyses of sonority

One of the major reasons that the Syllable Contact account fails to capture the epenthesis patterns found in this paper is that it bins together onsets that have the same sonority profile but different epenthesis patterns (e.g., /sl/ vs. /fl/). This is a consistent problem for analyses that treat sonority as a scalar value because onsets that share sonority profiles are often alike in some ways and different in others. For example, the SSP, described in Section 2 above, predicts that ST onsets should be marked because of their falling sonority profile. Although other onsets with a falling profile, such as /ft/, are indeed uncommon, ST onsets are not. Other definitions of sonority, such as the NAP model (Albert & Nicenboim, 2022), attempt to circumvent this issue by modifying the definition of sonority profiles to assign ST onsets similar sonority profiles to other unmarked onsets. Although binning the sonority profiles of ST onsets together with certain OR onsets solves the markedness problem, it also means that we can no longer use differences in sonority profile to account for the distinct behavior of ST onsets: If we assign /st/ the same sonority profile as /bɹ/ (which NAP does), we can no longer use their sonority profiles to distinguish their behavior in other respects, such as acquisition trajectories or epenthesis patterns. It seems unlikely that we will converge upon a single scalar definition of sonority/sonority profiles that is sufficient to capture the variety of ways in which onsets clusters are similar or different.

Although analyses that use scalar definitions of sonority and sonority profiles have provided much insight into the behavior of complex onsets, as well as many other domains, they struggle with providing a consistent and holistic account of the rich variety of phenomena that are related to onset type. We expect that additional progress in this area will come from adopting a more nuanced view of sonority and its phonological reflexes that is grounded in perception and articulation.

5.3 Future research

In this paper, we showed that the perceptual analysis of epenthesis asymmetry outperforms a sonority-based analysis. However, it is generally not clear whether Fleischhacker’s perceptual analysis really reflects language-general perceptual constraints or something that is specific to English and/or Farsi. A more robust series of experimental studies would be useful to confirm that her perceptual hierarchy is truly language-general.

In addition, the presence or absence of an epenthetic vowel is a coarse measurement of a speaker’s skill in producing different onset types. Simply producing the onset without epenthesis does not necessarily mean that the onset is produced in a native-like fashion. We will get greater insight into the acquisition trajectory of complex onsets by investigating acoustic or articulatory data to get finer-grained measurements of timing and investigate how these change with language ability.

Lastly, it is unclear whether the patterns found in this paper also apply to languages that use medial epenthesis more broadly within the class of SC onsets. Farsi is a language that treats almost all SC onsets differently from OR onsets. As described earlier, however, this pattern is relatively rare cross-linguistically. It is more common for only ST onsets to be repaired with pre-epenthesis. In the current paper we do not differentiate between onsets within the class of SC clusters, but find that, on average, SC clusters are more difficult to acquire than OR onsets. This raises the question of whether all SC onsets are equally difficult to acquire, and whether the phonological repair of these onsets in a language (pre-epenthesis vs. medial epenthesis) tracks with their acquisition difficulty. The epenthesis rates across individual onsets shown in Figure 5 in Section 3 suggest some within-class differences, where SC onsets with greater sonority rises are repaired less frequently than those with smaller rises. This is consistent with some past work on L2 learning (see Carlisle, 2001). We leave these as exciting questions for future research.