1.1. Closure voicing and [voice] in stops

Closure voicing in stops is relatively ‘unnatural’ (e.g., Ohala, 1983). In order to maintain vocal fold vibration, sufficient transglottal pressure drop is required. As air continually flows from the lungs, supraglottal air pressure will quickly rise if both the oral and nasal cavities are sealed off. This means that it is impossible to maintain closure voicing for a long duration of time. Ohala and Riordan (1979) claim that sufficient transglottal pressure drop can be maintained only for roughly 5–10 ms if the size of the supraglottal cavity remains constant. The size generally does not remain constant, though, as the vocal tract automatically enlarges due primarily to compliance of the soft tissue making up the inner walls of the cavity. This should allow for approximately 60–70 ms of closure voicing for a male speaker (ibid., Westbury, 1983), varying depending on e.g., the point of occlusion. Voicing is maintained longest for a fronted occlusion (e.g., bilabial) due to the large cavity between glottis and point of occlusion, which yields a slower build-up of air pressure and crucially yields a larger total area of soft, expandable cavity walls. Keating (1984a) shows that bilabial stops naturally retain voicing for roughly 30% longer than velar stops. When some languages show yet longer closure voicing, it is due to an active process of vocal tract enlargement during the occlusion, such as jaw lowering or velum raising.

Westbury and Keating (1986) investigate the issue of articulatory naturalness in detail, using a model of breath-stream control with the vocal folds appropriately adducted and tensed for voicing. They show that syllable-initially, closure voicing is articulatorily unnatural, since subglottal and supraglottal air pressure will rise roughly synchronously unless the vocal folds are initially fully abducted to allow for a build-up of subglottal air pressure. Closure voicing is also unnatural syllable-finally due to an inspiratory force that gradually but quickly counteracts the initially high subglottal pressure from the preceding vowel. However, it is natural for a significant portion—usually most—of intervocalic stop closures to be voiced due to the high initial subglottal pressure following the preceding vowel.

Articulatory naturalness does not always translate directly into attested typological patterns. On the one hand, in accordance with articulatory naturalness, there is a strong implicational hierarchy regarding voiced stops in phonological inventories: In almost all cases, languages with voiced stops also have voiceless stops (e.g., Ohala, 1983; Maddieson, 1984). Furthermore, final obstruent devoicing is a very common typological pattern, partially because syllable-final segments tend to be lengthened, resulting in longer stretches of voicelessness in coda stops, and as such a lesser chance of closure voicing being interpreted as an important phonological cue (e.g., Blevins, 2004, p. 103ff.). On the other hand, in spite of their unnatural status, syllable-initial voiced stops are actually quite common. Furthermore, voicing is most articulatory natural in medial position, but languages with no laryngeal distinction in stops generally have voiceless stops in all positions (Keating et al., 1983). This illustrates an important point: There is more to phonetic and phonological patterning than ease of articulation.

Below, we will characterize three general approaches to the representation of laryngeal contrasts in the phonological literature, and the predictions they make with regards to intervocalic stop voicing. There is a huge literature on the topic, so some approaches will necessarily be missed, while others may be grouped together even if they differ in some respect. We will refer to these approaches as ‘concrete [voice]’ approaches, ‘abstract [voice]’ approaches, and gesture-based approaches.

The phonological feature [voice] has been conceptualized in different ways. It sometimes refers quite narrowly to the presence of voicing during closure, which is what we refer to as concrete [voice]. This is how [voice] is conceptualized in the laryngeal feature geometry of Lombardi (1995) and the ‘laryngeal realism’ approach of Iverson and Salmons (e.g., 1995). These are approaches that assume a direct relationship between different physical laryngeal constellations and phonological laryngeal features. Such approaches usually assume that languages with aspiration contrasts employ an active feature [spread glottis] to distinguish between laryngeal stop series. It is common to assume that sonorant sounds are unmarked for [voice], since vocal fold vibration is the natural state of affairs in these sounds (Lombardi, 1995). This creates a problem in determining the phonological origin of intervocalic closure voicing; surrounding vowels are unmarked for [voice], so it cannot spread from those. One possible solution to this is Rice and Avery’s (1989) proposal of a non-laryngeal [spontaneous voice] feature node, which can spread from sonorants to obstruents. Another solution is to simply relegate intervocalic voicing to phonetic implementation, placing it outside the purview of phonology. This would predict that intervocalic stops that are unmarked for laryngeal features always follow the phonetically natural pattern.

Jessen and Ringen (2002) and Beckman, Jessen, and Ringen (2013) argue that the intervocalic behavior of stops is relevant for determining whether [voice] or [spread glottis] are active in a language. Beckman et al. show that Russian /b d ɡ/ are voiced throughout their closure intervocalically with very few exceptions, while German /b d ɡ/ are variably voiced intervocalically (roughly 60% of tokens are voiced throughout). They take the consistent voicing in Russian as evidence for an active [voice] feature, and the variable voicing in German as evidence for a gradient phonetic process of passive voicing. Following Chomsky and Halle (1968), they assume that at some level in the phonological derivation, segments are assigned numerically-valued features; the degree of intervocalic voicing in a [spread glottis] language will depend on the values assigned to [spread glottis] at this later stage.¹ It should be noted that the findings of Beckman et al. can only be taken as evidence for underlying features if one assumes a transparent relationship between phonology and phonetics; see e.g. Keating (1984b) for a general critique of this stance.

In abstract [voice] approaches, the feature needs not directly refer to closure voicing. Chomsky and Halle (1968) and Keating (1984b) both assume that [voice] can refer to either stops with closure voicing or stops where voicing begins approximately at the time of release, depending on which contrast the language in question employs. Kingston and Diehl (1994) similarly assume a feature [voice] that does not always entail closure voicing. This argument partially relies on the finding that [voice]-induced F₀-perturbations behave similarly, regardless of how the feature is phonetically implemented. In their account, the feature [voice] lowers F₀ on the following vowel.² Kingston and Diehl recognize that there is a discrepancy between initial and intervocalic position when it comes to naturalness of closure voicing; an ‘automatic phonetics’ will output initial stops with no closure voicing and intervocalic stops with closure voicing, while a ‘controlled phonetics’ is necessary to divert from that pattern.

If we expect a direct relationship between phonetics and phonology, then there should be a correspondence between phonologically and phonetically unmarked material. Given the aerodynamic account of stop voicing given above, this means that a phonologically unmarked stop should be voiceless initially and voiced intervocalically. It also means that phonetic reduction will be positionally defined: Devoicing of [voice] stops is a lenition phenomenon syllable-initially, whereas voicing of stops without [voice] is a lenition phenomenon intervocalically.³ This is difficult to account for in a feature-based framework but seems to hold up for intervocalic position, where voicing of stops without underlying [voice] is crosslinguistically common (Kaplan, 2010). In an optimality-theoretic analysis of this problem, Smith (2008) proposes constraints militating against voiced obstruents in onset position and voiceless obstruents in intervocalic position, which compete with faithfulness constraints (see also Hayes, 1999).⁴

Gesture-based approaches of phonological representation can straightforwardly account for these positional markedness relations. One such approach is Articulatory Phonology (Browman & Goldstein, 1986, 1992). In Articulatory Phonology, articulatory gestures are taken as the primary units of phonological representation rather than segments or features. A consequence of this is that the duration and magnitude of glottal gestures can be represented separately from other gestures that make up traditional segments. The unmarked state of the glottis is adducted and tensed, which will not cause voicing initially but will result in voicing intervocalically, as per the discussion above.

These are a few predictions about the patterning of intervocalic stop voicing based on different conceptualizations of laryngeal representation: In concrete [voice] approaches, closure voicing is a necessary and sufficient criterion for [voice] and a different feature like [spread glottis] is needed to represent aspiration. From a concrete [voice] perspective, we would predict essentially categorical intervocalic voicing of all stops in ‘true voice’ languages, since [voice] ensures voicing in one category, and there are no available phonological mechanisms to counteract voicing in the other (unmarked) category. We would predict varying degrees of intervocalic voicing of unmarked stops in ‘aspiration’ languages, and very little voicing in [spread glottis] stops (following Beckman et al., 2013). In abstract [voice] approaches, where [voice] can have different phonetic interpretations, it is less straightforward to predict intervocalic behavior, but following Kingston and Diehl (1994), a ‘controlled phonetics’ is necessary to divert from the natural pattern of intervocalic voicing. A gesture-based approach such as Articulatory Phonology also predicts the natural pattern of intervocalic stop voicing if no underlying glottal gestures are present; however, Articulatory Phonology allows a great deal of flexibility in how glottal gestures are represented, making it a very powerful representational framework. Below, we will discuss the literature on voicing and laryngeal representation in Danish stops, and how this relates to these predictions.

1.2. Danish stops

Standard Danish has six phonemic stops, /b d ɡ p t k/. A common analysis of Danish holds that there are strong and weak syllabic positions: Strong position refers to onsets before full vowels, while weak position refers to codas and onsets before neutral vowels (e.g., Jakobson, Fant, & Halle, 1951).⁵ This determines the positional allophone of many consonants, including the stops: /b d ɡ/ are voiceless unaspirated in strong position and manifest as approximants or zero in weak position. /p t k/ are voiceless aspirated in strong position and voiceless unaspirated in weak position. This analysis goes back to e.g., Uldall (1936) and Jakobson et al. (1951) and is more fully fleshed out by e.g., Rischel (1970) and Basbøll (2005). A detailed account of the proposal is beyond the scope of this paper, but we argue elsewhere that it is outdated in some regards (Horslund, Jørgensen, & Puggaard, 2021; Horslund, Puggaard-Rode, & Jørgensen, 2022). As such, in strong position, the laryngeal contrast is based on aspiration, whereas in weak position, only /p t k/ are actually realized as stops. When we refer to /b d ɡ/ and /p t k/ in the following, we do not refer to this rather abstract analysis, but rather to something closer to the surface contrast: /b d ɡ/ refer to stops that would be unaspirated in distinct speech, and /p t k/ refer to stops that would be aspirated in distinct speech. We will refer to the two series as laryngeal categories.

Similar to some traditions of English transcription, /b d ɡ/ are in narrow transcription usually given as [b̥ d̥ ɡ̊], indicating that they are voiceless but phonetically lenis. /p t k/ are usually transcribed phonetically as [pʰ tˢ kʰ], with the superscript s indicating salient affrication of /t/. In neat transcription, they are sometimes transcribed as [b̥ʰ d̥ˢ ɡ̊ʰ] (Grønnum, 1998), indicating that although aspirated, both sets are equally phonetically lenis. The terms fortis–lenis do not have clearly defined phonetic correlates, so this deserves further unpacking.

The terms fortis and lenis are used in quite distinct ways in the phonetic and phonological literature. One use is as an essentially arbitrary label for stop contrasts in languages where the said contrast does not depend on voicing. Fortis–lenis has often been used in this sense when discussing Germanic languages, where the historic voiced-voiceless distinction has a diverse set of phonetic reflexes in the modern languages (Kohler, 1984; Henton, Ladefoged, & Maddieson, 1992). Another use is as a phonetically substantial phonological feature referring to force of articulation. This in turn may correlate with pulmonic force, muscular tenseness of the articulators, closure duration, or indeed closure voicing (Jaeger, 1983, and references therein). Either use of the terminology is usually too imprecise for a phonetic or phonological description of a group of sounds. Fischer-Jørgensen (1972) suggests that Danish /b d ɡ/ are in fact fortis and /p t k/ lenis, since the closure duration is longest for /b d ɡ/ and results from electromyographic investigations show higher organic pressure for /b/ than /p/ (Fischer-Jørgensen & Hirose, 1974).

Regarding the [b̥]-style notation of lenis voiceless stops, this is only briefly mentioned in the Handbook of the International Phonetic Association (International Phonetic Association, 1999, p. 24): “The voiceless diacritic can … be used to show that a symbol that usually represents a voiced sound in a particular language on some occasions represents a voiceless sound.” This certainly does not apply to Danish, where stops from both laryngeal series are voiceless (nor is it clear that it applies to English stops, for that matter). The IPA has no way of indicating a fortis–lenis distinction, so it is surprising that indicating lenis should take precedence over transparent representation of voicing in the transcription of /b d ɡ/ for Grønnum and Basbøll, especially considering their claim that Danish stops do not actually show a fortis–lenis contrast.

Overall, little has been written about closure voicing in Danish stops, and to our knowledge, no quantitative studies have been made of the topic. In essence, what we know from the existing literature is that all stops show some degree of voicing during the first portion of the closure when they occur between other voiced sounds (Fischer-Jørgensen, 1954), and that intervocalic word-medial stops are continuously voiced categorically or near-categorically (Abrahams, 1949; Fischer-Jørgensen, 1954, 1979, 1980; Spore, 1965; Keating et al., 1983; but see also Jessen, 2001, and Beckman et al., 2013, who assume that Danish stops are categorically voiceless). It is generally assumed that /b d ɡ/ were voiced in previous stages of the language, and according to Brink and Lund (2018), this was lost sometime before 1700.

Articulatory studies of carefully read speech have shown that intervocalically before stressed syllables, both /b/ and /p/ are accompanied by a glottal opening gesture during the closure (Frøkjær-Jensen et al., 1971; Hutters, 1985), although the opening gesture varies significantly in magnitude and timing. Similar studies of English found no such gesture during /b/ (Sawashima, 1970; Hirose & Gay, 1972); in Icelandic, which has a contrast between unaspirated and pre-aspirated stops intervocalically, both series of stops have a significant glottal opening gesture (Pétursson, 1976). Frøkjær-Jensen et al. (1971) hypothesized that the gesture in Danish /b/ is an artifact of the articulatory transition from vowel to consonant, while in /p/ it is “effectuated by neural commands” (ibid: 134). However, electromyographic studies by Fischer-Jørgensen and Hirose (1974) and Hutters (1985) show that the posterior crico-arytenoid muscles are active in achieving the glottal opening during /b/.⁶ Hutters (1985) proposes that the intervocalic glottal opening gesture is a measure taken to reinforce voicelessness in /b/, although she leaves the question relatively open; more recently, Möbius (2004) has shown that a glottal spreading gesture maintains voicelessness in German intervocalic stops, and Pape and Jesus (2014) have shown the same for European Portuguese and Italian.

From a phonological perspective, Iverson and Salmons (1995) and Basbøll (2005) assume that [spread glottis] is the laryngeal feature that distinguishes between the two sets of stops, and that [voice] plays no role in distinguishing between Danish stops. [spread glottis] is taken to be an active feature, which causes devoicing of following sonorants. This process has usually been taken for granted, but a recent paper by Juul, Pharao, and Thøgersen (2019) shows that devoicing of sonorants following aspirated stops is much less categorical in Danish than usually assumed.

Kingston and Diehl (1994) assume that [voice] (in the abstract sense discussed in Section 1.1 above) distinguishes between the two sets. The account then holds that [+voice] is only implemented as actual voicing in Danish when voicing is phonetically natural (i.e., intervocalically). A key motivation for this representation is that F₀ is lowered by [+voice] stops. This is not exactly straightforward in Danish; Fischer-Jørgensen (1968) finds no evidence for this, while Jeel (1975) and Petersen (1983) both do. However, while Petersen does find that the different stop series trigger different F₀-perturbations, he crucially finds that both series trigger high initial F₀ in following vowels relative to nasals. As Goldstein and Browman (1986) point out, this is consistent with an account where F₀-perturbations follow directly from glottal aperture, something that Kingston and Diehl (1994) explicitly reject. Nevertheless, Kingston and Diehl’s dichotomy between automatic and controlled phonetics (see Section 1.1) can potentially account for both the presence and absence of closure voicing in stops in Danish.

As mentioned in Section 1 above, a number of facts about Danish stops make it difficult to predict the relative likelihood of intervocalic voicing. First of all, most of the relevant literature seems to assume that intervocalic voicing is categorical or near-categorical. Some say that muscular tension is overall low in Danish stops, increasing the chances of voicing; but all Danish stops are also characterized by a glottal opening gesture, decreasing the chances of voicing. Closure duration is shorter and muscular tension weaker in the production of /p t k/ relative to /b d ɡ/, but /p t k/ also have a glottal opening gesture of greater magnitude.

The results may allow us to compare some of the predictions from different approaches to phonological laryngeal specification. If [spread glottis] is indeed the only active laryngeal feature, we would predict at most variable voicing in /b d ɡ/, and little voicing in /p t k/ (following Beckman et al., 2013). If the laryngeal contrast is maintained with phonologized glottal gestures (as in Articulatory Phonology), we would assume that the two series have underlying glottal opening gestures of different magnitudes, both of which are expected to counteract voicing. This gestural account predicts that lenition leads to a reduction in the magnitude of these gestures, potentially causing voicing in either laryngeal series, but more readily in /b d ɡ/. Neither of the two featural accounts (i.e., the abstract and concrete [voice] approaches) make any clear predictions about lenition and voicing.

2.1. Potential predictors

The detailed annotations of the DanPASS corpus (see Section 3.1) allowed us to test how a large number of mostly categorical predictors may affect closure voicing. These predictors relate to segmental, prosodic, morphosyntactic, and other factors, which are discussed in the following subsections. Variables are capitalized when they are first mentioned.

4.1. Categorical predictors

Table 3 and Figure 5 show the proportions of voiced tokens for each level of each of our categorical variables. The majority of categorical variables show at least some degree of correlation with closure voicing in the direction we predicted in Table 1 above.

Figure 5

Stacked bar plots showing the proportions of tokens with and without continuous voicing for each level of each categorical variable. (Morphological boundary levels = internal, inflectional, derivational, compound, word).

4.2. Continuous predictors

Having discussed all categorical predictors, we now turn to the continuous ones. Figure 6 visualizes the proportion of stops with and without continuous voicing with density plots.

Figure 6

Density plots showing the tokens with and without continuous voicing relative to continuous variables on a log-scale.

It is clearly (and logically) the case that there are most tokens of the most Frequent words in both the voiced and voiceless group. It is also clearly the case that the words with very high frequency show a higher proportion of voiced tokens, and similarly that the words with medium frequency, particularly between 50–500, show a higher proportion of voiceless tokens.

As predicted, Speech Rate clearly correlates with voicing, such that voiceless tokens are more common during slow speech, and voiced tokens are more common during quick speech (recall that speech rate is coded as the duration of the syllables flanking the stop, so a low value equals high speech rate). In both lexical frequency and speech rate, the distribution of fully voiced tokens is visibly more peaked than tokens which are not fully voiced.

We also see a correlation in the expected direction between Age and voicing. Most speakers in the corpus are younger than 25 years old, so it follows naturally that most tokens, both voiced and voiceless, are also produced by this age group. It is, however, also the case that speakers in their thirties and forties produce a relatively higher proportion of voiceless stops.¹⁴

Having examined the correlations that are found in the empirical data, we will now move on to analyzing the data with mixed-effects regression modeling.

5.1. Model selection

Our data comes from a corpus that was not collected for our purposes, and we are interested in quite many independent variables. Given the lack of experimental control and the partly exploratory nature of the study, our data is presumably not structured in a way that allows us to retain a maximal random effects structure; this is a common problem with mixed-effects models in linguistics (Meteyard & Davis, 2019). This loss in optimal data structure is also a corresponding gain in ecological validity, which is highly necessary when discussing potential lenition phenomena. There has been a lot of discussion of how to handle this issue in linguistics, with opinions ranging from maximizing random effects (Barr, Levy, Scheepers, & Tily, 2013) to balancing statistical power and Type I errors by including only random effects that contribute sufficiently to the model’s predictive power (Bates, Kliegl, Vasishth, & Baayen, 2015; Matuschek, Kliegl, Vasishth, Baayen, & Bates, 2017). These papers generally assume 1) experimental data, and 2) a continuous dependent variable (i.e., linear mixed-effects models). This is important because experimental data is ideally more balanced than ours, and linear models are overall more likely to converge than logistic models with binary dependent variables (Seedorff, Oleson, & McMurray, 2019). We opt for a data-driven model selection procedure, largely inspired by the heuristics proposed by Sonderegger (2022).

The raw values of all our continuous variables are positively skewed, so they were log-transformed in order to reach a normal-distribution, and standardized to aid interpretation of the model.¹⁵ The categorical variables are contrast coded (see Schad, Vasishth, Hohenstein, & Kliegl, 2020 for an introduction to this). We coded sum contrasts for the binary variables. Variables corresponding to articulatory features are all coded as +½ (‘present’) and –½ (‘absent’). Laryngeal Category is coded as –½ unaspirated, +½ aspirated; Sex is coded as –½ female, +½ male; Word Class Type is coded as –½ open, +½ closed. For the three-level variable Place of Articulation, we coded two theoretically-guided Helmert contrasts: One to test the distinction between velars and non-velars, and one to test the distinction between alveolars and labials:

The five-level Morphological Boundary variable is rather complicated. Here we coded four theoretically-guided Helmert contrasts: 1) Internal Contrast, testing the distinction between morpheme-internal and non-morpheme-internal; 2) Affix Contrast, testing the distinction between affix-boundaries and non-affix-boundaries; 3) Affix Type Contrast, testing the distinction between derivational affix-boundaries and inflectional affix-boundaries; and 4) Compound Contrast, testing the distinction between word-boundaries and compound boundaries.

The data is modeled using logistic mixed-effects regression.¹⁶ The model selection procedure followed two main steps: 1) Fixed effects selection with minimal random effects, and 2) pruning of the maximal random effects structure to achieve convergence with (almost) non-singular fit.

Fixed effects selection: All independent variables were theoretically motivated in Section 2 above, and are all included in the model. We have no theoretical motivation for including interactions. However, we saw in Section 4 that voicing in /p t k/ is near-floor, and this could be masking true effects in the data. For this reason, we tested all possible interactions with Laryngeal Category in a random intercepts-only model, in case some effects could be found only in /b d ɡ/. Only significant interactions were kept.

Random effects selection: All meaningful by-speaker and by-item random slopes were then added to the model; Sex and Age can of course not vary by-speaker, and all by-item slopes for phonological or morphosyntactic variables are at least potentially problematic. We used strictly uncorrelated random effects; this leads to much higher convergence rates in logistic models, and Seedorff et al. (2019) show in simulations that this does not inflate Type I error rates even if the random effects are correlated in the underlying data (although it has a slight adverse effect on statistical power). This model converges with a singular fit, which in our case means that the model estimates zero-variances within some random slopes. In other words, the variance explained by these random slopes is not found to be different from that explained by random noise in the data. This is a symptom that the model is overparametrized, but should have no influence on the interpretation of the corresponding fixed effects (Brauer & Curtin, 2018). Accordingly, we removed all random slopes with estimated zero variances except Laryngeal Category, since this is a variable of key interest in our study. This means that the resulting model is probably slightly overparametrized, since it is highly unlikely that there is actually no by-speaker variance for laryngeal category, but a reasonable interpretation is that the by-speaker variance for laryngeal category is very close to the random variation for laryngeal category in the data. The entire model selection process is documented in Puggaard-Rode, Horslund, Jørgensen, and Vet (2022), and the final model is summarized in Table 4.

None of the included independent variables shows problematic collinearity; the variance inflation factor (VIF) is below 1.5 for all variables except those appearing in interaction effects.

The coefficients of a generalized linear model correspond to log-odds. These are suitable for regression modeling, as they are unbounded and normally distributed. Odds and odds ratio (OR), on the other hand, are easier to interpret. In order to aid interpretability, we report both the model coefficients and standard error in the log-odds scale, and odds (ratio), which corresponds to exponentiated coefficients. The odds for the intercept can straightforwardly be interpreted as the odds of closure voicing with all other variables kept at zero. Since all variables are either contrast-coded or standardized, the ORs can be interpreted straightforwardly as the change in probability associated with that variable (see Sonderegger, in press, chapter 6). Odds and ORs are given as fractions – if OR>1, the odds of voicing are higher in the variable level corresponding to + in the contrast coding; if OR<1, the odds of voicing are higher in the variable level corresponding to –. For the standardized continuous variables, OR refers to the change in predicted likelihood of voicing associated with an increase of 1 standard deviation.

5.2. Results

The results of the logistic mixed-effects regression model described above is summarized in Table 5; we do not include a random effects table here, but it can be found in Puggaard-Rode et al. (2022). The model has a reasonably high marginal effect size of (delta) R² = 0.5 and conditional effect size of (delta) R² = 0.63; this is the variance explained by the fixed effects alone and the fixed and random effects combined, respectively (see Nakagawa, Johnson, & Schielzeth, 2017 for details of how this is calculated for generalized linear mixed-effects models).

In some cases, the results of the mixed effects model tell quite a different story than the exploratory analysis presented in Section 4. In these cases, the results of the mixed effects model should be taken as the best possible description of the data. The odds for the intercept means that the relative likelihood of a stop being fully voiced is predicted as 11.34 times lower than not being fully voiced if all other variables are controlled for (i.e., kept at their average).

The significant variables overwhelmingly pattern as predicted. For the following categorical variables, this means that they are significant in the same (expected) direction as we saw in the exploratory analysis: Laryngeal Category, Neutral Vowel, Stress, and Preceding Stød. The effect of laryngeal category is very strong, with the unaspirated set being more than 20 times more likely to be voiced intervocalically. The probability of voicing is approximately doubled in syllables with neutral vowels as well as in unstressed syllables, and the probability is around 10 times lower immediately following syllables with stød.

The Place of Articulation variable patterns differently from what we saw in the exploratory analysis. The model finds that voicing in stops with a fronted occlusion, i.e., in bilabials and alveolars, is around four times more likely than in velar stops, but there is no significant difference between bilabials and alveolars. This is in line with our aerodynamically motivated predictions. Recall that alveolars were overall voiced at a much higher rate than other places of articulation; this effect disappears in a model that also takes e.g., stress and lexical item into account.

We actually see a fairly strong effect of Preceding Stress in the expected direction; voicing is around four times more likely following stressed syllables. This is interesting, because in the exploratory analysis there was essentially no correlation between preceding stress and voicing.

Unexpectedly, the Stød variable patterns in the opposite direction of our predictions and what we saw in the exploratory analysis. Closure voicing is found to be around twice as likely in syllables with stød. We return to this in the discussion in Section 6.3 below.

Only one of the contrasts for Morphological Boundary Type is found to have a significant effect on closure voicing: Affix-initial stops are voiced at a much higher rate (around four times) than stops at other morphological boundaries. There are good reasons to expect this at face value: /p t k/ are rarely found in affixes and never in inflectional affixes, affixes are almost never stressed, and affixes often have neutral vowels. However, these are all variables that we control for independently in the model, and because of this, we predicted that word-internal stops would be voiced at a higher rate than affixes. We return to this in the discussion.

Other categorical variables—Preceding Approximant, Preceding High Vowel, High Vowel, Preceding Central Vowel, Word Class Type, and Sex—have no significant influence on voicing in the model, although in some cases, there seemed to be clear correlations in the exploratory analysis. In all cases, we must assume that the correlation we saw at face value can be better explained by other (potentially random) variables in the data.

The influence of continuous predictors is visualized in Figure 7. There is a clear increase in the predicted likelihood of voicing as Lexical Frequency increases, and a clear decrease in the predicted likelihood of voicing as Age increases. The Local Speech Rate variable in particular has an extremely strong influence on voicing, such that quicker speech leads to more intervocalic voicing. In fact, the predicted likelihood of voicing is near ceiling for the quickest tokens, and near floor for a large portion of the slower tokens.

Figure 7

Plots showing the likelihood of fully voiced stops of continuous variables as predicted from the mixed-effects model. The x-axes are standardized units. Note that y-axes differ due to the very high likelihood of voicing in very quick speech, so keeping y-axes identical would blur the effect in other variables.

Figure 8 shows the predicted significant interaction effects. The interaction effect between Laryngeal Category and Preceding Stress is as predicted: There is a fairly marginal difference in predicted voicing after stressed syllables in /p t k/, whereas the effect is much more pronounced in /b d ɡ/. The predicted interaction effect between Laryngeal Category and Local Speech Rate is similar: Both laryngeal categories show near-ceiling voicing in the fastest tokens and near-floor voicing in the slowest tokens, but near-floor voicing is predicted in much faster speech for /p t k/ than /b d ɡ/.

Figure 8

Plots showing the likelihood of fully voiced stops of interaction effects as predicted from the mixed-effects model. The x-axes are standardized units. Note that y-axes differ due to the very high likelihood of voicing in very quick speech, so keeping y-axes identical would blur the effect in other variables.

6.1. RQ1: Closure voicing and laryngeal category

The strongest predictor of closure voicing is laryngeal category. There are two main findings here: 1) /p t k/ are voiced only very rarely, and much more rarely than /b d ɡ/, and 2) /b d ɡ/ are voiced commonly, albeit still at lower than chance rate. The three major accounts of laryngeal representation in (Danish) stops that we presented in the introduction all have mechanisms that can account for the second finding.

Abstract [voice] approaches straightforwardly predict the first finding; [–voice] stops are naturally voiced less frequently than [+voice] stops. With regards to the second finding, in Kingston and Diehl’s (1994) abstract account of [voice], we could postulate a controlled phonetic mechanism that actively counteracts voicing in [+voice] stops in order to account for the data. Such a mechanism seems intuitively strange but is already independently needed for Icelandic, in which intervocalic voicing of unaspirated stops is seemingly even rarer than in Danish (Pétursson, 1976).

Concrete [voice] approaches also straightforwardly account for the first finding, but not necessarily the second finding. [spread glottis] should block voicing, while unmarked stops are expected to be voiced whenever natural (i.e., intervocalically). In Beckman et al.’s (2013) account of [spread glottis], they assume that there is a point in the phonological derivation where active privative features are reinterpreted as numerically valued features. Since [spread glottis] is the active laryngeal feature in e.g., German, Danish, and Icelandic, /p t k/ are assigned a high numeric value for [spread glottis], while /b d ɡ/ are assigned lower values. They go on to suggest that German /b d ɡ/ are assigned [1sg], allowing for passive intervocalic voicing, and that Danish /b d ɡ/ are assigned [5sg], blocking passive voicing. This predicts our results quite well. Note, however, that other proponents of [spread glottis] in Danish (like Iverson & Salmons, 1995, and Basbøll, 2005) do not necessarily assume this mechanism; without such a mechanism, we would simply expect the unmarked /b d ɡ/ to be near-categorically voiced, since this is the unmarked realization of stops in this position (see Section 1.1).

In the end, we believe the best explanation of our acoustic results is one that relies on our existing knowledge of glottal activity in Danish stops from research by Frøkjær-Jensen et al. (1971), Fischer-Jørgensen and Hirose (1974), and Hutters (1985). Recall from Section 1.2 that /p t k/ have shorter closure duration and are produced with less muscular tension than /b d ɡ/. Either both sets are phonetically lenis, or /b d ɡ/ are in fact the fortis set. The shorter closure duration and lower muscular tension of /p t k/ would predict more closure voicing in this set if the vocal folds were properly adduced and tensed for voicing. In careful speech, however, all Danish stops are usually accompanied by a glottal opening gesture, the purpose of which is presumably to enforce voicelessness. The glottal gestures are different in magnitude across the laryngeal series. /p t k/ have a glottal opening gesture of great magnitude that lasts throughout the closure and into the release, whereas /b d ɡ/ have a smaller glottal opening gesture that peaks during the closure. Maintaining glottal spreading in /p t k/ is prioritized, because it is required for aspirated release, which is the primary cue to the contrast between the two sets. /b d ɡ/ also actively block voicing through glottal spreading, but for these phones it serves little to no role during the release, and it is not crucial to maintaining the contrast. The differences in magnitude of the glottal gesture can explain both findings: the probabilistic differences between the two series, and the fact that the majority of stops in spontaneous speech are not voiced throughout. Such fine-grained differences in duration and magnitude of gestures can be straightforwardly encoded in the gestural scores of Articulatory Phonology.

The results relating to laryngeal category can be accounted for by all three major accounts of laryngeal representation, but not all theories predicted the results equally well. Recall from Section 1.1 that an abstract [voice] account did not allow us to make any specific predictions. A concrete [voice] account only predicts the results with the added machinery of gradient phonetic interpretation of feature values. A gesture-based account predicts the results well with no additional machinery: The necessary ‘ingredients,’ so to speak, are already built into the representational grammar.¹⁷

On a final note, Schachtenhaufen (2019) recently suggested abandoning the transcription standard using [b̥ d̥ ɡ̊ b̥ʰ d̥ˢ ɡ̊ʰ] for [p t k pʰ ts kʰ], since fortis/lenis is not traditionally indicated in IPA, and IPA guidelines suggest using [b̥]-style transcription to indicate devoicing of sounds that are usually voiced. This study further cements that Danish /b d ɡ/ are clearly not usually voiced: Not only are /b d ɡ/ categorically voiceless in most positions, voicing is also regularly blocked in the one syllabic position where it would actually be phonetically natural. We are therefore strongly in favor of Schachtenhaufen’s proposal.

6.2. RQ2: Closure voicing as phonetic and phonological lenition

Closure voicing is to a large extent found in environments where we expect to find phonetic lenition: Its occurrence increases with speech rate; it is found more frequently in unstressed syllables, in syllables with schwa, and in affixes. On the basis of our results, it seems sensible to consider intervocalic closure voicing a lenition phenomenon in itself.

This has some interesting phonological consequences. As discussed in Section 1.1, it is often difficult to account for phonetic voicing processes with reference to spreading of a [voice] feature. In phonological representational frameworks relying on privative features, the voiceless unaspirated stop is generally considered the unmarked one, i.e., it carries no laryngeal features. Similarly, voicing is generally not considered phonologically marked for sonorant sounds (e.g., Lombardi, 1995). As such, [voice] is not specified for sonorant sounds and cannot spread from them, and the addition of a [voice] feature to a stop appears to be phonological fortition rather than lenition, since material is added, making for a more complex underlying structure. Spreading of Rice and Avery’s (1989) non-laryngeal [spontaneous voice] feature node may be able to represent the process, but it does not capture the lenition aspect, as it still entails the addition of phonological material. It also does not capture the probabilistic nature of the process’ distribution. We can approach a statistical model of when continuous voicing is more or less likely to occur, but even if the context is exactly right, it may not occur.

The question remains: Why is closure voicing a lenition phenomenon in intervocalic stops? A gesture-based approach to laryngeal representation can account for this. We propose that closure voicing in /b d ɡ/ follows from the loss of the glottal opening gesture that is usually associated with these stops. When the vocal fold configuration is optimal for voicing and subglottal pressure is high, some duration of closure voicing is natural and requires no extra effort (Westbury & Keating, 1986; see Section 1.1). This vocal fold configuration is required for producing vowels both before and after intervocalic stops, so maintaining it throughout the stop will require the least articulatory effort. In contexts where we generally expect gestural undershoot, it is unsurprising that we also see the loss of a non-distinctive glottal opening gesture (as in /b d ɡ/), and to a much lesser extent, the loss of a distinctive glottal opening gesture (as in /p t k/).

This type of lenition is not predicted from either of the featural representational accounts discussed above. If /b d ɡ/ are abstractly specified as [voice], we would not expect lenition to be a requirement for phonetic voicing—in fact, Kingston and Diehl (1994) explicitly use the presence of intervocalic voicing as an argument for why Danish has [voice]. If /b d ɡ/ receive some value for [spread glottis] late in the phonological derivation, there is no explicit mechanism for reducing this number in the case of lenition. However, intervocalic voicing as a consequence of lenition follows directly from the established facts about glottal activity, and as such, can also follow from a representation relying on gestural scores as in Articulatory Phonology. Recall from Section 1.2 that only a gesture-based account of underlying representation leads to any specific predictions about lenition, namely that lenition would lead to reduction in the timing and magnitude of associated glottal gestures. This is in line with our results. The difference in lenition rates in the two laryngeal series follows directly from the difference in magnitude of the underlying gestures. This account also correctly predicts that voicing-as-lenition is only found intervocalically; the loss of a glottal opening gesture would not result in voicing in initial position, where voicing requires a separate, active gesture.

In Table 6, we summarize the predictions following from different theoretical approaches, and whether or not we found support for these predictions in the current study.

6.3. RQ3: The relative predictive power of different variables

We have already discussed the predictive power of some of our variables. Laryngeal Setting was a very strong predictor of voicing, as were a number of variables associated with lenition. Particularly strong lenition variables are Local Speech Rate, Preceding Stress, and Affix Boundaries —but overall, the majority of lenition variables have a significant influence on voicing in the expected direction. It is interesting that no effect was found for morpheme-initial stops, but one was found for stops at affix boundaries. In Section 2.1.3, we hinted that this may have an exemplar theoretic explanation: Affixes are so often encountered with closure voicing that it has seeped into the underlying representations at the morpheme-level in a way that is not predictable at the phoneme-level. This is obviously controversial, in large part because it is impossible to represent in many modular frameworks (where phonetic information is invisible to morphology), and it represents a quite different conception of phonological representation than those we have discussed above. The effect of affix boundaries remains an interesting problem for further research.

Many of the other variables that we expected to influence closure voicing were aerodynamic in nature, and fewer of those have an observable effect on closure voicing in our data. This may be either because these variables truly have no effect on closure voicing, or because the influence of these variables is more gradient in nature. It is possible that these variables would affect the relative duration of closure voicing within those stops that we simply categorize as ‘not fully voiced.’

We had a number of predictions for how the tongue position before and after the occlusion would affect the prevalence of closure voicing, which mostly come down to this: We expected a narrower constriction in the oral cavity before and after the occlusion to decrease the odds of closure voicing, because such sounds are sometimes taken to be less sonorous (e.g., Parker, 2002), and voicing follows more naturally from sounds with higher sonority; in fact, Chomsky and Halle (1968) define their distinctive feature [±sonorant] exclusively with reference to whether voicing follows naturally from the vocal tract configuration. However, none of these predictions holds up; we found no effect of tongue body position except for point of occlusion in the stop itself.

Place of articulation has quite a strong effect on voicing, and this has an aerodynamic explanation. The supralaryngeal cavity is relatively small during a velar occlusion and provides little opportunity for passive expansion, and as such, velar stops are generally voiced at a lower rate. Alveolar and bilabial occlusions are more amenable to voicing, and the difference in size between the resulting cavities is negligible, which may be why they do not differ significantly in their amenability to voicing.

The influence of stød on the potential for closure voicing can also be thought of as an aerodynamic effect. The naturalness of intervocalic closure voicing crucially depends on high subglottal pressure at the time of occlusion and on vocal fold configuration being amenable to voicing. Closure voicing following stød is very rare—this was a strong effect in spite of the total number of relevant tokens being quite small—presumably because laryngeal contraction in the production of stød causes a vocal fold configuration that is less amenable to voicing than that of modally voiced vowels. Tautosyllabic stød was found to increase the chances of voicing, which is surprising, given that stød has many of the same syllable-initial cues as stress. However, one initial articulatory correlate of stød reported by Fischer-Jørgensen (1987, 1989) is increased subglottal pressure (although note that subglottal pressure was measured for only one participant, and no words with initial oral stops were measured). This may serve to explain why tautosyllabic stød empirically shows a negative correlation with voicing (see Table 3), but correlates positively with voicing in a model that also controls for stress (see Table 5).