Stød Timing and Domain in Danish

Abstract

This study investigates the timing of stød, a type of phonological nonmodal phonation related to creaky voice in Danish, relative to the syllable. Stød-bearing syllables are characterized by high fundamental frequency (F0) and modal phonation at the beginning of the syllable followed by nonmodal, often creaky phonation and low F0 towards the end of the syllable (the stød phase proper). However, the timing of these two phases relative to the syllable and to each other has been debated. To investigate this, F0 throughout the word and the timing of the stød phase proper relative to the syllable were analyzed in five types of monosyllabic words. The results show that across word types the first stød phase (high F0) coordinates with the syllable rhyme onset, whilst the second phase is timed to the center of the sonorant rhyme, in contrast to previous hypotheses of stød timing. This relationship is formalized using the framework of Articulatory Phonology. In doing so, two additions to the theory are proposed to account for the biphasic nature of stød and the timing of the stød phase proper relative to the syllable.

1. Introduction

This paper investigates the timing of stød, a type of phonological, nonmodal phonation related to creaky voice in Danish (Fischer-Jørgensen 1989; Grønnum 1998; Basbøll 2005), relative to the syllable. Previous work has shown that stød is best characterized as biphasic in its realization, with high fundamental frequency (F0) and modal phonation at the beginning of stød-bearing syllables followed by a second phase often characterized by irregular vibratory pulses and nonmodal, creaky phonation (Fischer-Jørgensen 1989). This second phase has been termed the ‘stød phase proper’ or simply ‘stød’ in previous literature, and its timing relative to the syllable has been the subject of much debate, with some research claiming it is linked to a mora, and other literature claiming it is a property of the syllable (Fischer-Jørgensen 1989; Grønnum and Basbøll 2001; Basbøll 2005; Grønnum et al. 2013).

This study investigates the timing of the two stød phases relative to each other and to the syllable. Here, three timing hypotheses between the stød phase proper and the syllable are investigated, as well as independent evidence for morae in Danish from durational data, following Broselow et al. (1997) and Morén and Zsiga (2006). The results of this study suggest that the relationship between stød and the syllable is not modulated by morae. Furthermore, the timing relationship between stød and the syllable can be modeled using the framework of Articulatory Phonology (Browman and Goldstein 1986, 1989a, 1989b, 1990, 1992; Browman et al. 1990). To do so, two theoretical additions are proposed. First, I propose that the GLOTTAL tier in traditional frameworks of Articulatory Phonology can be subdivided into two tiers, the PHONATION tier and the F0 tier. This division allows for the phonological specification of multiple glottal configurations in the production of laryngeal/glottal phenomena, each of which may have independent effects on phonation and pitch. I motivate this division by showing its necessity to account for stød’s biphasic realization. Second, I propose that, analogous to the c-center effect wherein onset clusters act as a single unit relative to a following vowel gesture, the sonorant portion of the syllable rhyme, henceforth referred to as the sonorant rhyme, acts as a single unit relative to stød’s gestural constellation in Danish. This allows for the implementation of a new articulatory landmark, the sonorant rhyme center, which can enter into coordination relationships with other articulatory gestures.

In the remainder of the introduction, I first outline the acoustic and articulatory differences between modal and nonmodal phonation, particularly as it pertains to stød in Danish, before reviewing three possible timing relationships between stød and the syllable. I then outline the research questions of this paper before reviewing the key aspects of Articulatory Phonology (Browman and Goldstein 1986, 1989a, 1989b, 1990, 1992) relevant to this study. Section 2 details the methods of this study before the results of the analyses are presented in Section 3. The results are discussed in Section 4, before the conclusion in Section 5.

1.1. Acoustics and Articulation of Modal Phonation, Creaky Phonation, and Stød

Some languages use phonation phonologically to create lexical contrasts, e.g., Gujarati (Khan 2012), Mazatec (Garellek and Keating 2011), White Hmong (Esposito and Khan 2012; Garellek 2012), and Zapotec (Avelino 2010; Esposito 2010). This paper focuses on one such language, Danish, which contrasts modal phonation with a type of nonmodal phonation related to creaky voice, termed ‘stød’ in previous literature (Ege 1965; Basbøll 1985, 2005; Fischer-Jørgensen 1989; Grønnum 1998).

Acoustically, modal phonation, the most common vocal register used in speech, is best described in contrast to nonmodal phonation. Modally phonated segments, particularly sonorants, are typically characterized by higher F0, higher and more regular intensity, and more periodicity in the acoustic signal than segments produced with nonmodal phonation (Garellek 2015, 2019; Esling et al. 2019). Articulatorily, this is achieved with regular, periodic vocal fold vibration during pulmonic egressive airflow with minimal or no laryngeal constriction (Esling et al. 2019). In contrast, segments produced with creaky phonation, a type of nonmodal phonation, are characterized as having lower F0, more irregular intensity, and less periodicity in the acoustic signal than modally phonated ones (Keating et al. 2015; Davidson 2020).

Traditionally, the acoustic differences between modal and creaky phonation have been attributed to differing states of the glottis (Catford 1964, 1977). However, recent evidence suggests that the articulation of creaky phonation often involves constriction of multiple laryngeal articulators, not just the vocal folds at the glottis, and that differences in the precise articulation can lead to distinct acoustic outputs (Esling et al. 2019). For example, Esling et al. (2019) review three types of creaky phonation, which they refer to as creaky voice, also called ‘glottal fry’ or ‘vocal fry’ (Hollien et al. 1966; Hollien and Michel 1968), harsh voice (Laver 1980), and ventricular voice (Laver 1980), each of which has a distinct articulatory state of the larynx associated with it, though there is overlap across the three types. According to Esling et al., in the production of creaky voice, not only are the vocal folds shortened and thickened, generally due to thyroarytenoid muscle contraction, but the ventricular folds also often encroach upon the vocal folds. This increases the vibratory mass during voicing, lowering speakers’ F0 and increasing irregularity in vocal fold vibration. In contrast, what Esling et al. refer to as harsh voice, with greater noise and aperiodicity in the acoustic signal, results from additional aryepiglottic constriction and ventricular adduction. Narrowing of these structures constricts the region immediately above the glottis, which they claim induces vibration in epilaryngeal structures during voicing, introducing more noise into the acoustic signal. For a full review of the different types of nonmodal phonation, see Esling et al. (2019).

Returning to the language at hand, in many Danish dialects, including the standard and dialects spoken around Copenhagen, the capital, the nonmodal phonation type stød phonologically contrasts with modal phonation, as show below in

Table 1. Minimal pairs in Danish, contrasting in phonation. Stød-bearing words are on the left, and stød-less words are on the right.

Stød-Bearing Words	Stød-Less Words
[vɛnˀ] ‘turn (imperative)’	[vɛn] ‘friend’
[khʌmˀ] ‘come (past)’	[khʌm] ‘come (imperative)’
[ˈlɛːˀ.sɐ] ‘reads (present)’	[ˈlɛː.sɐ] ‘reader’

. Stød is represented by a superscript [ˀ]. In terms of its distribution in the lexicon, stød can only occur in stressed syllables with either a long vowel (Danish has contrastive vowel length) or a short vowel followed by a sonorant coda consonant (V+S), a requirement referred to as ‘stød-basis’ (Basbøll 1985). Stød occurs in both monomorphemic and polymorphemic words, and in monosyllabic and polysyllabic words. It also displays complex interactions with morphology. As Basbøll (1985) notes, in most cases when an affix is attached to a stem in Danish, a stem that already had stød retains it, and a stem that did not have stød remains stød-less. However, some suffixes have been analyzed as causing stød-removal from a monosyllabic stem, some condition stød-addition, and some apply these processes inconsistently across the lexicon. Therefore, to limit the scope of this study, here, only monosyllabic words are examined; for a detailed account of stød’s phonological distribution, its interactions with morphology, and its distribution in polysyllabic words, see Basbøll (2005).

Previous acoustic work has shown that syllables with stød are typically characterized by modal phonation and high or rising F0 in the first part of the rhyme, followed by a second phase, the stød phase proper, or simply stød (Fischer-Jørgensen 1989). This phase can manifest with a variety of acoustic correlates, including irregular vocal fold vibration/aperiodicity in the spectrogram (creaky phonation), a local dip in F0, irregular amplitude, decreased intensity compared to modal phonation, and (rarely) full glottal closure (Fischer-Jørgensen 1989; Grønnum et al. 2013). However, studies have found a high degree of variability in stød realization, particularly with respect to the stød phase proper, and not all of these acoustic correlates may be present in any given instantiation (Fischer-Jørgensen 1989; Grønnum and Basbøll 2001; Grønnum et al. 2013). Descriptions of a prototypical stød phase, the most common manifestation, resemble descriptions of prototypical creak as described by Keating et al. (2015), often occurring with some combination of irregular vocal fold vibration and aperiodicity in the spectrogram, low F0, irregular amplitude, and decreased intensity. A maximally ‘strong’ stød phase is reported to result in full glottal closure, though this is said to be relatively rare and possibly related to focus (Grønnum et al. 2013). Finally, ‘weaker’ instantiations without obvious acoustic correlates are also reported (Fischer-Jørgensen 1989; Grønnum and Basbøll 2001, 2003a, 2003b; Grønnum et al. 2013). For these instantiations, stød is still said to be perceptually salient to Danish listeners, despite the lack of obvious acoustic correlates. These descriptions have led researchers to conclude that stød is related to but not exactly creaky phonation.

Articulatorily, stød has been linked to multiple laryngeal articulators, including the cricothyroid, the vocal folds, and the ventricular folds (Fischer-Jørgensen 1989).1 Fischer-Jørgensen (1989), in an electromyographic study of seven speakers, found that the cricothyroid was more contracted in the first half of stød-bearing rhymes than in the second half, and more contracted at the beginning of stød-bearing rhymes than in stød-less rhymes, where there was no contraction. Fischer-Jørgensen (1989) also reports on a fiberoptic study, which examined the vowels [iː] and [iːˀ] for six speakers. She found that whilst the position of the vocal folds at the beginning of [iː] and [iːˀ] was similar, five of the six participants showed transverse contraction of the vocal folds at the end of [iːˀ], and all speakers showed evidence of ventricular fold constriction, evidenced by decreased distance between the ventricular folds, at the end of [iːˀ]. However, the degree of constriction varied across speakers. For the one speaker who did not show transverse vocal fold constriction, the ventricular folds were nearly completely covering the vocal folds.

These various articulators have also been implicated in producing different acoustic correlates of stød. Fischer-Jørgensen notes that cricothyroid contraction lengthens the vocal folds, making them thinner and more tense, which she asserts is responsible for raising speakers’ F0 in the first part of stød-bearing syllables’ rhymes (Fischer-Jørgensen 1989; Woodson et al. 1989; Esling et al. 2019). In contrast, Fischer-Jørgensen notes that the beginning of vocal fold contraction aligns closely in time with the point at which F0 began to decrease abruptly for speakers, and that the point of maximum vocal and ventricular fold contraction corresponds to the F0 and intensity minimums for speakers.

In sum, prior research indicates that stød is articulatorily and acoustically biphasic, consisting of cricothyroid contraction which raises F0 in the first part of the syllable rhyme followed by a stød phase proper with vocal and ventricular fold contraction, leading to low F0, low intensity, and often creaky phonation in the second part of the rhyme. In the next section, I discuss how these findings have been used to inform the most comprehensive theory of stød distribution and timing in Danish, as well as how this theory parallels another proposal for suprasegmental-to-segmental timing in Thai.

1.2. Suprasegmental-to-Segmental Timing

In this section, I discuss two analyses of suprasegmental-to-segmental timing, both of which propose that a suprasegmental phonological feature is timed with respect to morae. The first analysis I discuss is the timing of stød in Danish, and the second analysis is the timing of the falling high-low (HL) tone in Thai. Crucially, these two analyses differ in how morae are formulated, and this difference in moraic formulation predicts different timing relationships between the suprasegmental feature and the syllable. The purpose of investigating two ways of formulating morae comes from the results of recent studies on stød onset timing which do not support the traditional moraic analysis put forth by Basbøll (1985, 2005) (see Section 1.2.1). Therefore, both methods of formulating morae are investigated in the analysis here with respect to stød timing in Danish to determine if an alternative way of conceptualizing morae, as in Thai, may better capture stød timing relative to the syllable than the analysis put forth by Basbøll (2005). This would allow for a moraic interpretation of the data, even if it does not support the timing relationship between the stød phase proper and the syllable that has been previously proposed.

1.2.1. Moraic Hypothesis of Stød Timing

The articulatory and acoustic findings reviewed in Section 1.1 have been used to support the most comprehensive phonological theory of stød distribution in Danish, henceforth referred to as the moraic hypothesis (Basbøll 1985, 2005). Under this hypothesis, stød is the default phonation for monosyllabic words. All stød-bearing, monosyllabic words are bimoraic, and stød is a suprasegmental feature licensed by the second mora in the syllable. In this analysis of Danish syllable structure, the first mora is projected by a vocalic element, and the second mora is projected by the phonological element that satisfies the conditions of stød-basis—either the second half of a long vowel or a sonorant consonant in a V+S sequence (Basbøll 1985, 2005). In contrast to these bimoraic, stød-bearing words, all stød-less monosyllabic words are considered monomoraic, including CVS words without stød in the native or native-like vocabulary. For these words, Basbøll proposes that the sonorant coda is extra-prosodic. Consequently, all monosyllabic words that meet the requirements of stød-basis have stød, the default phonation, unless the sonorant coda is extra-prosodic, and those that do not are categorically excluded from hosting stød. This is shown below in

Table 2. Distribution of stød-bearing and stød-less syllables in monosyllabic Danish words. ‘—’ indicates illegal syllabic configurations in Standard Danish.

Syllable Type	Stød	Non-Stød
CV	—	[ja] ‘yes’
CVO	—	[hɛsd̥] ‘horse’
CVS	[vɛnˀ] ‘turn (imperative)’	[vɛn] ‘friend’
CVː	[b̥yːˀ] ‘town’	—
CVːO	[lɔːˀs] ‘lock’	—
CVːS	[b̥eːˀn] ‘leg/bone’	—

. Here, only one onset consonant (C), coda obstruent (O), or sonorant (S) is shown for brevity, though clusters are permissible.

With respect to stød timing, the moraic hypothesis explicitly integrates the acoustic findings of Fischer-Jørgensen, positing that the stød phase proper should begin in the middle of a long vowel, or, for syllables with a V+S rhyme, at the onset of the coda sonorant. Concurrently, the moraic hypothesis frames the domain of stød as the second half of a long vowel or a sonorant in a V+S sequence.

However, recent experimental work has not corroborated this timing relationship between the stød phase proper and the syllable. In fact, for as long as stød has been studied acoustically, a great deal of variability in the stød phase’s timing has been robustly attested both within and across speakers (Fischer-Jørgensen 1989; Grønnum and Basbøll 2001; Grønnum et al. 2013). Fischer-Jørgensen (1989) explicitly highlights this variability, though she asserts that the onset of the stød phase proper generally falls around the middle of a long vowel or near the onset of a coda sonorant in a V+S rhyme. Grønnum and Basbøll (2001) also found that the onset timing of the stød phase proper did not differ between syllables with long vowels and those with V+S rhymes. However, this was likely due to a high degree of variability in stød onset timing, not because these two points were equidistant from the vowel onset. In fact, a close examination of the data in Grønnum and Basbøll (2001) reveals that the onset of the stød phase proper in syllables with long vowels usually occurs around the middle of the vowel, but that in V+S rhymes, the onset usually occurs in the last third of the vowel, not at the onset of the coda sonorant (see Grønnum and Basbøll 2001, Table 13, p. 247). Furthermore, a confounding factor in this study is that the long stød-bearing vowels occurred in the first syllable of disyllabic words, whereas stød-bearing V+S rhymes occurred in both monosyllabic and disyllabic words.

Also of note is that even early acoustic work has acknowledged the pervasive variability in stød offset timing, though it has never been subject to serious investigation. Fischer-Jørgensen (1989), Grønnum and Basbøll (2001), and Grønnum et al. (2013) note that various correlates of stød, including irregular vocal fold vibration, low F0, and low intensity, can spread from the second half of a long vowel or a sonorant in a V+S rhyme to following segments or even to a post-tonic syllable. These descriptions of spreading imply that the domain of stød is the syllabic configuration that satisfies stød-basis, that is, either the second half of a long vowel or a coda sonorant in V+S rhymes, and frame the presence of stød outside of these intervals as irrelevant to its phonological domain.

Another issue with the moraic hypothesis in Danish is the independent motivation for morae. As stated by Grønnum and Basbøll (2001), morae do not play any role in Danish other than to explain the distribution and timing of stød. For example, poetry in Danish counts syllables, not morae, and stress in Danish is said to be free, or quantity insensitive (Grønnum 1998; Kuznetsova 2018).2 This lack of phonological evidence has led researchers to look for other evidence for morae in Danish. For example, Basbøll (1985) predicts that moraic coda sonorants in stød-bearing V+S rhymes will be longer, and thus quantitatively heavier, than non-moraic coda sonorants in stød-less rhymes. Therefore, the coda [n] in words such as [vɛnˀ] ‘turn (imperative)’ are predicted to be longer than the coda [n] in words such as [vɛn] ‘friend’. However, Grønnum and Basbøll (2001) did not find a significant difference in coda sonorant durations between stød-bearing and stød-less words. Follow-up perception experiments conducted by Grønnum and Basbøll (2003a, 2003b) testing the cognitive status of stød-bearing syllables as biphasic also did not yield evidence that the onset of the stød phase proper is perceptually timed to a second mora.

Based on these results, recent work (Grønnum and Basbøll 2007; Grønnum et al. 2013; Grønnum 2015) has described stød as a feature of the syllable without referring to lower-level linguistic structure such as morae. In fact, this work goes so far as to explicitly state that morae in Danish are merely a theoretical convenience with no psychological reality for Danish speakers. This re-formalization of stød as a property of the syllable, however, remains agnostic as to the timing relationship between the syllable and the stød phase proper. Furthermore, the dearth of research specifically on the variation in stød timing has led Grønnum et al. (2013) to note that, at present, there is no evidence that stød realization is systematic.

However, as I discuss below, other languages besides Danish also evoke morae to explain suprasegmental-to-segmental timing relationships. In the next section I review how the coordination of the falling HL tone in Thai parallels stød coordination in Danish, and how adopting a different approach to moraic formulation, as proposed by Morén and Zsiga (2006), may allow for the preservation of a moraic analysis of stød timing in Danish.

1.2.2. Tonal Coordination in Thai and the Shared Mora Hypothesis

The use of morae as a prosodic mediator between a suprasegmental feature and its host syllable has been used to explain the timing of other suprasegmental phenomena relative to segments in languages besides Danish, namely tone. Here, I discuss one such analysis, that of tonal coordination in Standard Thai (Morén and Zsiga 2006; Karlin and Tilsen 2015), focusing on the distribution and timing of the HL tone, which strongly resembles that of stød in Danish.

Thai is a tonal language with five phonological tones, including a falling HL tone, which can only manifest on CVS, CVV, CVVO, and CVVS syllables,3 similar to the distribution of stød-bearing monosyllabic words in Danish (see Table 2). Morén and Zsiga (2006), in an acoustic study of tonal coordination in Thai, found that the fall in pitch in an HL tone is timed with respect to the onset of the coda sonorant in monosyllabic CVS words, which they claim is usually commensurate with the middle of the syllable rhyme, or to the middle of the syllable rhyme in CVV, CVVO, and CVVS words. Morén and Zsiga interpret these findings to mean that the L phase of the HL tone is timed to a second mora in a bimoraic syllable, and crucially that the second mora can be shared by multiple segments (Broselow et al. 1997). Thus, the syllable rhyme of CVV, CVVO, and CVVS words is divided in half, with each half corresponding to a mora. For CVV words, this effectively divides the long vowel in half, with each half corresponding to one mora. For CVVO and CVVS words, the syllable rhyme is divided in half, with the first half consisting of only a portion of the long vowel, corresponding to the first mora. In contrast to CVV words, however, in CVVO and CVVS words, the second half of the rhyme consists of the final portion of the long vowel (usually the last third or so) as well as the following coda consonant. Therefore, the second mora in CVVO and CVVS words is always shared by two segments, the latter part of the long vowel and the coda consonant. This accounts for why the L tone coordinates with the middle of the syllable rhyme in these syllables, and not the middle of the long vowel, in contrast to CVV words. This analysis of moraic formulation will henceforth referred to as the shared mora hypothesis.

Morén and Zsiga motivate this analysis of morae in Thai by pointing out three aspects of their data. First, across the different word types that bear the HL tone, (CVS, CVV, CVVO, CVVS), the syllable rhyme durations are quite similar. Second, coda consonants in CVVO and CVVS words are shorter than in CVO and CVS words in their study, respectively. Third, vowels in CVVO and CVVS words are shorter than in CVV words. Together, Morén and Zsiga interpret these results such that morae in Thai have a preferred duration independent of the syllabic configuration of the syllable, and furthermore, that the phonetic duration of segments is modulated by this specification. This leads to long vowels in CVVO and CVVS words shortening relative to those in CVV words and coda consonants shortening relative to those in CVO and CVS words to fit this preference.

In sum, previous literature on the timing of multiple suprasegmental features relative to their host syllable has proposed that the relationship is mediated by morae, specifically ones with biphasic realizations such as stød in Danish and the HL tone in Thai (Basbøll 1985, 2005; Morén and Zsiga 2006). However, the proposals for these two languages differ in how they conceptualize morae. Therefore, given the recent findings that cast doubt on the timing relationship between the stød phase proper and morae in Danish, in this study, I investigate whether reconceptualizing how morae are formulated provides a fruitful alternative to the traditional formulation of morae in Danish (Basbøll 1985, 2005), allowing a moraic interpretation of the data to be preserved under empirical investigation.

1.3. Research Questions and Predictions

In this section, I outline the research questions of this study and the predictions of three hypotheses of stød timing relative to the syllable. To restrict the domain of inquiry whilst still allowing for the results to be generalizable, here, I investigate stød timing in four types of monosyllabic words, CVSˀ, CVːˀ, CVːˀO and CVːˀS. In the following sections, the term stød will be used to refer to the stød phase proper, unless it is made clear from context that it is referring to both phases of stød (e.g., when discussing the distribution of stød-bearing syllables in the lexicon). The research questions are as follows:

• Across word types (CVSˀ, CVːˀ, CVːˀO and CVːˀS), which hypothesis of stød timing best captures the relationship between the stød phase proper and the syllable?
• How can stød timing relative to the syllable be modeled?
• Is there independent evidence from segmental durations (vowel duration, coda sonorant duration, and overall sonorant rhyme duration) for morae in Danish?

Regarding the first question, three hypotheses of stød onset timing are investigated and compared in this study, as shown in

Table 3. Predictions of the moraic hypothesis, shared mora hypothesis, and sonorant rhyme center hypothesis on stød timing across word types. Cells are combined across rows if the hypothesis makes the same predictions about various word types.

Word Type	Moraic Hypothesis	Shared Mora Hypothesis	Sonorant Rhyme Center Hypothesis
CVSˀ	Stød onset = Coda onset Stød offset = Coda offset	Stød onset = Coda onset Stød offset = Coda offset	Stød onset = Sonorant rhyme midpoint Stød offset = Sonorant rhyme offset
CVːˀ	Stød onset = Vowel midpoint Stød offset = Vowel offset	Stød onset = Vowel midpoint Stød offset = Vowel offset
CVːˀO
CVːˀS		Stød onset = Sonorant rhyme midpoint Stød offset = Sonorant rhyme offset

. To determine which hypothesis best represents the timing relationship between stød and its host syllable, I adopt the approach in Shaw et al. (2011) that measures of relative stability rather than absolute stability are a reliable index of coordination between two gestures. Shaw et al. (2011) implemented this idea in a study on Moroccan Arabic onset cluster gestural coordination. In this study, they measured the temporal distance between various articulatory landmarks of the onset consonant (cluster) to a fixed anchor, the offset of the vowel, to assess which measure induced the least variability across words with different numbers of onset consonants (see Section 1.4 for labels of landmarks). In their results, they found that the temporal distance between the release of the onset (cluster) and the anchor remained relatively stable across words with one to three onset consonants, in contrast to the temporal distance between the target of the first onset consonant gesture or the center of the consonant gestures to the anchor, evidenced by lower relative standard deviations. Following from this, here, I assume that the timing relationship between stød and the syllable which induces the least variability in stød onset timing, both within and across word types, best represents the phonological organization of stød relative to the syllable. This view permits variance in the actual realization of stød, suitable for empirical data, as the stability of each measure is assessed by comparing heuristics of variance (here, standard deviation) and does not require that stød aligns perfectly with a given phonological point.

The first timing hypothesis examined here is the moraic analysis put forth by Basbøll (1985, 2005), which predicts that the onset of stød relative to the syllable will align with the onset of a sonorant coda in words with V+S rhymes (CVSˀ words) and with the middle of the long vowel in CVːˀ, CVːˀO, and CVːˀS words. This hypothesis also predicts that stød offset will align with the offset of the sonorant coda in CVSˀ words and with the offset of the long vowel in CVːˀ, CVːˀO, and CVːˀS words, providing evidence that the domain of stød is the sonorant coda in words with V+S rhymes or the second half of a long vowel.

A second possibility is that stød aligns with the second mora, but that morae are formulated in Danish via the shared mora hypothesis, as in Thai. The differences in moraic formulation between this hypothesis and the moraic hypothesis are shown below in Figure 1. According to this hypothesis, the first mora in a stød-bearing word is projected by either a short vowel in a V+S rhyme or by part of a long vowel, but the second mora may be shared between multiple segments. Applying this principle to Danish, I follow the analysis in Basbøll (1985, 2005) that only sonorant codas can contribute to a mora, in contrast to obstruent coda consonants. This formulation of morae differs from Thai, in which both coda sonorants and coda obstruents can contribute to a mora. Based on this hypothesis, stød is predicted to begin with the onset of a sonorant coda in CVSˀ words and in the middle of the vowel in CVːˀ and CVːˀO words. For CVːˀS words, this hypothesis predicts that stød will align with the middle of the sonorant portion of the syllable rhyme, which includes the sonorant coda, mirroring the timing relationship between the HL tone and the syllable in Thai (Morén and Zsiga 2006). This hypothesis also predicts that across all word types, stød offset will align with the end of the sonorant rhyme. In this analysis, the domain of stød is the sonorant rhyme.

The third hypothesis of stød onset timing investigated here is that stød is a property of the rhyme and not mediated by morae, as stated in Grønnum and Basbøll (2007), Grønnum et al. (2013), and Grønnum (2015). This hypothesis, which I refer to as the sonorant rhyme center hypothesis, is a formalization of the previous claims that stød is a property of the syllable, not of morae. Here, I formalize this hypothesis by assuming that, like the shared mora hypothesis, if stød is a property of the rhyme then it is a property of the sonorant rhyme where it can be acoustically realized, and it is timed relative to the midpoint of this domain. Similar to the shared mora hypothesis, this hypothesis predicts that in CVːˀ, CVːˀO and CVːˀS words, stød onset will align with the midpoint of the sonorant rhyme. In contrast to the shared mora hypothesis, this analysis also predicts that stød onset will align with the midpoint of the sonorant rhyme in CVSˀ words, rather than the onset of the sonorant coda, and these points need not coincide. Finally, as with the shared mora hypothesis, this hypothesis predicts that stød offset will align with the end of the sonorant rhyme across all word types, and that the domain of stød is the sonorant rhyme. These timing predictions are spelled out in Table 3.

Regarding the final research question, given the similarity between the various hypotheses’ predictions on stød timing, it is imperative to investigate independent evidence for morae in Danish. Therefore, durational measures to support the existence of morae will be examined. If morae are formulated via the moraic hypothesis, then we predict that coda sonorants in CVSˀ words will be longer than those in CVS words, following previous arguments that mora-projecting sonorants are quantifiably “heavier” than non-moraic ones in Danish (Basbøll 2005). If, however, morae are formulated via the shared mora hypothesis, we predict that sonorant rhyme durations across all word types will be similar, vowel durations in CVːˀS words will be shorter than in CVːˀ and CVːˀO words, and coda sonorant durations in CVːˀS words will be shorter than in CVSˀ words. These findings would provide evidence that morae have a preferred duration in Danish that phonetically conditions segmental durations, as in Thai.

1.4. Overview of Articulatory Phonology

In the final section of the introduction, I outline the framework of Articulatory Phonology to foreground the discussion of modelling stød timing in terms of gestural coordination (Browman and Goldstein 1986, 1989a, 1989b, 1990, 1992, 2000). An advantage of conceptualizing stød as a laryngeal gesture in an articulatory framework is that its timing relative to the syllable can be represented in ways that are compatible with both moraic and nonmoraic analyses of stød timing, allowing for the direct comparison of the hypotheses put forth in Section 1.3. This is because Articulatory Phonology departs from autosegmental phonological theories in defining speech segments (including suprasegmentals) as discrete gestures made by articulators in the vocal tract, which can coordinate with other gestures (Browman and Goldstein 1986, 1989a, 1989b, 1990, 1992, 2000) or to morae (Gao 2008; Karlin and Tilsen 2015). Multiple gestures can also be coupled together into a constellation in order to produce gesturally complex segments (e.g., aspirated stops, nasals), which is ideal for capturing the biphasic nature of stød.

In Articulatory Phonology, gestures are defined by their location of constriction (CL) and the degree of constriction (CD). Five independent articulators are identified in the production of speech sounds, the lips (LIPS), the tongue tip (TT), the tongue body (TB), the velum (VEL), and the glottis (GLO). These articulators can be specified for CL values such as [protruded], [labial], [dental], [alveolar], [palatal], [velar], [uvular], and [pharyngeal]. There are five possible CD values: [closure], [critical], [narrow], [mid], and [wide]. For vowels, these can be combined (e.g., [wide mid]) when needed to indicate height distinctions between vowels. Independent gestures can be represented as timed relative to each other in the production of speech, as shown in the gestural score in Figure 2 for the word [sœn] ‘son’ in Danish. Time is represented on the x-axis and the articulators on the y-axis. As shown in this figure, the voiceless alveolar fricative [s] is produced by a constellation of two gestures, the [critical] gesture of the tongue tip on the TT tier and the spreading of the glottis on the GLO tier, as shown by the dotted-and-dashed lines. [œ] is also produced with a constellation of two gestures, the tongue body gesture on the TB tier and the lip protruding gesture on the LIPS tier in solid lines. Finally, the coda [n] is produced with another constellation of two gestures, an alveolar closure involving the tongue tip on the TT tier and a [wide] gesture on the VEL tier, shown in dashed lines.

The gestural score in Figure 2 also shows that, in addition to gestures coupling together into constellations corresponding to a single segment, gestures related to different segments are also coordinated relative to each other in speech (Browman and Goldstein 1990). Traditionally, gestures are described as following a 360° trajectory from beginning to end. Along this trajectory, certain gestural landmarks, which can enter into coordination relationships with other gestures, can be identified (Gafos 2002). The relevant landmarks, as defined in Gafos (2002), are given below in Figure 3.

Using this notation, coordination relationships between adjacent segments can be defined by stating the coordination relationship between the landmark of one gesture and the landmark of another. For example, in a CV sequence in English, the onset of the vowel has been found to coordinate with the center of the consonant (Browman and Goldstein 1990). Furthermore, in some languages, including English (Browman and Goldstein 1988; Marin and Pouplier 2010), German (Pouplier 2012), and Romanian (Marin 2013), the most stable coordination relationship between an onset cluster and the following vowel is between the center landmark of the entire onset cluster and the onset of a vowel gesture. This effect has been termed the c-center effect in previous literature. In contrast, in VC sequences the release of the vowel gesture coordinates with the center of the coda consonant gesture (Browman and Goldstein 1990). Phenomena similar to the c-center effect have not been found between coda clusters and preceding vowels (Browman and Goldstein 1988, 2000; Honorof and Browman 1995). These coordination relationships are shown in Figure 4. I return to the modeling of stød using an articulatory framework in the discussion, in which I show how stød coordination relative to the syllable can be represented gesturally by proposing a new articulatory landmark analogous to the c-center, the sonorant rhyme center.

2. Materials and Methods

2.1. Participants

Nine native Danish speakers were recruited through word of mouth (4M, 5F, ages 25–28, mean age = 26.1). Eight were from Copenhagen or the greater-Copenhagen area and one (a male) was from Greve, a municipality southwest of Copenhagen, whose accent was judged to be similar to the Copenhagen accent by two Danish consultants.4 All speakers were living in Copenhagen at the time of recording and had lived in Copenhagen for at least three years. All the speakers were bilingual Danish–English speakers whose primary language was Danish, and only one speaker had lived outside of Denmark for longer than six months.5 The same speaker also had issues with their hearing at a young age but has since undergone a corrective procedure and has passed the national military hearing exam. The other participants did not report any hearing or speech disorders.

2.2. Stimuli

The stimuli consisted of one type of stød-less word, CVS (29 words), and of four types of stød-bearing monosyllabic words, CVSˀ (63 words), CVːˀ (21 words), CVːˀO (40 words), and CVːˀS (55 words). For CVS, CVSˀ, and CVːˀS words, the manner of articulation of the coda sonorant was varied between a nasal ([n] or [m]) or an approximant ([l]).6 Due to the relative infrequency of some types of monosyllabic words (e.g., there are fewer CVːˀ words in the lexicon than CVSˀ words) and segmentability concerns, it was not possible to elicit the same number of target words per word type, and some words were repeated in the task. For the full list of target words, see the Supplementary Materials.7

In sum, 179 target words with stød and 29 CVS words without stød were elicited per speaker, for a total of 208 words per speaker and 1872 tokens across speakers. Of these, all tokens for which the vowel could not be segmented from the following tautosyllabic sonorant were excluded (96 tokens). Tokens were also excluded if stød was masked by phrasal creak (55 tokens), if the word began with a period creak on a word-initial vowel (e.g., [ɔ̰ːˀl], ‘eel’, 44 tokens), or if the voice quality could not be categorized (3 tokens). Five additional words were excluded for all speakers, on the criteria that they were unknown to at least four of the speakers (45 words total). Individual tokens were excluded if a hesitation or mispronunciation occurred on the target word, the preceding word, or the following word, if the speaker was unfamiliar with the word, or if they placed excessive emphasis on the word, evidenced by noticeably louder intensity and a following pause (69 tokens) or if they were realized with a full glottal stop (100 tokens). After these exclusions, 1460 tokens remained. Of these, the remaining CVSˀ, CVːˀ, CVːˀO, and CVːˀS words were analyzed for stød presence. Words with only an F0 dip (76) were excluded because, in the absence of creaky phonation, it was unclear whether the F0 dip was due to regular sentence intonation or due to stød. Finally, words for which stød could not be reliably segmented (172) were also excluded, leaving 1212 words in the final dataset, 1014 of which had stød. The distribution of these words across word types is given below in

Table 4. Stimuli by word type. The total number of tokens per word type included in the final study is given in parentheses below the example (total = 1212).

CVS	CVSˀ	CVːˀ	CVːˀO	CVːˀS
[ɡ̊ul] ‘gold’ (198)	[sd̥alˀ] ‘stable’ (331)	[hiːˀ] ‘hibernation’ (101)	[ɡ̊ɔːˀs] ‘goose’ (284)	[ɡ̊eːˀn] ‘gene’ (298)

.

2.3. Procedure

Speakers were recorded in a quiet room in Copenhagen, Denmark, using the Tascam-DR 40 recorder and a head-mounted Shure WH20 microphone at a sampling rate of 44.1 kHz. Speakers first filled out a questionnaire about their language background before reading blocks of ten sentences with embedded target words on a Microsoft PowerPoint slide. Each target word was embedded into a semantically meaningful sentence. If a target word was elicited twice, it was embedded in two unique sentences. To examine how often stød spread beyond the end of the target word, all CVSˀ, CVːˀ, and CVːˀS words were followed by a /j/-initial word with a stød-less first syllable. /j/ was chosen as the initial consonant to allow the coda sonorant in CVSˀ and CVːˀS words to vary between a nasal and an approximant whilst still being segmentable from the following word. These words varied in length from one syllable (jeg [jaj] ‘I’) to six syllables (jernbaneselskabet [ˈjæɐ̪nb̥æːnəsεlsɡ̊æːˀb̥ð̞], ‘the railroad company’). The sentences were randomized into three unique orders, and every five blocks a screen appeared instructing the participant to take a break, though they were informed that they could take a break at any time. Speakers were instructed to read the sentences as if talking to a native Danish speaker, but no instructions about speech style or speech rate were given explicitly. If there was a disfluency on the target word or a surrounding word, speakers were asked to re-record the sentence. After the sentence reading task, speakers also read a word list containing the same target words, but these data are not reported here. In total, the study took approximately two hours.

2.4. Segmentation and Acoustic Analysis

2.4.1. Target Word Segmentation

Target words were segmented from the surrounding speech for analysis using the acoustic analysis software Praat (Boersma and Weenink 2021). For CVSˀ, CVːˀ, and CVːˀS words, the following word was also segmented to examine the extent of stød spreading. For each target word, the sonorant rhyme, consisting of either a vowel (CVːˀ and CVːˀO words) or a vowel and a sonorant consonant (CVS, CVSˀ, and CVːˀS words) was then segmented from the syllable onset and any coda obstruents, if present. The onset of the vowel was identified as the onset of clear first and second formants (F1 and F2), characteristic of a vowel, and periodicity in the waveform, following Garellek (2012) and Styler (2017). This procedure was uniform across all words.

For CVːˀO words ending in obstruents, the offset of the vowel was defined as the offset of F1 and F2, corresponding to the closure of a coda stop or the onset of aperiodic noise of a coda fricative. Stød-bearing words with coda sonorants (CVSˀ and CVːˀS) were always followed by a /j/-initial word, characterized by a low F1 and a high F2 and F3. For CVSˀ and CVːˀS words ending in nasals, the offset of the nasal was defined using both the spectrogram and the waveform to identify the point at which the waveform shape changed from relatively simple, characteristic of a nasal (Styler 2017), to more complex, characteristic of /j/, and F2 became visible in the spectrogram, indicating the beginning of [j] in the following word. For CVSˀ and CVːˀS words ending in [l], also characterized by a low F1 and high F2, though not as high as the F2 of [j], the offset of liquid was defined as point at which F2 began to rise usually from a relatively high plateau to the onset of [j]. CVS words were followed by a variety of words, usually stop-initial. For these words, the offset of the nasal or [l] was taken to mark the end of the word. Finally, for CVːˀ target words, the formant patterns of the long vowel impacted the formant transitions from the end of the target word to the onset of the following /j/. For CVːˀ words with the front unrounded vowel [iːˀ], F2 remained high throughout the vowel and the following [j]. However, F3 was observed to rise towards F4 before lowering at the onset of [j]. Concurrently, the vowel offset was defined as the point at which F3 and F4 diverged from each other, as shown in Figure 5. CVːˀ words with back vowels and front rounded vowels exhibited a rise in F2 towards F3 at the end of the target word, indicating the onset of the following /j/. For these words, the offset of the vowel was defined as the point at which F2 and F3 began to diverge, signifying the onset of [j].

For words with complex rhymes (CVS, CVSˀ and CVːˀS), the vowel and coda sonorant were also segmented from each other. When the coda sonorant was a nasal, the offset of the vowel/onset of the nasal was defined as the point at which F2 disappeared from the spectrogram, anti-formants characteristic of nasals appeared in the spectrogram, and the amplitude of the waveform decreased (Styler 2017). When the sonorant coda was [l], the formant transitions from vowel offset to the onset of the following [l] differed as a function of vowel backness and roundedness. First, the front unrounded vowels [i(ː), eː, ɛ(ː)] and [aː]8 were produced with a very high F2, even greater than F2 for [l]. Concurrently, the boundary between the vowel and [l] was placed where F2 dipped from the offset of the vowel towards the onset of [l]. For words with the front rounded vowels [y(ː)] and [ø(ː)], which had lower F2 values than [l], the point at which F2 began to rise was selected as the onset of [l]. For the back rounded vowels [u(ː)] and [ɔ(ː)], the boundary was placed where F2 rose and came together with F3 in a pinch, indicating the onset of [l]. Finally, for the back and central unrounded vowels [ʌ] and [a], F1 was higher than the F1 of [l], and the boundary was placed where F1 dipped, indicating the onset of [l]. Examples are given in Figure 5.

2.4.2. Phonation Segmentation and Acoustic Analysis

First, to verify the biphasic realization of stød that has been previously reported, F0 measures were taken every millisecond over the course of the vowel for all word types as well as over the course of the sonorant coda for CVS, CVSˀ, and CVːˀS words using the straight algorithm in VoiceSauce (Shue et al. 2011). The data were then averaged over fifths of the vowel or sonorant, respectively, using a custom Python script to obtain the average F0 per fifth of the vowel/sonorant across word types.

Regarding the stød phase proper, stød can manifest with a variety of acoustic correlates, including low F0, decreased intensity, creaky phonation, and full glottal closure, whilst in other cases, it can be difficult to detect visually. Therefore, each target word was marked for multiple acoustic cues of stød, though in this analysis, only tokens with a visible period of creaky phonation in the spectrogram or a period of decreased intensity and F0 were included in the final analysis. Creak onset and offset were visually identified as the onset/offset of irregular amplitude in the waveform accompanied by irregular glottal pulses in the spectrogram and often perturbations in the pitch tracker (Keating et al. 2015). Tokens with low intensity and F0 but no visible creak (22 tokens) were included if there was an observable period of low intensity that could not be attributed to a coda consonant, evidenced by lightening of the spectrogram, a localized dip in pitch of at least 20 Hz rounded to the nearest hertz, and often significant perturbations in the formant tracker. Onset boundaries were placed where the formants began to lighten, and offset boundaries were placed where intensity began to increase, evidenced by darkening of the formants in the spectrogram. Examples are given below in Figure 5, with the target word written orthographically on the first tier, vowels and any sonorant consonants transcribed in IPA on the second tier, and creak (c) and intervals of low intensity (i) marked on the third tier. When two words are transcribed on tier 1, the first word is the target word.

3. Results

The format of this section is as follows. In Section 3.1, the results of the F0 analyses are presented. Section 3.2 consists of the stød onset analysis, which compares three measures of stød onset timing based on the moraic hypothesis, the shared mora hypothesis, and the sonorant rhyme center hypothesis. Stød offset timing is analyzed in Section 3.3, and segmental durations (vowel, coda sonorant consonant, and overall rhyme duration, respectively) are analyzed in Section 3.4. For each acoustic measure, linear mixed-effects models were run in R using the lmer() function in the lme4 package (Bates et al. 2015)9, and post hoc Tukey tests (Bretz et al. 2010) were used to confirm statistical significance at the 0.05 level between levels of the categorical fixed effects, except for the F0 analyses, for which the 0.01 level was used due to the large number of tests that were performed, following Garellek (2012). For all the durational models and the stød onset/offset models, a random slope for word type by speaker and random intercepts for speaker and token were included. For the F0 models and the SD model, random intercepts for speaker and token were included.

3.1. F0 Analyses

The purpose of the F0 analyses is twofold. The first analysis is to verify that F0 at the beginning of stød-bearing rhymes is higher than for stød-less rhymes, confirming previous findings that the first stød phase is characterized by modal phonation and high F0. The second analysis is to determine when in the rhyme F0 decreases, in order to shed light on the timing relationship between the first and second stød phases.

In the first F0 analysis, the average F0 for each fifth of the vowel was calculated across all speakers.10 Five linear mixed-effects regression models were then run, one for each fifth of the vowel, with F0 as the dependent variable and word type (CVSˀ, CVːˀ, CVːˀO and CVːˀS) as a categorical fixed effect.11 In each model, the average F0 of CVS words, the only type of word without stød, was the baseline. Due to the large number of tests, p values under 0.01 were considered significant, following Garellek (2012). The results of the models are shown below in

Table 5. F0 differences between stød-bearing words and CVS words per fifth of the vowel. ↑ indicates that the word type with stød has significantly higher F0 that CVS words during that time interval. ↓ indicates that the word type with stød has significantly lower F0 than CVS words during that time interval. Dashes indicate no significant difference.

F0 at Each Vowel Fifth (Compared to CVS)
	1	2	3	4	5
CVSˀ	↑	↑	↑	—	—
CVːˀ	↑	↑	↑	—	—
CVːˀO	—	—	—	↓	—
CVːˀS	↑	↑	↑	—	↓

. ‘↑’ indicates that the word type has a significantly higher average F0 than CVS words for the given interval, and ‘↓’ indicates that the word type has a significantly lower average F0 than CVS words. Dashes indicate no significant difference.

As shown in Table 5, CVSˀ, CVːˀ, and CVːˀS words have a significantly higher average F0 than CVS words in the first 3/5 of the vowel, indicated by the upwards arrows (first fifth: CVS–CVSˀ: β = 12.065, p < 0.001; CVS–CVːˀ: β = 24.685, p < 0.001; CVS–CVːˀS: β = 18.091, p < 0.001; second fifth: CVS–CVSˀ: β = 13.527, p < 0.001; CVS–CVːˀ: β = 26.364, p < 0.001; CVS–CVːˀS: β = 18.886, p < 0.001; third fifth: CVS–CVSˀ: β = 14.404, p < 0.001; CVS–CVːˀ: β = 21.578, p < 0.001; CVS–CVːˀS: β = 14.711, p < 0.001). In contrast, the average F0 for CVːˀO words does not differ from CVS words in the first 3/5 of the vowel (first fifth: β = 0.038, p = 0.99; second fifth: β = 2.160, p = 0.56; third fifth: β = −4.971, p = 0.20). During the 4/5 interval, CVSˀ and CVːˀ, and CVːˀS words do not differ from CVS words, and CVːˀO words have a significantly lower average F0 than CVS words (CVS–CVSˀ: β = 9.651, p = 0.03; CVS–CVːˀ: β = 4.46, p = 0.45; CVS–CVːˀO: β = −14.864, p < 0.01; CVS–CVːˀS: β = 1.384, p = 0.75). Finally, in the last fifth of the vowel, only CVːˀS words differ from CVS words by having a significantly lower F0 (CVS–CVSˀ: β = −1.438, p = 0.77; CVS–CVːˀ: β = −2.446, p = 0.72; CVS–CVːˀO: β = −8.885, p = 0.08; CVS–CVːˀS: β = −20.687, p < 0.001). These results indicate that the average F0 for stød-bearing words is significantly higher than for stød-less words in the first part of the syllable rhyme, except for CVːˀO words. I will return to why this may be in the discussion.

In the second F0 analysis, to investigate the timing relationship between the first and second stød phases, the change in F0 over the course of the rhyme per word type was examined. To do so, the average F0 for each fifth of the vowel was calculated for each word type, as well as the average F0 per fifth of the coda sonorant for CVS, CVSˀ, and CVːˀS words. Linear mixed-effects regression models were run for each word type with the average F0 per fifth of the interval, vowel, or sonorant, as the dependent variable and the time interval (first fifth, second fifth, etc.) as a categorical fixed effect. In these models the fixed effect of time interval was sum-coded. Significant effects thus represent intervals for which F0 differed significantly from the overall average F0 across all intervals for that word type. Post hoc Tukey tests were used to establish significant differences between adjacent intervals. The results of the models are shown below in

Table 6. F0 differences from the overall F0 average per word type. ↑ indicates that the average F0 for that interval is significantly higher than the overall average F0 of that word type. ↓ indicates that the average F0 for that interval is significantly lower than the overall average F0 of that word type. Arrows in parentheses indicate marginally significant effects (significant at the 0.05 level), and dashes indicate no significant difference. For CVːˀ and CVːˀO words, the sonorant coda cells are greyed out, indicating the absence of a coda sonorant.

F0 Differences from the Overall Average F0 per Word Type
	Vowel					Sonorant
	1	2	3	4	5	1	2	3	4	5
CVS	—	—	(↓)	↓	↓	—	—	↑	↑	—
CVSˀ	↑	↑	↑	↑	—	(↓)	↓	↓	↓	↓
CVːˀ	↑	↑	(↑)	↓	↓
CVːˀO	↑	↑	—	↓	↓
CVːˀS	↑	↑	↑	↑	↓	↓	↓	↓	↓	↓

, with p values under 0.01 considered significant, following Garellek (2012). For each comparison, ‘↑’ indicates that the average F0 of that interval was significantly higher than the overall average F0 of that word type, and ‘↓’ indicates that the average F0 of that interval was significantly lower. Parentheses indicate marginally significant effects (significant at the 0.05 level only), and dashes indicate no significant difference between the interval’s F0 average and the word type’s overall F0 average. For CVːˀ and CVːˀO words, the sonorant coda cells are greyed out, indicating the absence of a coda sonorant.

As Table 6 shows, over the course of the rhyme, the average F0 for stød-less CVS words follows a different trajectory than the average F0 for stød-bearing words. For CVS words, F0 during the first 2/5 of the vowel is not significantly different from the overall average F0 (first fifth: β = 2.079, p = 0.10; second fifth: β = −1.251, p = 0.32). F0 during the middle of the vowel is marginally lower than the overall average, but this effect did not reach the 0.01 threshold of significance (third fifth: β = −2.882, p = 0.02). Finally, F0 during the 4/5 and 5/5 vowel intervals is significantly lower than the overall average F0 (fourth fifth: β = −3.418, p < 0.01; fifth fifth: β = −5.141, p < 0.001) but significantly higher than the overall average during the 3/5 and 4/5 sonorant intervals (third fifth: β = 4.086, p < 0.01; fourth fifth: β = −4.59, p < 0.001). Post hoc Tukey tests comparing each interval’s average F0 to the preceding interval’s average F0 revealed no significant differences between adjacent intervals. This indicates that the change in F0 over time for CVS words was more gradual and less extreme compared to stød-bearing words, as shown in Figure 6. No other effects for CVS words reached significance.

In contrast to stød-less CVS words, the average F0 during the first 2/5 of the vowel in CVːˀ and CVːˀO words is significantly higher than each word types’ average F0 (first fifth: CVːˀ: β = 15.457, p < 0.001; CVːˀO: β = 9.933, p < 0.001; second fifth: CVːˀ: β = 13.306, p < 0.001; CVːˀO: β = 8.555, p < 0.001). F0 is also marginally higher than the average F0 during the middle of the vowel in CVːˀ words, but this effect did not reach the 0.01 threshold of significance (third fifth: β = 6.011, p = 0.03). For CVːˀ and CVːˀO words, F0 is significantly lower than the average during the last 2/5 of the vowel (fourth fifth: CVːˀ: β = −12.891, p < 0.001; CVːˀO: β = −11.057, p < 0.001; fifth fifth: CVːˀ: β = −21.884, p < 0.001; CVːˀO: β = −6.796, p < 0.001). Post hoc Tukey tests comparing each interval’s average F0 to the preceding interval’s average F0 revealed a significant F0 decrease from the 3/5 to the 4/5 of the vowel in CVːˀ words (β = −18.902, p < 0.001). For CVːˀO words, post hoc Tukey tests revealed a marginally significant decreased in F0 from the 2/5 interval to the 3/5 of the vowel, and a significant decrease in F0 from the 3/5 to the 4/5 of the vowel (second fifth–third fifth: β = −9.189, p = 0.03; third fifth–fourth fifth: β = −10.423, p < 0.01).

Similarly, the average F0 during the first 4/5 of the vowel in CVSˀ and CVːˀS words is significantly higher than each word types’ average F0 (first fifth: CVSˀ: β = 23.776, p < 0.001; CVːˀS: β = 36.486, p < 0.001; second fifth: CVSˀ: β = 21.625, p < 0.001; CVːˀS: β = 33.912, p < 0.001; third fifth: CVSˀ: β = 20.335, p < 0.001; CVːˀS: β = 28.071, p < 0.001; fourth fifth: CVSˀ: β = 14.642, p < 0.001; CVːˀS: β = 14.091, p < 0.001). For CVSˀ words, F0 is marginally lower than the average during the first fifth of the sonorant and significantly lower than the average during every following interval (first fifth: β = −5.089, p = 0.04; second fifth: β = −10.761, p < 0.001; third fifth: β = −19.471, p < 0.001; fourth fifth: β = −25.027, p < 0.001; fourth fifth: β = −22.463, p < 0.001). Post hoc Tukey tests revealed a marginally significant decrease in F0 from the 4/5 vowel interval to the 5/5 interval, but this effect did not reach the 0.01 threshold of significance (fourth fifth–fifth fifth: β = −12.209, p = 0.03). For CVːˀS words, F0 during the final fifth of the vowel is significantly lower than the overall average F0 (β = −9.321, p < 0.001) as well as during every interval of the sonorant coda (first fifth: β = −17.929, p < 0.001; second fifth: β = −20.259, p < 0.001; third fifth: β = −23.311, p < 0.001; fourth fifth β = −21.509, p < 0.001; fifth fifth: β = −20.231, p < 0.001). Post hoc testing further revealed a significant decrease in F0 from the 3/5 vowel interval to the 4/5 interval and from the 4/5 vowel interval to the 5/5 interval (third fifth–fourth fifth: β = −13.979, p < 0.01; fourth fifth–fifth fifth: β = −23.413, p < 0.001). No other main effects or post hoc comparisons between adjacent time intervals were significant.

Overall, the second F0 analysis reveals F0 patterns across stød-bearing word types consistent with previous descriptions of stød, which differ from the F0 trajectory in stød-less CVS words. This is shown in Figure 6. For CVS words, F0 at the beginning of the word does not differ significantly from the average. F0 then decreases towards the end of the vowel, before increasing towards the end of the coda sonorant. In contrast, for stød-bearing words, F0 begins high before decreasing significantly near the center of the words’ sonorant rhyme. For CVːˀ and CVːˀO words in this study, F0 is significantly higher than the average during the first 2/5 of the vowel and significantly lower during the final 2/5. F0 decreased significantly after the middle of the vowel in CVːˀ words, whereas for CVːˀO words, F0 began decreasing slightly earlier, after the first 2/5 of the vowel, though this effect was marginal, and continued decreasing during the middle of the vowel. For CVSˀ words, F0 is high during the first 4/5 of the vowel and low during the last 4/5 of the sonorant. In this study, vowels in CVSˀ words composed approximately 53% of the sonorant rhyme. The sonorant rhyme center therefore usually falls within the last fifth of the vowel. Concurrently, post hoc testing revealed a marginally significant decrease in F0 from the 4/5 to the 5/5 of the vowel. Finally, for CVːˀS words, F0 is high for the first 4/5 of the vowel and low during the final fifth as well as during the entire coda sonorant. In this study, the vowel in CVːˀS words composed approximately 69% of the sonorant rhyme with an average duration of 124 ms (mean sonorant rhyme duration = 180 ms). Therefore, the sonorant rhyme center usually falls within 4/5 interval of the vowel. Concurrently, post hoc tests revealed a significant F0 decrease from the 3/5 to the 4/5 and from the 4/5 to the 5/5 of the vowel. These results are shown in Figure 6. Average sonorant rhyme durations, vowel durations, and coda sonorant durations are given in

Table 7. Average rhyme, vowel, and sonorant durations in milliseconds per word type. Greyed out cells indicate the lack of a sonorant coda for CVːˀ and CVːˀO words.

Word Type	Sonorant Rhyme Duration	Vowel Duration	Coda Sonorant Duration
CVS	139 ms	70 ms	70 ms
CVSˀ	167 ms	90 ms	77 ms
CVːˀ	131 ms	131 ms
CVːˀO	145 ms	145 ms
CVS	180 ms	124 ms	56 ms

.

Together, the two F0 analyses point towards the conclusion that stød is acoustically biphasic, with high F0 relative to stød-less CVS words in the first part of the rhyme and a significant decrease in F0 beginning around the middle of the sonorant rhyme. These results provide evidence for analyses of stød timing such that across word types, the second stød phase is related to the second half of the sonorant rhyme, regardless of word type. These results will be discussed further in the Section 4.

3.2. Stød Onset Timing

3.2.1. Comparing Different Hypotheses of Stød Onset Timing

In this section, only words with stød were analyzed (n = 1014). To analyze stød onset timing, relativized measures were adopted. By expressing stød onset timing as a proportion of the relevant phonological domain (the vowel, coda sonorant, or sonorant rhyme), the measures normalize stød onset timing across CVːˀ, CVːˀO, and CVːˀS words, for which differences in phonetic vowel duration were found (see Section 3.4.1). To compare the timing predictions of the moraic hypothesis, the shared mora hypothesis, and the sonorant rhyme center hypothesis, three measures of stød onset timing were calculated, and the correspondence between measure and hypothesis is given in

Table 8. Predictions made by the moraic hypothesis, shared mora hypothesis, and sonorant rhyme center hypothesis per word type. In each cell, the measure that is proposed to induce the least variability in stød onset timing, according to the stated hypothesis, is given for each word type.

Word Type	Moraic Hypothesis	Shared Mora Hypothesis	Sonorant Rhyme Center Hypothesis
CVSˀ	Coda sonorant measure	Coda sonorant measure	Sonorant rhyme center measure
CVːˀ	Vowel midpoint measure	Vowel midpoint measure
CVːˀO
CVːˀS		Sonorant rhyme center measure

.

The first measure, henceforth the vowel midpoint measure, is a direct reflection of the timing predictions made by the moraic hypothesis for all words with long vowels and by the shared mora hypothesis for CVːˀ and CVːˀO words. For this measure, the stød onset timing is expressed as the difference between stød onset and the vowel midpoint as a percentage of the vowel’s duration. Using this measure, the moraic hypothesis predicts that all words with long vowels will have stød onset times that cluster around 0%, indicating that stød onset is timed to the middle of the long vowel. The shared mora hypothesis predicts that CVːˀ and CVːˀO words will have stød onset times of approximately 0%, whilst CVːˀS words will have a later onset time.

Vowel midpoint measure = ((stød onset − vowel midpoint)/vowel duration) × 100

The second measure, henceforth the coda sonorant measure, represents the predicted timing relationship between stød onset and the syllable in CVSˀ words by both the moraic hypothesis and the shared mora hypothesis. For this measure, stød onset is calculated as the difference between stød onset and the sonorant coda onset, expressed as a percentage of the coda sonorant duration. Both the moraic hypothesis and the shared mora hypothesis predict that CVSˀ words will have stød onset times that cluster around 0%, indicating that stød onset is timed to the onset of the sonorant coda.

Coda sonorant measure = ((stød onset − sonorant coda onset)/sonorant coda duration) × 100

The last measure, the sonorant rhyme center measure, represents the predicted timing relationship between stød onset and the sonorant rhyme center as a percentage of the sonorant rhyme. This measure quantifies the predictions made by the shared mora hypothesis for CVːˀS words, as well as those for all word types made by the sonorant rhyme center hypothesis. The shared mora hypothesis predicts that only CVːˀS words will have stød onset times that cluster around 0%, indicating that stød onset is timed to the center of the sonorant rhyme. In contrast, the sonorant rhyme center hypothesis predicts that all word types will have stød onset times that cluster around 0%.

Sonorant rhyme center measure = ((stød onset − sonorant rhyme midpoint)/sonorant rhyme duration) × 100

As stated in the introduction, variation in production is expected. It is therefore not the absolute timing of stød per utterance that matters, but rather the measure that minimizes variability across the word types. That is, like the c-center effect that has been found for vowel-onset cluster coordination, the measure of stød onset timing that induces the least amount of variability best represents how stød is timed relative to the syllable (Shaw et al. 2011). Here, I adopt standard deviations (SD) as my index of stability. For each word type, the mean and SD of each measure by hypothesis is given below in

Table 9. Means and SDs for measures of stød onset timing by hypothesis and word type, as a percentage of the relevant phonological domain. For CVSˀ and CVːˀS words, the measure which induces less variability is bolded, and columns are combined when multiple hypotheses predict the same timing relationship.

Word Type	Moraic Hypothesis	Shared Mora Hypothesis	Sonorant Rhyme Center Hypothesis
CVSˀ	μ = −12.81, SD = 36.85		μ = −0.50, SD = 15.33
CVːˀ	μ = 9.08, SD = 18.16
CVːˀO	μ = −4.36, SD = 16.82
CVːˀS	μ = 19.50, SD = 22.03		μ = −2.51, SD = 14.45

. These means and SDs are based on the formula specified in Table 8. For CVSˀ and CVːˀS words, the measure which induces the least variability is bolded. For CVːˀ and CVːˀO words, the means and SDs predicted by all hypotheses are the same.

As shown in Table 9, for CVSˀ and CVːˀS words, the sonorant rhyme center measure (bolded) reduces variability compared to the alternative moraic measure. To determine if this difference is significant, a linear mixed-effects model was run for CVSˀ and CVːˀS words with speakers’ SDs per measure type as the dependent variable and word type (CVSˀ versus CVːˀS words) and stød measure type (coda sonorant measure for CVSˀ words and the vowel midpoint measure for CVːˀS words, collectively referred to as the moraic measure, versus the sonorant rhyme center measure for both word types) as categorical fixed effects. The sonorant rhyme center measure for CVSˀ words was the baseline, and speaker was included as a random intercept.

The results show that for both CVSˀ and CVːˀS words, the sonorant rhyme center measure has significantly smaller SDs than the alternative moraic measure (Moraic measure: β = 18.867, p < 0.001) but that the sonorant rhyme center measure does not differ significantly between CVSˀ and CVːˀS words (β = −0.505, p = 0.825), as shown below in Figure 7. An interaction between word type and stød onset measure type was found (β = −11.732, p < 0.01), indicating that the difference between stød onset measures for CVːˀS words was significantly smaller than for CVSˀ words.

3.2.2. Sonorant Rhyme Center Measure Analysis

The results in Section 3.2.1 indicate that the sonorant rhyme center measure represents the most stable timing relationship between stød and the syllable investigated here, evidenced by significantly lower SDs across word types. To determine whether the differences in stød onset timing between word types for the sonorant rhyme center measure are significant, a linear mixed-effects regression model was carried out with stød onset time as a percent difference from the rhyme center (the sonorant rhyme center measure) as the dependent variable and word type as a categorical fixed effect. To determine whether the average stød onset time across the different word types differed significantly from the sonorant rhyme midpoint, the fixed-effect word type was sum-coded and the dependent variable was scaled from −50–50%, centering the measure’s means around 0.

Model results revealed that the model intercept was not significantly different from 0 (β = −0.451, p = 0.834), indicating that the average stød onset time across all word types does not differ significantly from the sonorant rhyme center. CVːˀ words have significantly later stød onset times than the overall average (β = 10.947, p < 0.001), and CVːˀO have significantly earlier stød onset times (β = −3.486, p = 0.03). A post hoc Tukey test found that CVːˀ words have a later stød onset time than all other word types (CVːˀ–CVSˀ: β = 10.320, p < 0.001; CVːˀO–CVːˀ: β = −14.433, p < 0.001; CVːˀS–CVːˀ: β = −12.032, p < 0.001). No other significant effects were found. This is shown in Figure 8. Negative rhyme duration percentages indicate stød onset times in the first 50% of the rhyme, and positive percentages indicate stød onset times in the last 50%.

3.3. Stød Offset Timing

Turning to stød offset timing, preliminary visualization revealed that for all word types with fully sonorant rhymes (CVSˀ, CVːˀ, and CVːˀS), it is usually the case that stød offset occurred after the end of the word (88.36% of tokens). In contrast, CVːˀO words do in fact prevent stød from spreading due to the presence of a coda obstruent, which cannot host stød. Only two CVːˀO words had a stød offset time after the word’s end due to lenition of the word-final stop in [sd̥aːˀb̥] ‘staff/employees’ and [seːˀd̥] ‘seen’ to an approximant, allowing stød to spread beyond the target word. Therefore, unlike stød onset, stød offset cannot be analyzed using a relativized measure, since it consistently takes place at or after the word’s end. Stød offset lag was thus calculated as the raw difference in milliseconds between the offset of stød and the end of the sonorant portion of the syllable rhyme for all word types.

A linear mixed-effects regression model was run with stød offset lag in milliseconds as the continuous dependent variable, word type as a categorical fixed effect, and CVːˀO words as the baseline, as they were expected to have stød offset times near 0 ms. The results show that CVːˀO tokens’ stød offset times did not differ significantly from 0 (β = −0.171, p = 0.943). All other word types have significantly later stød offset times than CVːˀO words (CVSˀ: β = 42.890, p < 0.001; CVːˀ: β = 50.572, p < 0.001; CVːˀS: β = 33.616, p < 0.001). A post hoc Tukey test confirmed these results, additionally finding that CVSˀ and CVːˀ words have later offset times than CVːˀS words (CVːˀS–CVSˀ: β = −9.274, p = 0.01; CVːˀS–CVːˀ: β = −16.956, p < 0.01) but do not differ from each other (CVːˀ–CVSˀ: β = 7.682, p = 0.279). These results are shown in Figure 9.

3.4. Segmental Durations

3.4.1. Vowel Duration

The final set of segmental duration analyses was conducted to address the third research question: is there evidence from segmental durations for morae in Danish? The moraic hypothesis put forth by Basbøll (2005) does not make specific predictions about vowel duration across word types, but if Danish is a moraic language that formulates morae based on the shared mora hypothesis, then, following Morén and Zsiga (2006), vowels in CVːˀS words should be shorter than vowels in CVːˀ words, since the sonorant coda contributes weight to the second mora, which has a preferred length.

To investigate vowel duration, a linear mixed-effects model with vowel duration in milliseconds as a continuous dependent variable and the word type as categorical fixed effects was run with word type sum-coded. The results of the model show that all word types’ vowel durations differ significantly from the overall average. Short vowels in CVS and CVSˀ words are significantly shorter than the overall average (CVS: β = −41.778, p < 0.001; CVSˀ: β = −20.624, p < 0.001), whereas long vowels in CVːˀ, CVːˀO, and CVːˀS words are significantly longer (CVːˀ: β = 18.376, p < 0.001; CVːˀO: β = 33.684, p < 0.001; CVːˀS: β = 12.337, p < 0.001). Post hoc Tukey tests further revealed significant differences between all word types except CVːˀ and CVːˀO words (CVːˀO–CVːˀ: β = 15.038, p = 0.16) and CVːˀ and CVːˀS words (CVːˀS–CVːˀ: β = −6.038, p = 0.85). Vowels in all types of stød-bearing words are also significantly longer than vowels in CVS words (CVSˀ–CVS: β = 21.154, p < 0.001; CVːˀ–CVS: β = 60.154, p < 0.001; CVːˀO–CVS: β = 75.462, p < 0.001; CVːˀS–CVS: β = 54.115, p < 0.001), and long vowels in CVːˀ, CVːˀO, and CVːˀS words are longer than short vowels in CVSˀ words (CVːˀ–CVSˀ: β = 39.000, p < 0.001; CVːˀO–CVSˀ: β = 54.308, p < 0.001; CVːˀS–CVSˀ: β = 32.962, p < 0.001). Finally, vowels in CVːˀS words are significantly shorter than vowels in CVːˀO words (CVːˀS–CVːˀO: β = −21.346, p < 0.001). This is shown below in Figure 10.

3.4.2. Coda Sonorant Duration

Sonorant consonant durations were analyzed to test the predictions of the moraic and the shared mora hypotheses. The moraic hypothesis predicts that non-moraic coda sonorants in CVS words are shorter than moraic codas in CVSˀ words. The shared mora hypothesis is agnostic to the relationship between coda sonorant durations in CVS and CVSˀ words. Rather, the shared mora hypothesis predicts that coda sonorants in CVSˀ words will be significantly longer than coda sonorants in CVːˀS words. To investigate these predictions, a linear mixed-effects regression model with only CVS, CVSˀ, and CVːˀS words (n = 827) was run with sonorant coda duration in milliseconds as a continuous dependent variable and word type as a sum-coded categorical fixed effect. The results of the model show that coda sonorant durations in CVS words do not differ from the overall average (β = 2.677, p = 0.20). In contrast, coda sonorants in CVSˀ words were slightly longer than the overall average (β = 6.852, p = 0.04) and coda sonorants in CVːˀS words were shorter than the overall average (β = −12.363, p < 0.001). Post hoc Tukey tests found a significant difference between sonorant durations in CVS and CVSˀ words compared to CVːˀS words, but not compared to each other (CVːˀS–CVS: β = −15.041, p < 0.001; CVːˀS–CVSˀ: β = −21.893, p < 0.001; CVSˀ–CVS: β = 6.852, p = 0.08). This is shown below in Figure 11.

3.4.3. Sonorant Rhyme Duration

The last durational analysis on overall sonorant rhyme duration was conducted to test the predictions of the shared mora hypothesis, which predicts that all stød-bearing word types will have approximately the same sonorant rhyme duration. To investigate differences between sonorant rhyme durations, a linear mixed-effects model was run with sonorant rhyme duration as a continuous dependent variable and word type as a sum-coded categorical fixed effect. The results show that sonorant rhyme durations for all word types differ significantly from the overall average. CVS, CVːˀ, and CVːˀO words have significantly shorter sonorant rhymes (CVS: β = −16.946, p < 0.001; CVːˀ: β = −28.103, p < 0.001; CVːˀO: β = −13.059, p < 0.001), whereas CVSˀ and CVːˀS words have significantly longer sonorant rhymes compared to the overall average (CVSˀ: β = 10.559, p < 0.001; CVːˀS: β = 21.501, p < 0.001). Post hoc Tukey tests revealed that sonorant rhymes in CVS, CVːˀ, and CVːˀO words do not differ significantly from each other (CVːˀ–CVS: β = −11.157, p = 0.56; CVːˀO–CVS: β = 3.887, p = 0.97; CVːˀO–CVːˀ: β = 15.044, p = 0.25), but are all shorter than sonorant rhymes in CVSˀ and CVːˀS words, which do not differ significantly (CVSˀ–CVS: β = 127.505, p < 0.001; CVːˀS–CVS: β = 38.447, p < 0.001; CVːˀ–CVSˀ: β = −38.662, p < 0.001; CVːˀO–CVSˀ: β = −23.618, p < 0.001; CVːˀS–CVːˀ: β = 49.604, p < 0.001; CVːˀS–CVːˀO: β = 34.560, p < 0.001; CVːˀS–CVSˀ: β = 10.942, p = 0.18). This is shown below in Figure 12.

4. Discussion

4.1. General Discussion

The goals of this study are threefold. The first goal is to determine which hypothesis of stød timing best captures the relationship between stød and the syllable. The second goal is to establish how to model the relationship between stød, a suprasegmental phonation type, and the syllable, using the framework of Articulatory Phonology. The final goal of this study is to assess if there is sufficient independent evidence to substantiate a moraic interpretation of stød timing. I address the first question here, before developing a sketch of glottal phonology in Section 4.2. I show how stød coordination can be modeled in an articulatory framework in Section 4.3. In Section 4.4, I focus on stød realization in CVːˀO and CVːˀ words, the two word types for which stød onset differed significantly from the overall average, before concluding the discussion in Section 4.5, where I discuss the segmental duration analyses with respect to moraic analyses of stød timing.

Overall, the analyses confirmed previous findings that stød realization is biphasic with modal phonation and high F0 in the first part of the syllable rhyme followed by a stød phase proper in the second part of the syllable rhyme. Furthermore, the analyses here support a refinement of this broad statement, such that the first phase is timed relative to the first half of the sonorant rhyme, and the second phase is timed relative to the second half. The first F0 analysis confirmed that F0 in CVSˀ, CVːˀ, and CVːˀS words is higher during the first 3/5 of the vowel than in CVS words. The exception to this pattern was that F0 at the beginning of CVːˀO words did not differ significantly from stød-less CVS words. This is discussed further in Section 4.4. Furthermore, the second F0 analysis revealed that F0 decreases significantly near the middle of the sonorant rhyme across all stød-bearing word types. This result corroborates the findings of the stød onset timing analysis, which confirmed that for the two crucial word types, CVSˀ and CVːˀS, the sonorant rhyme center measure minimized variability in stød onset timing across word types compared to the alternative measures (the sonorant coda measure for CVSˀ words, and the vowel midpoint measure for CVːˀS words), evidenced by significantly lower SDs. The sonorant rhyme center measure also reduces differences in stød onset timing means across word types, all of which cluster around the center of the rhyme. Thus, the results here support the conclusion that the sonorant rhyme center hypothesis best represents the coordination relationship between stød and the syllable, allowing for an interpretation of stød timing that is unified across word types.

The stød offset analysis also has significant implications. In the data presented here, stød spread to the following word in 88.36% of the data, indicating that spillover to a post-tonic syllable is in fact the norm rather than the exception. This is particularly notable for CVːˀS words, as previous work has claimed that the relevant phonological domain of stød is the second half of a long vowel or a coda sonorant in V+S rhymes. This claim has framed stød in coda sonorants in CVːˀS words as both irrelevant to the phonological specification of stød’s domain and, implicitly, as deviant from an ideal stød realization. However, the data here suggest that, rather than being exceptional, stød is nearly always present in the entire latter portion of the sonorant rhyme, regardless of its segmental contents.

Together, the stød onset and stød offset timing analyses show that the sonorant rhyme center hypothesis best captures how stød is realized relative to the syllable. Furthermore, the analyses point towards a conceptualization of stød domain as the sonorant portion of the syllable rhyme, in line with Grønnum and Basbøll (2007), Grønnum et al. (2013), and Grønnum (2015), which unifies the predictions of stød timing across all stød-bearing syllables, regardless of their rhyme’s segmental content. Furthermore, the timing relationship between stød and the syllable can be expressed quite simply using Browman and Goldstein’s theory of Articulatory Phonology (Browman and Goldstein 1986, 1989a, 1989b, 1990, 1992, 2000). In the next subsection, I develop an account of stød timing in which I propose two additions to the theory. First, building on articulatory work from Esling et al. (2019), I develop a theory of glottal articulatory phonology that allows for the theoretical modeling of the biphasic nature of stød. Second, I posit the existence of a new articulatory landmark for coordination, the sonorant rhyme center, and show how integrating this new landmark allows for a straightforward account of stød timing relative to the syllable.

4.2. Developing a Theory of Glottal Articulation

In this section, I develop a theory of glottal articulatory phonology that allows for the theoretical modeling of the biphasic nature of stød. Note that whilst I focus on modeling stød in Danish, this proposal is meant to be a universal addition to Articulatory Phonology which is motivated by and can be used to model the acoustic realization of nonmodal phonation types in multiple languages.

There are several advantages to modeling stød timing using the framework of Articulatory Phonology. First, it dispenses with the need to propose that the relationship between stød and the syllable is mediated by a prosodic intermediary, such as morae. Second, by specifying that the gestures which produce stød have a specific coordination relationship with each other and with a new articulatory landmark, the sonorant rhyme center, the biphasic nature of stød can be straightforwardly accounted for. This is beneficial as it neatly explains why stød affects the first half of the sonorant rhyme differently than the second half, something that previous theories have had to merely stipulate. Third, this approach dispenses with the notion that stød realization is random and not under speakers’ control (Grønnum et al. 2013), which, as this study shows, does not appear to be the case.

In order to model stød realization in Danish, I depart from previous theories of articulatory phonology which treat all glottal phenomena (aspiration, tone, voicing, etc.) as emerging from various states of the glottis (Catford 1964, 1977). Instead, I integrate the view that the larynx is a complex structure composed of multiple articulators (Esling et al. 2019). This allows for the larynx to have numerous possible configurations resulting from the coupling of various laryngeal/glottal gestures which contribute to the acoustic quality of phonation. Crucially, adopting this view allows for the phonological representation of multiple glottal articulators whose gestures can be represented on independent gestural tiers. Here, I operationalize this by dividing the GLO tier into two sub-tiers. The first tier represents articulatory gestures that primarily affect phonation, and the second tier represents articulatory gestures that primarily affect F0. This is shown below in Figure 13 with the addition of the PHON(ATION) sub-tier and the F0 sub-tier.

One motivating factor behind this division is the robust variability in non-modal phonation production, both within and across languages. For example, as Fischer-Jørgensen (1989) notes, Danish speakers consistently showed activation of the cricothyroid in the first part of stød-bearing syllables and increased vocal and ventricular fold constriction in the second part of the syllable. However, speakers varied in their use, and in the extent of their use, of other glottal articulators, such as the lateral cricoarytenoid. Cross-linguistically, Keating et al. (2011) found that the same phonation types (breathy/creaky) differed along multiple acoustic measures between Gujarati, Hmong, Mazatec, and Yi. This may indicate that speakers have phonologized a voice quality contrast, but the precise articulatory configuration that creates the contrast may vary, both within and across languages.

Another motivating factor for this division of the GLO tier is the complex interaction between nonmodal phonation and F0 cross-linguistically. Esposito and Khan (2020) systematically review languages that utilize phonation phonologically, showing that for some non-tonal languages, F0 is used phonetically as a cue for phonation, e.g., Javanese (Brunelle 2010) and Kedang (Samely 1991), whilst for others it is not, e.g., Gujarati12 (Khan 2012), and for others, phonation is a cue for phonological tone, e.g., Mandarin (Yang 2011; Kuang 2017) and Cantonese (Yu and Lam 2014). Furthermore, in some languages, phonation and tone are redundant cues, e.g., Green Hmong (Andruski and Ratliff 2000) and Vietnamese (Alves 1995), whereas in others they seem to act independently of each other, e.g., Mazatec languages (Garellek and Keating 2011). For example, in Yucatec Maya, creaky phonation is accompanied by a preceding phonological high tone (Frazier 2013). However, acoustically, creaky phonation is usually produced with low F0 (Keating et al. 2015), making an argument in which the preceding tone is an acoustic consequence of the same articulatory gesture that produces the following period of creaky phonation difficult. Rather, it seems more likely that separate laryngeal/glottal gestures are involved, one which results in high F0, and another which results in creaky phonation. More evidence that different articulators can be manipulated for phonation and F0 changes comes from Garellek and Keating (2011), who found that in Jalapa Mazatec, phonation did not affect speakers’ F0. Together, these languages show that the interplay of phonation and F0 is complex and multidimensional, and languages differ drastically in the utilization of these acoustic dimensions and how they implement then articulatorily as well as in how they represent them phonologically.

The final argument for the division of the GLO tier comes from articulatory work by Esling et al. (2019). Traditionally in Articulatory Phonology, glottal phenomena are produced by varying degrees of constriction at the glottis, usually formalized of in terms of vocal fold constriction. However, Esling et al. have found robust evidence that glottal constriction is often the result of other glottal articulators’ motion. That is, at the glottal place of articulation, the vocal folds are not always the primary articulators, independent of other laryngeal structures; rather, other laryngeal articulators often affect the state of the vocal folds, and therefore the glottis. For example, Esling et al. (2019) found that glottal stops, usually represented on the GLO tier with the constriction degree [clo(sure)], are often produced with ventricular fold–vocal fold coupling, in which the ventricular folds press down on the vocal folds, increasing the vibratory mass, thereby slowing and eventually ceasing vocal fold vibration, resulting in a full glottal stop. Likewise, a speakers’ F0 can be raised by contraction of the cricothyroid, which lengthens and thins the vocal folds. Accordingly, I have chosen to divide the GLO tier based on phonologized phonation and F0 targets rather than by particular articulators.

The possibility of independence between phonation type (modal, creaky, and breathy) and F0 (phonological pitch or not) cross-linguistically and articulatorily thus empirically motivates the division of the GLO tier as proposed here, allowing for a full and faithful account of the relationship between these two acoustic events. With this structure of the GLO tier in mind, in the subsequent section, I show how this addition to the theory allows for the biphasic realization of stød to be straightforwardly modeled in an articulatory framework. Note that even though here I am only concerned with modeling Danish, this structure may be used to model other languages with a variety of phonation and F0 contrasts, phonological or not. Cross-linguistic work should establish if further subdivisions of the GLO tier are needed, but for the current purposes, the subdivision into the PHON and F0 tiers are sufficient.

4.3. Developing a Model of Gestural Coordination between Stød and the Syllable

In this section, I present the formal analysis of how stød is gesturally coordinated relative to the syllable, as shown below in Figure 14. In these diagrams, gestures are assumed to be audible during their plateaus (from target to release). For readability, in these scores, I use Gafos (2002)-style notation to depict the coordination relationships between different gestures’ articulatory landmarks but separate the gestures onto different tiers. Here, CVS words without stød are shown as a reference to orient the reader towards the notation scheme in Figure 14a, before examples of stød-bearing word are given in Figure 14b–e, and only the coordination relationships between segmental gestures and stød gestures are represented for succinctness. Between the tiers, solid vertical lines represent coordination between a stød gesture’s and a segmental gesture’s landmark, and dotted lines represent coordination between the two stød gestures themselves. Vowel gestures are given in solid lines, consonant gestures in dotted-and-dashed lines, and stød gestures in dashed lines. An audibility schematic is given below each diagram with the articulatory sonorant rhyme center labeled. When the sonorant rhyme consists of only one segment, as in CVːˀ and CVːˀO words, the sonorant rhyme center is the center of the plateau of the TB gesture. When complex, as in CVSˀ and CVːˀS words, the sonorant rhyme center is calculated as the center of the plateaus of the vowel’s TB gesture and the gesture that produces the constriction for the sonorant coda consonant in the oral tract. Note that the two stød gestures in Figure 14b–e are part of the same phonological phenomenon, as indicated by the fact that both are represented by dashed lines, and the F0 gesture is not posited to be a phonological tone. This contrasts with languages such as Yucatec Maya (Frazier 2013), in which creaky phonation is preceded by a phonological high tone. This difference could be represented with differing line types across the PHON and F0 tiers to show their independent phonological status in the language.

In these gestural scores, stød gestures are represented as having the constriction degree value [crit]. For the F0 tier, this is a somewhat arbitrary label meant to evoke the fact that the cricothyroid is contracting, which lengthens and tenses the vocal folds and thus raises F0; currently, there is a dearth of research showing whether different degrees of cricothyroid constriction are distinguished phonologically by speakers. On the PHON tier, the CD value [crit] is nonarbitrary and is based on articulatory descriptions of glottal constriction in Esling et al. (2019) for various laryngeal phenomena, including the production of [h], aspiration, voicelessness, breathy phonation, whispery phonation (similar to breathy phonation but slightly more constricted), creaky phonation, and glottal stops. Based on their descriptions, creaky phonation is produced with greater glottal constriction than [h], aspiration, voicelessness, breathy phonation, and whispery phonation but less constriction than full glottal stops. Concurrently, the second stød gesture, which is often acoustically linked to creaky phonation (Fischer-Jørgensen 1989), is denoted by the CD value [crit], indicating that the glottal aperture is small enough to impede airflow and cause perturbations in vocal fold vibration, leading to aperiodicity.13

The results of this study provide support for a biphasic analysis of stød, such that across word types, the first and second stød gestures are sequentially coordinated. This is shown in Figure 14b–e by the gestural constellation on the PHON and F0 tiers. Across the word types, the target of the first stød gesture (cricothyroid contraction), represented on the F0 tier, is coordinated with respect to the target of the vowel gesture on the TB tier, as shown by the solid vertical line connecting the two. This coordination relationship between the vowel and stød accounts for the presence of modal phonation with high F0 in the first half stød-bearing rhymes.

With regards to the second stød phase, this study finds that across word types, the PHON gesture of stød (ventricular fold-vocal fold coupling, following from Fischer-Jørgensen (1989)’s articulatory study of stød) is coordinated with respect to the center of the sonorant rhyme, as shown in Figure 14b–e. This finding necessitates the addition of a new articulatory landmark, the sonorant rhyme center, which can enter into coordination relationships with other gestures. This relationship is shown by the solid vertical line connecting the second stød gesture on the PHON tier and sonorant rhyme center on the TB tier. This relationship between stød and the sonorant rhyme is reminiscent of the c-center effect found for complex onsets. That is, just as the timing of vowel gestures is most stable relative to the center of an onset consonant (cluster) gesture(s), the timing of the target of the stød phase proper (the point at which it becomes audible) is most stable relative to the center of the sonorant rhyme, which, like onsets, may be complex.

Finally, turning to the relationship between the two stød gestures themselves, the results of the second F0 analysis show that across word types the decrease in F0 aligns with the onset of the stød phase proper at the sonorant rhyme center. This could be for two reasons. The first is that the F0 stød gesture releases at the sonorant rhyme onset, leading to a decrease in F0. The second is that the F0 stød gesture does not release at the sonorant rhyme center, but the second stød gesture on the PHON tier is what leads to the F0 decrease, as creaky phonation is associated with low F0. Differentiating between these two possibilities is difficult when lacking articulatory data. Therefore, here, I choose to represent the relationship between the two stød gestures such that the onset of the second stød gesture, represented on the PHON tier, coordinates with respect to the release of the first stød gesture on the F0 tier, as shown by the dashed vertical line connecting the two stød gestures in Figure 14b–e. This posits a maximally strong interpretation for the F0 decrease in the middle of the rhyme—that is, at the sonorant rhyme center, the F0 gesture is at the release point, and the PHON gesture reaches its target, leading to a decrease in F0. Further articulatory work on the exact coordination between the two stød gestures is needed to confirm this coordination relationship.

Thus, by proposing that the sonorant rhyme is a formal phonological unit that can enter into timing relationships with other gestures, the notion of morae can be dispensed with for this particular phenomenon, and the stød gestural constellation can be coordinated relative to the syllable without a prosodic intermediary. Furthermore, the biphasic nature of stød with its modal phonation and high F0 in the first half of the rhyme and nonmodal, often creaky phonation in the second half can be straightforwardly accounted for as a natural byproduct of the specific timing relationships between the gestures that produce stød without having to specify that Danish has a phonological high tone. Finally, this theory dispenses with the notion that stød realization is random and not under speakers’ control, providing an alternative theory of coordination that is predictive of stød coordination in other types of words.

4.4. Stød in CVːˀO and CVːˀ Words

As shown in Figure 14b–e, the target of the second stød phase is posited to be phonologically linked to the sonorant rhyme midpoint. This timing relationship holds well for CVSˀ and CVːˀS words. However, the results of the stød onset analysis revealed that the second stød phase began significantly earlier in CVːˀO words and significantly later CVːˀ words, compared to the overall average. What, then, may be responsible for these start times?

First, with respect to CVːˀO words, it is notable that the coordination relationship between stød and the sonorant rhyme, as shown in Figure 14d, predicts that the second stød phase should only be audible for less than half of the vowel. This is due to coarticulatory overlap between the end of the vowel gesture and the beginning of the voiceless coda gesture, which is assumed to acoustically mask the end of the vowel. The center of the articulatory sonorant rhyme therefore occurs after the auditory center of the vowel (Browman and Goldstein 2000). Thus, if stød does gesturally coordinate with the sonorant rhyme center, this predicts later stød onset times for CVːˀO words than for other words with long vowels. Despite this prediction, the acoustic data in this study suggest that the onset of the second stød phase in CVːˀO words occurs earlier than the overall average across word types. What, then, leads to this early onset?

One explanation for this could be that the stød phase proper begins early relative to the articulatory sonorant rhyme center to maximize its perceptibility in CVːˀO words. This is in line with other studies which have shown that gestures may realign in order to increase the recoverability of a segment (Löfqvist and Yoshioka 1980, 1981; Löfqvist and McGarr 1987; Munhall and Löfqvist 1992; Byrd 1996; Chitoran et al. 2002). For example, stop–stop clusters, in which the release of the first stop is its only percept, exhibit less gestural overlap within the cluster than in other phrasal positions to preserve the release of the first stop (Byrd 1996; Chitoran et al. 2002).

Similarly, I propose that here the [wide] gesture of the coda obstruent (coda obstruents in Danish are voiceless) on the PHON tier is what causes the gestural realignment between the second stød gesture and the rhyme. If the second stød gesture were to align with the sonorant rhyme center in CVːˀO words, its duration would be relatively short due to the presence of the following [wide] gesture of the coda obstruent. This could make recoverability more difficult for listeners. By beginning the second stød gesture earlier, the duration of the second stød phase increases, thereby increasing its perceptibility, as shown in Figure 15. This early coordination of the second stød gesture also explains why F0 at the beginning of CVːˀO and CVS words is not significantly different. If the PHON stød gesture is coordinated relatively early, then low F0, an acoustic correlate of creaky phonation, may depress the F0 effects of the first stød gesture to the point that the average F0 across the first 3/5 of the vowel do not differ significantly from stød-less words.

Other evidence that supports the hypothesis that speakers make articulatory adjustments to increase stød’s perceptibility comes from the durational data. As shown in the vowel duration analysis, long vowels in CVːˀO and CVːˀ words are phonetically the longest vowels analyzed here. This is somewhat unexpected, given that in many languages vowels in closed syllables tend to be phonetically shorter than in open syllables (e.g., Thai). It may therefore be the case that speakers phonetically lengthen vowels in CVːˀO words in order to increase the domain during which stød can be realized. This argument is supported by typological data, such that there is a cross-linguistic tendency for phonologically complex tones to only appear in syllables with phonetically long sonorant rhymes (Gordon 2004; Zhang 2004). Furthermore, this vowel lengthening is similar to what has been found for other languages, such as Hausa (Zhang 2002). Zhang (2002) found that in Hausa, vowels in CVO syllables with the complex falling HL tone are phonetically longer than vowels in CVO syllables with simple H or L tones.14 Zhang interprets these findings to mean that the lengthening occurs to support the HL tone, which requires a longer duration to be realized than an H or L tone. Similarly, the lengthening of long vowels in CVːˀO words in Danish may be interpreted as compensatory, given that stød cannot spread to a post-tonic syllable. Therefore, to increase stød duration, speakers may lengthen vowels in CVːˀO words.

Turning to stød in CVːˀ words, a gestural score of the phonetic realization of stød in CVːˀ words is shown below in Figure 16. Note that the second stød phase begins after the sonorant rhyme center. Here, the discussion is more speculative, though of note is that during the first stød phase, F0 begins higher in CVːˀ words than any other word type. In fact, the F0 in CVːˀ words is significantly higher than the F0 in CVS and CVːˀO words during the first 3/5 of the vowel, before decreasing sharply after the 3/5 interval of the vowel. The late onset of the second stød phase may therefore be a phonetic consequence of the relatively high starting point of F0 in CVːˀ words. Why, then, does F0 begin so high in CVːˀ words?

Again, one potential explanation is a perceptual one. Of the stød-bearing words examined here, CVːˀ words have the shortest sonorant rhyme, which did not differ significantly from CVS or CVːˀO words. Furthermore, the stød offset analysis revealed that stød does not spread more outside of CVːˀ words than other types of words, e.g., CVSˀ words. This indicates that in CVːˀ words, stød is being realized over a relatively short domain, which speakers may try to compensate for by enhancing the phonetic realizations of the stød phases to aid listeners’ perception of stød. This phonetic enhancement could result in relatively high F0 at the beginning of stød-bearing syllables, which in turn may lead to late onset times for the second stød phase. However, this explanation is still speculative, and further investigation of the relationship between the sonorant rhyme duration, F0, and creak onset timing in CVːˀ words is needed.

4.5. Durational Data with Respect to Morae in Danish

In the final section of the discussion, I discuss the results of the durational analyses as they pertain to the moraic hypothesis and the shared mora hypothesis of stød timing.

First, coda sonorant durations in CVS and CVSˀ words were compared, following the prediction from Basbøll (1985, 2005) that moraic codas are longer than nonmoraic codas. The results here show that coda sonorants CVS and CVSˀ words do not differ significantly in duration, replicating previous findings (Grønnum and Basbøll 2001). This study thus finds no independent evidence to support a moraic interpretation of the data, given the traditional view of moraic formulation.

Second, duration measures were examined under the working hypothesis that similar sonorant rhyme durations across all word types indicate that morae have a predefined length in Danish, as in Thai (Morén and Zsiga 2006). Following from this, vowels in CVːˀS words are expected to be shorter than vowels in CVːˀ and CVːˀO words, and coda sonorants in CVːˀS are expected to be shorter than those in CVSˀ words, in order to preserve the relatively fixed length of the mora. Given that obstruents in Danish do not contribute to morae, unlike in Thai, vowels in CVːˀO words and CVːˀ words are predicted to be similar in duration.

The results of the rhyme duration analysis revealed significant differences such that CVSˀ and CVːˀS words have significantly longer sonorant rhyme durations than CVːˀ and CVːˀO words. This is likely due to the fact that CVSˀ and CVːˀS words have two sonorant segments in the rhyme, whereas CVːˀ and CVːˀO words only contain one. Furthermore, the vowel duration analysis revealed no significant differences in vowel duration between CVːˀ and CVːˀS words. With respect to the coda sonorant duration analysis, the results revealed that coda sonorants in CVːˀS words are significantly shorter than coda sonorants in CVSˀ words, as predicted by the shared mora hypothesis. However, the coda sonorants do not shorten to the point that the sonorant rhyme in CVːˀS words is commensurate in length to that of CVːˀ words, casting doubt as to whether the shortening of coda sonorants in CVːˀS words in Danish is due to an abstract phonological preference to preserve the duration of mora, as in Thai.

Overall, this study does not find sufficient evidence to interpret the acoustic findings as supporting either moraic analysis of stød timing. Of the four acoustic measures investigated, only one result was in line with the predictions of the shared mora analysis. Furthermore, as previously stated, morae do not play any role in Danish other than to explain the distribution of stød-bearing syllables. For example, stress in Danish is free and is not sensitive to syllable weight (Grønnum 1998). I therefore reject a moraic interpretation of the data here and conclude that a gestural theory of stød coordination relative to the syllables’ sonorant rhyme better captures the timing relationship between stød and the syllable.

5. Conclusions

In conclusion, this study contributes to the body of work finding that stød in Danish is realized as biphasic, with modal phonation and high F0 at the beginning of stød-bearing rhymes and non-modal, often creaky phonation at the end of stød-bearing rhymes. The study also finds new evidence that the stød phase proper is timed with respect to the center of the sonorant rhyme across word types examined here and not to morae. This finding is formalized in the discussion, where I expand upon previous theories of articulatory phonology in order to capture the biphasic nature of stød realization. This expansion of the theory has implications for theories of Articulatory Phonology, allowing for the modeling of many complex glottal phenomena which have yet to receive adequate attention under this framework. A new articulatory landmark, the sonorant rhyme center, is also posited, which can enter into coordination relationships with other gestures. Finally, this study rejects a moraic interpretation of the data, showing that there is no unambiguous, independent evidence for morae in Danish.