2.1 Length trade-off: Estonian and English

Estonian is famous for its three degrees of length (short/Q1, long/Q2, overlong/Q3; with Q = quantity) in both vowels and consonants, and the literature is legion (Posti 1950; Lehiste 1960; 1965; Hint 1973; Tauli 1973; Ojamaa 1976; Prince 1980; Bye 1997; Hint 1998). In contrast, “English overlength” is not a term one is likely to come across in the literature, though the effect it refers to is well known by another name: (Lack of) “pre-fortis clipping” (literature anon). Pöchtrager (2006; 2015) argues in detail why both phenomena should be treated in the same fashion, even though mainstream accounts usually do not, and we will look at the main points here very quickly. Consider first the examples in Table 1.⁴

Table 1 gives three monosyllabic words in Estonian (examples from Ojamaa 1976: 9 and passim), which show a trade-off in length: The more room is taken up by the consonant (C), the less remains for the preceding vowel (V) and vice versa. Put differently, the difference between each pair of words lies not only in the length of the vowel, but also that of the consonant. This is of course problematic for a phonemic analysis, which was pointed out as early as Ojamaa (1976), since any two members of the triplet differ from one another in two aspects, making localisation of a phonemic contrast impossible. The fact that the lengths of vowels and consonants are less restricted in bisyllabic words (more precisely: paroxytones, to which we shall turn shortly) does not invalidate the mutual dependency between the vowel and the consonant in monosyllabic words.⁵

If looked at the right way, striking parallels can be seen in English, as the right-hand side of Table 1 already suggests. From a phonological point of view, English bead/beat are usually taken as a minimal pair differing in the final consonant only. However, when looking at the phonetic realisation, two differences are discernible: Not only do these words differ in the final consonant, the vowel before the lenis consonant d is also much longer than that before the fortis t. (Put differently, the fortis consonant clips the length of the vowel, as this is usually presented.) In an account that insists on the final consonant being the only phonological difference in bead/beat, any difference in vowel length must be relegated to the status of “purely allophonic” and as devoid of phonological significance. But the rejection of the phoneme (and hence the distinction between phonemic and allophonic) was one of the earliest defining characteristics of Generative Phonology, cf. Halle (1959), Chomsky (1964). Government Phonology is a clearly generativist model where the phoneme/allophone dichotomy plays no role.⁶ The alternative then, is to take the difference in vowel length seriously⁷ and to ask why a difference in consonant quality has an effect on vowel quantity. In an account taking the fortis/lenis difference in consonants as qualitative (one series possessing a quality that the other lacks, no matter which way expressed) this is indeed puzzling. But this is only one possible interpretation of the facts, and there is an alternative, which requires that we change our traditional way of looking at things a second time. If fortis/lenis is interpreted as quantitative (as indeed it is, going by duration), with lenis the shorter counterpart of fortis, then differences in vowel length follow quite easily: We are faced with a trade-off entirely parallel to the one in Estonian (Pöchtrager 2006; 2015). The more room is taken up by the consonant, the less remains for the preceding vowel.⁸ A Q1 consonant will be preceded by a Q3 vowel, a Q2 consonant by a Q2 vowel; in both languages. In other words, a representational format that is needed independently in order to capture the length trade-off in Estonian (the left side of Table 1) will provide the means to handle the English facts, too.⁹

Now, what makes the issue somewhat more complex is that in English, and unlike Estonian, two different dimensions of length are distinguished, and those two dimensions need to be considered individually. The vowels in bead/beat are lexically long, in contrast to words pairs like bid/bit, where the vowels in both words are lexically short.¹⁰ But in each pair, the vowel will be shorter before fortis t, independently of whether we are dealing with a vowel that is lexically long or short. The literature is quite substantial (Heffner 1937; Rositzke 1939; Denes 1955; Peterson & Lehiste 1960; Klatt 1976; Luce & Charles-Luce 1985; Crystal & House 1988). This dimension of length that is sensitive to the following material will be referred to as phonological length. (As the pair bit/beat shows, the lexical length of the vowel is not sensitive to its environment, as the consonantal environments are identical here.) The axis of lexical length intersects with the axis of phonological length, giving rise to the four-way distinction that we see in Table 2.¹¹

The four-way distinction as such is nothing new, though it is usually interpreted differently, as we have already said. (Lexically short/long is usually interpreted as short/long and/or tense/lax; while phonologically short/long is typically ignored as allophonic.) The alternative interpretation adopted here brings out parallels between Estonian and English that would otherwise go unnoticed. As we shall see anon, the similarities go even deeper.

The discussion so far has focused on monosyllabic words, whose behaviour generalises to oxytones. What is relevant is not so much that the forms are monosyllabic but that stress is final: The trade-off in bead/beat could also have been illustrated by recede/receipt. In paroxytones the situation is slightly different, as a (line-by-line) comparison of the words in Table 3 shows.

That is, a trade-off (and thus phonological length) is possible in oxytones (segment (a) of Table 3), but not in paroxytones (segment (b) of Table 3). Here, the literature is somewhat less extensive (Lisker 1957; Lehiste 1970; Umeda 1975; Luce & Charles-Luce & McLennan 1999). The effects that a lenis consonant has on the preceding stressed vowel are quite dramatic in oxytones and lead to length ratios of around 1: 1.9, whereas for paroxytones the ratio is around roughly 1: 1.1, and only unreliably so, with absolute differences often close or below the threshold of perception, cf. Lehiste (1976).

The lack of phonological length in English paroxytones has a counterpart in Estonian, as can be seen in Table 4, whose organisation parallels Table 3.¹²

Segment (a) of Table 4 presents combinations of a Q3 vowel and a Q1 consonant as well as of a Q1 vowel and a Q3 consonant in oxytones, with a trade-off just as expected based on what we saw in Table 1. In segment (b.i) of Table 4 we see that the Q1 nasal m is not preceded by a Q3 vowel, but only by one that is Q2, and in segment (b.ii) a Q1 vowel is followed by a Q2 consonant, not by one in Q3. The lack of vowels/consonants in Q3 in paroxytones will be taken up again in sections 2.5 and 5.1. What is crucial for us is that there is such a gap with respect to Q3, just as there is in English.

Now that the table is set we can look in more detail at several parallels between the distribution of stød and that of length, while keeping in mind the crucial differences that do exist. The areas we will consider are briefly outlined in (7–8), with (7) focusing on the parallels and (8) on the differences.

This looks like a random collection of contexts and conditions. Their interconnectedness will become clear as the analysis proceeds, showing that there is nothing random about that list. Furthermore, it is possible to reinterpret the content of (8a), to be presented in section 2.6, in such a way that it can be seen as a parallel, rather than a point of difference between Danish and Estonian/English. That is, (8a) might well have to be grouped with (7). We will address this reinterpretation (and also the unclear aspects that remain) in section 5.5.

2.2 Stress as a necessary ingredient

A certain amount of prosodic prominence is a necessary condition for both stød and length trade-off.¹³ Thus, function words, which are usually unstressed, are not eligible for either one, cf. Table 5.

In Danish fon we find stød and stress, and in the morphologically related form fonem, where stress shifts to the end, stød becomes impossible on the first nucleus. The same can be said for phonological length in English, where overlength (of the diphthong in this case) requires stress. Estonian, with its main stress firmly fixed on the first syllable in the majority of cases, does not furnish a comparable example, but again, Q3 vowels or consonants are impossible in the absence of stress.

2.3 Behaviour of vowel-final oxytones

Oxytones ending in a vowel are overlong/take stød, as shown in Table 6.¹⁴

For Danish, this is of course in accordance with (2) since we are dealing with an odd-numbered syllable. Words of this type must have a long vowel which is then automatically accompanied by stød. For Danish and English there is no trade-off to speak of (since there is no following consonant), and the vowel by itself is overlong. The lack of a final consonant as a confounding factor (cf. section 2.7) makes this case ideally suited for understanding the nature of stød, as section 3.1 will show.

2.4 Behaviour of paroxytones (without analytic morphology)

Paroxytones do not allow stød and do not show a length trade-off, provided that they are morphologically simplex, or that they involve non-analytic morphology (Kaye 1995) at most (Table 7).¹⁵

For Danish, this is of course the condition in (2) that only odd-numbered syllables qualify. Crucially, the same restriction applies in English and Estonian when it comes to where overlength is possible, as we saw in the discussion in section 2.1.

2.5 Interaction with morphological structure

Taking morphological structure into consideration is crucial for both stød and overlength. Consider the apparent minimal pairs in Table 8, where round brackets indicate the relevant grouping. “Apparent”, in that the examples are not only distinguished by the presence/absence of stød/overlength, but also differ in their morphological structure.

For each language two paroxytones are compared. In the English example, taken from Abercrombie (1964), to is interpreted as a clitic attaching to the preceding word. One member of each pair shows stød/overlength, which is not what we expect given what have been saying about paroxytones and how they differ from oxytones. As the bracketing already suggests, morphological structure plays a crucial role, in that a pair like Danish [muː^ʔsən]/[muːsən] is really to be treated as oxytone plus suffix versus paroxytone plus suffix. What is crucial for us at this stage is that the deviation goes in the same direction in all three languages: We find stød/overlength in the same unexpected position (paroxytone) under the same circumstances (i.e. when the paroxytone is the result of morphological concatenation).

Not controlling for morphological structure in Estonian leads to claims such that a classic example like lina [lina] ‘linen’, linna [linːa] ‘city gen.sg.’, linna [linːːa] ‘city par.sg.’ would be minimal triplets establishing an independent quantity contrast between Q1, Q2, and Q3 in paroxytones. That this is problematic has already been suggested in footnote 5. Firstly, the length of the unstressed vowel is not constant, and we could also write [linaˑ]/[linːaˑ]/[linːːa] (one, if not the first to point out the significance of this, was Posti 1950). This already makes the triplet non-minimal. Secondly, cases with a Q3 consonant in a paroxytone, like the last form [linːːa], are always morphologically complex, while paroxytones with Q2 may or may not be.¹⁶

So far we have looked at aspects where the three languages show similarities. Any analysis capitalising on those will have to make sure that the differences that do exist are also accounted for. We will look at two important differences in the next two sections.

2.6 Behaviour of consonant-final oxytones

As we saw in section 2.1, both in English and Estonian oxytones, the (phonological) length of the vowel depends (to some extent) on the nature of the final consonant or cluster. (Of course this is not the case for lexical length in English, as in bit/beat, at least not in words ending in a single consonant.) This relationship can be seen as a trade-off in length, on the condition that the fortis/lenis contrast is reinterpreted as quantitative, instead of qualitative. The phonological length of the vowel then correlates inversely with the quantity of the final consonant: Q1 (lenis) or Q2 (fortis) or, in the case of Estonian (cf. footnote 9), Q3 (geminate).

Here, Danish differs in two aspects: For one thing, the fortis/lenis distinction, to the extent that anything is left of it, does not seem to have an effect on stød. Before a stressed vowel, Danish shows a contrast in stops (pil [piː^ʔl] ‘arrow’/bil [biː^ʔl] ‘car’) and (some) fricatives (falk [fal^ʔɡ] ‘falcon’/valg [val^ʔ(j)] ‘choice’).¹⁷ Nearly all of that is gone post-vocalically, with many obstruents having lenited into approximants. And even in cases where a (very non-minimal) contrast can be constructed, such as chef [ɕɛː^ʔf] ‘boss’ (ending in a fortis consonant) vs. sen [seː^ʔn] ‘late’ (ending in a lenis consonant), the nature of the final consonant has no effect on the occurrence of stød; both words have it. This is also illustrated by several of the words in (1a). The important factor is of course the long vowel, which guarantees that the syllable is bimoraic.

This leads naturally to the second aspect where Danish differs from the other two languages: In case the vowel is short (monomoraic), the nature of the following consonant does become relevant. But here it is the distinction between sonorants and obstruents that plays a role. Only a sonorant can provide the second mora that stød requires; an obstruent never can, as already illustrated in (1) with several examples. The contrast between Danish and the other two languages is tabulated in Table 9.

Table 9

Type of final consonant.

Even though it seems blatantly obvious that the distinction between obstruents and sonorants is relevant for Danish stød, we will have to reappraise the issue in section 5.5.

2.7 Stød possible vs. necessary

Let us finally address one remaining issue that clearly sets apart Danish on the one hand from English and Estonian on the other. That is the question to what extent stød is fully predictable, as opposed to the trade-off in length. While the latter must happen (if the conditions are met), the former can: An English/Estonian oxytone ending in a single Q1/lenis consonant will be preceded by a vowel that is (phonologically) long. On the other hand, a Danish oxytone with a short vowel and a sonorant consonant can or cannot have stød, as shown in Table 10. Note that [ð̞] is an approximant and thus a sonorant.

In final position, Danish has laid waste to many of its consonantal contrasts and many former obstruents have turned into approximants (thus sonorants). In addition, preceding vowels have often been shortened (when not short to begin with). Earlier liv [liː^ʔv] ‘life’, for example, has been all but replaced by modern [liʊ̯^ʔ] (Brink & Lund 1975). These changes, along with the loss of r (footnote 14), have increased the number of examples that could be added to Table 10, on either side. In some cases there is even variation, as in the last example.

2.8 Interim summary

The parallels in previous sections 2.2–2.5 taken together suggest that the analysis of English/Estonian can shed light on Danish. Stød and overlength seem to share a common property at some level of abstraction that would explain the similarities in distribution, while at the same time making sure that the differences in sections 2.6–2.7 are adequately accounted for. Having addressed the first claim in (6a), viz. that the distributional pattern of Danish stød is neither specific to Danish nor to stød, we will now move on to the second claim in (6b), that the location of stød (the special status of the mora) can be derived.

This requires that we look at how stød is actually represented, which is the subject matter of the next section.

3.1 Stød as a relational concept

We will begin with the simplest cases, and come back to the fortis/lenis contrast later when discussing English in section 4.1. As we saw in section 2.3, vowel-final oxytones always show overlength and stød, with some qualifications as given in footnote 14. The representations in (9) contrast the relevant parts (i.e. the nuclei) of English bee (with an overlong vowel) and Danish bi [biː^ʔ] (with a long vowel and stød).

In both examples the stressed vowel has the nuclear head xn at its core. This head xn is annotated with the element I, since we are dealing with a high front vowel. Heads combine with other material (the terminals x₁ and x₂ in this example, projections of other heads in later examples) to form x-bar like structures that express constituency. The head xn expands to its maximal size, n″, which for Estonian is true of all stressed nuclei and for English of vowel-final oxytones.¹⁹

The arrows in (9a) indicate melodic command (or m-command for short), which ensures that the m-commandee receives the same interpretation as the m-commander.²⁰ Since xn m-commands both x₁ and x₂ all three positions receive the same interpretation and we get an overlong, high front vowel. Exactly the same could be said about an Estonian word like pii ‘tooth (of a comb)’.

Danish differs, and I submit that there are two differences. Firstly, there is no m-command from xn to x₂. I will assume that this is linked to the generally weak status of the word-final position in Danish, cf. section 2.6 and footnote 14: The position is still there, but it is not made use of. (That it is still there will become relevant in just a moment.) Secondly, there is also no m-command going from xn to x₁. Instead, what we find is a relationship called control. This relationship is what is responsible for stopness in consonants (Pöchtrager 2006; 2021c), and here it is extended to express laryngealisation in vowels, an equivalence established in Backley (2011: 122–124) (for the old stop element ʔ, though). The positions xn and x₁, together with the relationship of control holding between the two, gives us a long (but not overlong) vowel with stød. As we shall see in section 4.2, long vowels without stød also comprise two positions. The particular representation chosen for a long vowel with stød in (9b) captures that fact that long vowels with and without stød are of the same duration (Basbøll 1988: 121); each kind involves two skeletal positions. At the same time, the relational nature of control allows us to make sense of why stød occurs in the second half of the vowel: x₁ (which represents this second half) is on the receiving end of an asymmetric relationship with the nuclear head xn to its left; stød is the audible realisation of x₁ being controlled. The special status of Basbøll’s “second mora” falls out. We will return to the notion “mora” once again in section 5.2.

Let us look at control in a bit more detail. Control is very local in that it can only hold between a head and its sister; this is obviously met in (9b). In contrast, m-command is not limited to sisters of heads, as can be seen in (9a) and in several examples later on. In addition, there is a weird property of control in that it is only possible if the specifier position is available. “Available” here means (i) that it is present (rather self-explanatory) and (ii) that it forms part of the same syllable. The relevance of the first condition will become clearer in the next section, 3.2, where we will look at what happens when there is no specifier. The second condition will be of key importance in section 4.2, since it not only captures the conditions under which stød can occur in oxytones, but also predicts that stød is not found in paroxytones. This condition, that the establishment of a relationship between a head and its sister should depend on yet a third position, the specifier, seems surprising, but it is also true of consonants; cf. Pöchtrager (2006: 2.3.2.) and (in particular) Pöchtrager (2021c), as well as section 5.4, where we will return to that issue for stops and affricates and see that once again control between head and complement depends on the availability of a specifier. At this point, this connection between head, complement, and specifier is a poorly understood axiom of the theory, but one that will get us a long way, also in Danish: Many further aspects of stød can be derived from it. We will turn to consonant-final oxytones next to illustrate this. To make things more manageable we will divide up that group into cases with (at least a potential for) stød and those without.

3.2 Stød: extension to consonant-final oxytones

The basic x-bar structure in (9b) affords us three positions to utilise: head, complement, and specifier. In the last section we looked at vowel-final oxytones like Danish bi [biː^ʔ] and saw how the specifier remained empty (despite being present), with stød ensuing as a result of a control relationship between head and complement. This leads us to expect that any time the specifier is present we should find stød.

Now, in consonant-final oxytones (such as skib ‘ship’ [sɡiː^ʔb] or film ‘film’ [fil^ʔm]), consonants will also have to fit into this basic scaffolding. The (nuclear) head will always represent a short vowel or the first half of a long one, which still leaves us with two other positions, the complement and the specifier. If the vowel is long (i.e. takes up the head and the complement), then any final consonant can only sit in the specifier. If the vowel is short and there are two consonants following, then one will sit in the complement and the other in the specifier. This is the maximum for (most) Danish oxytones that are morphologically simplex, which is of course similar to what we find in other Germanic languages.²¹

In this way, our basic x-bar structure provides an upper cap for the complexity of phonological structures. (This limit is expressed in terms of a familiar notion in linguistic theory, rather than an arbitrary numerical maximum on mora counts.) At the same time, we make predictions about the occurrence of stød, since (at least in Danish) the presence of a specifier guarantees control between a head and the complement. With this in mind, consider (10), which shows all the logical possibilities for consonant-final oxytones with (at least the potential for) stød: If the vowel is long (coded as V+V), only one consonant is possible (in the specifier). If the vowel is short and there is a (sonorant) consonant in the complement, then the specifier can be filled or not.

What stands out is that stød is guaranteed when both complement and specifier are used up as in (10a, c). This is exactly what we predict.²² In (10b), where there is only a single sonorant following a short vowel, there are lexical differences. It might not be obvious yet, but (10b) can be made to follow from our account as well. Let us walk through a representative example for each type.

In the type represented by (10a) we have a long vowel (head and complement positions) and a single consonant, which must sit in the specifier. We correctly predict stød, as shown in (11), giving the relevant part of the word skib ‘ship’ [sɡi:^ʔb]. The ‘o’ stands for the final stop, whose internal structure is irrelevant at the moment.²³ Note that it is also irrelevant whether the final consonant is an obstruent, as in skib ‘ship’ [sɡi:^ʔb], or a sonorant, as in bil ‘car’ [biː^ʔl]. What matters is that it can only sit in the specifier position given that the preceding vowel takes up two positions.

Next let us take type (10b), where we see lexical variation. I propose that (the relevant part of) a word like pen ‘pen’ [pɛn^ʔ] (with stød) has the representation in (12a), while (12b) gives ven ‘friend’ [vɛn] (without stød).

Both words end in a sonorant, abbreviated as ‘O’ (cf. footnote 23), which sits in the complement position both times. The two words differ in whether there is a specifier or not. If there is a specifier we get stød, since the nuclear head xn will control its complement,²⁴ otherwise we will not.

That there should be lexical differences exactly in this type is expected under our account, where we have three positions at our disposal (head, complement, specifier), but only two objects (short vowel and sonorant) to house. It is precisely the cases where the specifier is not needed for a consonant that there is this freedom for the specifier to be present or absent.²⁵

Finally, let us address (10a), with a short vowel followed by two consonants, the first of which a sonorant, such as folk ‘people’ [fʌl^ʔg] or film ‘film’ [fil^ʔm]. Again, we (correctly) predict that there will be stød since both the complement and (crucially) the specifier are taken up by the consonants. (13) illustrates this with the relevant part of film ‘film’ [fil^ʔm].

The only difference between film ‘film’ [fil^ʔm] in (13) and pen ‘pen’ [pɛn^ʔ] in (12a) is that in the former there are two consonants, the second of which has to sit in the specifier. Stød ensues automatically.

Let us contrast our results so far to the analysis given in Basbøll (1988). I will focus on the difference between (10b) vs. (10a, c), i.e. why we find a contrast like pen ‘pen’ [pɛn^ʔ] as opposed to ven ‘friend’ [vɛn], while words like skib ‘ship’ [sɡiː^ʔb] or folk ‘people’ [fʌl^ʔg] are guaranteed stød. In Basbøll (1988) this result is achieved as follows: (i) Long vowels as in skib ‘ship’ [sɡi:^ʔb] are always bimoraic, which automatically qualifies the syllable for stød, accounting for why long vowels have stød (10a). (ii) Sonorants between a short vowel and another consonant (e.g. in folk ‘people’ [fʌl^ʔɡ]) are assumed to be lengthened by rule and thus become moraic. Together with the mora from the preceding short vowel the entire syllable becomes bimoraic. We derive why the sonorant consonant will have stød in those cases, i.e. (10c). (iii) Sonorants that are preceded by a short vowel but are not in turn followed by a consonant are lexically marked as long or short, which in turn determines whether they are moraic or not, giving us the two subtypes in (10b).

While this derives the correct result, there are certain problematic assumptions. For one thing, the length difference assumed in (iii) is far from obvious, and attempts to measure it have failed or yielded inconclusive results at best (Grønnum & Basbøll 2001).²⁶ No difference in (underlying) length needs to be assumed in the present account, and the lexical variability seen in (10b) follows from considerations about the general structure of a nuclear projection, i.e. that it conforms to the x-bar format. In a slightly updated approach, Basbøll (2003) suggests that words like ven ‘friend’ [vɛn] involve extrametricality: The final sonorant (or rather: its mora) is simply ignored for moraic considerations, and since the vowels in all words are short, the two-mora minimum is never reached and stød excluded. While invoking extrametricality certainly does the trick, it remains unclear why it should play a role in exactly this case. It does not link to other differences between the two groups.²⁷ Again, the alternative presented here derives the existence of lexical variation from general considerations of structure.

Lastly, Basbøll’s rule in (ii), similar to one expressed in Hjelmslev (1973: 23), is completely arbitrary and does not follow from any higher principle. In contrast, what the rule in (ii) achieves follows again from considerations of space in our approach: Stød is guaranteed because the specifier is the only position to host the final consonant.

3.3 Consonant-final oxytones without stød

Let us now move on to cases where the complement position is neither the second half of a long vowel, nor is it occupied by a sonorant. In contrast to the oxytones in (10), all of which had stød, none of the ones in (14) do.

(Note that ‘any C’ in (14b) really means another obstruent.) The two representations in (15) contrast skib ‘ship’ [sɡiː^ʔb], repeated from (11), to gik ‘went’ [ɡiɡ] (14a).

Since (15a) has a long vowel, the consonant must sit in the specifier and stød follows as discussed before. In (15b) we have a short vowel followed by an obstruent, and this is crucial since obstruents cannot be controlled by the nuclear head xn, even though there is a specifier. That is, for control to happen, not only do we need a specifier but we also need a potential controllee of the right kind. Obstruents do not qualify, which at this point is a stipulation (the equivalent of “obstruents are not moraic in Danish” in other accounts).

One might be tempted to suggest that structures like that in (15b) be modified and have the specifier removed. If there was no specifier, control would automatically be barred, irrespective of the nature of the consonant. Such a move would still require reference to obstruents, though, since we would then have to assume that obstruents in complement position make empty specifiers impossible or at least optional, i.e. (15b) could be modified and the empty specifier removed or the structure could remain as is, with the specifier. Such indeterminacy did not exist for sonorants. That a limitation to empty specifiers would be required becomes clear when looking at words like gigt ‘gout’ [ɡiɡd] in (14b), ending in two obstruents. The second obstruent must sit in the specifier as there is no other place it could be in. In other words, not only will an obstruent in complement position coexist quite happily with a (filled) specifier, but there will also still be no control (and no stød). It is true that for (15b) the specifier could be left out without changing anything, but that does not mean that specifiers are generally impossible in this context. It thus seems that the lack of control can only be blamed on the obstruent nature of the consonant in complement position. However, as we shall see in section 5.5 the theory does provide the means to derive this property from a more general principle, allowing us to abstract away from sonorants and obstruents.

To complete the dicussion, the trees in (16) contrast two words ending in a cluster: gigt ‘gout’ [ɡiɡd], where both members of the cluster are obstruents, and pulp ‘pulp’ [p^hul^ʔb], where only the second one is. (As before, ‘O’ refers to a sonorant, ‘o’ to an obstruent.)

In both examples, all positions are used up. If the first consonant is an obstruent, stød is precluded; no matter what the following consonant (if any). If the first consonant is a sonorant, and since there is another consonant following (in the specifier), we will have stød.

This concludes discussion of the second claim, that the location of stød on the second “mora” can be derived: The position representing the second half of a long vowel or the first member of a sonorant-initial cluster is on the receiving end of an asymmetric relation. Note that all of this has been achieved without reference to the mora. We will return to this in section 5.2.

We will now address the last claim, viz. that the restriction to odd-numbered syllables can be derived. This requires contrasting oxytones to paroxytones which, recall, represent the majority of cases. (Proparoxytones will be briefly looked at in section 5.3.) For this we will have to return to English and Estonian first, in order to present the machinery necessary.

4.1 Accessibility of unused positions

In section 2.1 we saw that the length trade-off we find in oxytones becomes impossible in paroxytones, in both English and Estonian. (Apparent counterexamples in both languages usually involve morphology, as we saw in section 2.5.) Incidentally, this is the same context where stød fails to occur, as seen in Table 11.

This parallel suggests that understanding one will also help us understand the other. In section 3 we saw that earlier versions of GP provided no insights into the length trade-offs in English, since they took the fortis/lenis contrast in English as a qualitative property, viz. the element H (present in the fortis series, absent in the lenis series). There was simply no non-arbitrary link between the absence of H as in the v of leave and the longer vowel, as opposed to a shorter vowel preceding the fortis f (containing H) of leaf. Structure (length) interacted with a melodic property (presence/absence of H) in a way that was not understood. The problem with Estonian was different in that the trade-off was more obvious, but the theory of constituent structure at the time provided no obvious way to express it (Pöchtrager 2006: Chapters 1,4).

In GP 2.0 (Pöchtrager 2006; 2015; 2020b; Kaye & Pöchtrager 2013) the fortis/lenis contrast is expressed structurally: Lenis consonants have the same number of positions as their fortis counterparts, but differ in that lenis consonants have one position that is unused. This position can then be taken up by a preceding vowel (under the right conditions). In fortis consonants, on the other hand, all positions are used up. As a result, vowels before lenis consonants will be longer (since there is a position inside the following lenis consonant that they can claim) than before fortis consonants, and we derive the trade-off in vowel length.

A simple example will illustrate this. The structures in (17) represent [iːf] as in leaf and [iːːv] as in leave. The vowel in leaf is lexically long (Q2); that in leave is lexically and phonologically long (Q3). For our purposes we will focus on the vowel and the following consonant, ignoring the remainder of the representation. In both examples the stressed vowel has the nuclear head xn at its core which projects up to n″. The final consonant is embedded as a daughter of this n″, and the fact that nuclear head and following consonant are dominated by the same node allows vowel and consonant to interact, due to their structural closeness; we will get back to the importance of locality later in this section. The final labial in both words is a projection of the onset head xo. This is of course entirely parallel to the examples we have seen for Danish so far, with the only exception that for the first time we are looking at the internal structure of a consonant (which for Danish was not necessary).

(17a–b) share the same structure, but differ in crucial details in the distribution of individual positions. In both words the nuclear head xn claims its complement x₁ by m-command. This expresses lexical length. The head xn is annotated with the element I and both xn and its sister receive the same interpretation; that of a long, high front vowel.

The two representations differ in their final consonants (fortis [f] vs. lenis [v]). More precisely, they differ in the distribution of positions that make up the final consonant (o′ in both cases). Here again m-command plays a crucial role. In (17a) the final consonant is fortis, since x₂ is m-commanded by xo. In contrast, (17b) has a final lenis consonant. Lenis consonants involve a non-head position (x₂ in this case) that is not m-commanded by their head. This position is available and can therefore be claimed by the preceding xn, which m-commands it. This allows for a non-arbitrary expression of the trade-off in length. The difference between Q2 and Q3 can be directly read off in these examples, as it corresponds to the number of positions involved in an m-command relationship.²⁸

The structures in (17) illustrate two out of three logical possibilities: In (17b) xo claims no other position and xn claims two, in (17a) xo claims one other position and so does xn. The third possibility would have xo claim two positions and xn none. This is a structure that English does not have (cf. section 2.1 and in particular footnote 9), while Estonian does allow it: A short (Q1) vowel followed by an overlong (Q3) consonant. The total amount of room that is to be distributed between xn and xo stays the same; what differs is who gets how much (0+2, 1+1, 2+0). This is a natural representation of the trade-off in length.

For the sake of completeness, let us look at lexically short vowels, as in pairs like riff/give. This case is quite comparable to the previous one; the trade-off between vowel and final consonant takes place in exactly the same way as before. The only difference is that since a lexically short vowel is shorter than a lexically long vowel, there are fewer positions for xn to manipulate. In Pöchtrager (2006) this is represented as in (18).

The trade-off is again a result of who m-commands x₁. There is only one non-head position, so there are two logical possibilities, both of which occur in English: In (18a) x₁ is m-commanded by xo, in (18b) by xn. The first possibility gives us a Q1 vowel followed by a Q2 consonant (i.e. fortis), the second a Q2 vowel followed by a Q1 consonant (lenis). Unlike English, Estonian has no structures like the ones in (18). This can be interpreted as a requirement on the minimal size of words which (18) does not meet for Estonian.²⁹

Paroxytones behave somewhat differently, in that the effect of a lenis/fortis consonant following the stressed vowel has no (or only a negligible) effect on the length of that vowel, cf. the discussion in section 2.1. This can be derived from the theory, which assumes that the unstressed syllable of the foot is embedded inside the stressed nucleus. (19) juxtaposes the structure of leave (with a Q3 vowel), repeated from (17b), and that of beaver (where the stressed vowel is only Q2, i.e. lexically but not phonologically long).

Subscripts serve to distinguish the two nuclear heads (xn_a, xn_b) in (19b).³⁰ In addition, a dashed line separates the projections of the two nuclear heads from each other and also draws attention to the fact that the second is embedded in the first. Such embedding of weak syllables is not only assumed in GP 2.0, but also in other models (van der Hulst 2010; Golston 2016). This is not only a way to build metrical prominence into the representation, but also captures distributional asymmetries between stressed and unstressed position (cf. Pöchtrager 2020a: Section 7). Most importantly for us, it allows us to explain the lack of Q3 despite the presence of a following lenis consonant. In (19) the lenis consonant is grouped together with the preceding nucleus (they belong to the same “syllable”), making the unused position within the consonant available to the nuclear head xn, i.e. it can be m-commanded by it. In (19b), on the other hand, (unstressed) xn_b is closer to the preceding onset than (stressed) xn_a, where closeness can be calculated by reference to the lowest dominating node: n_b″ dominates both v and the following unstressed vowel, whereas we would need to travel even higher up to n_a″ for a node that covers both the stressed vowel and the following lenis v. As a result, intervocalic v is too far removed for the stressed vowel, making the empty position contained in the consonant inaccessible to xn_a. The lack of Q3 is derived.³¹

4.2 The application to Danish

We now have all the ingredients to return to Danish. In the previous section the lack of Q3 in paroxytones was derived from the unstressed syllable being embedded in the stressed one. The same kind of analysis applies to the unstressed syllable in Danish. (20) juxtaposes English dealer [diːlə] to Danish mile [miːlə] mile.³²

The lateral contains a control relationship (between xO and x₃) since it is a non-continuant. In addition there is an unused specifier x₂ since the consonant is lenis. The two structures are the same in all relevant aspects, and the results (lack of phonological length, lack of stød) are similar, but for slightly different reasons: In English, the unused position contained in l is not available to the preceding nuclear head since we are dealing with a paroxytone, as discussed in the previous section. (The position is available in oxytones as in deal, of course.) In that respect dealer (20a) behaves exactly like beaver (19b). As for Danish, the entire specifier of xn_a (i.e. the sister to n_a′) is inaccessible to xn_a since that is the domain of the following syllable. As a result, there can be no control between xn_a and x₁ (and thus no stød), but there can be a relationship of m-command: This gives us the long vowel without stød that we see in (20b).

Capitalising on the inaccessibility of the specifier means that we achieve a very streamlined account. Paroxytones like mile [miːlə] ‘mile’ lack stød for the same reason that words like ven lack it: There is no accessible specifier. Whether it is present but inaccessible (as in paroxytones) or simply not present at all (and then trivially not accessible) amounts to the same thing. This also means that the behaviour of paroxytones is no longer stipulated as it was in (2), but rather follows from an account originally designed to explain the distribution of length in two other languages.

5.1 Morphology

As shown in section 2.4, paroxytones that seem to violate the distribution of overlength always involve morphology. A similar case can be made for Danish stød.³³ Table 12 repeats the crucial examples from Table 8.

Danish [muː^ʔsən]/[muːsən] are classic examples. That we should find stød in an even-numbered syllable (counting from the right) is troubling, but removal of the suffixed definite article not only solves that problem but also immediately reveals why only one word has stød: The stem [muː^ʔs] ‘mouse’ by itself is an oxytone (its only syllable is in an odd-numbered position), while [muːsə] ‘muse’ is a paroxytone and thus ineligible for stød. The suffix masks the relevant difference.³⁴

A structurally similar argument can be made for Estonian. Table 12 gives two inflected forms of the word for ‘jam’; a monosyllabic base. The theme vowel i is attached within the same domain in the genitive case, but in a separate domain in the partitive, as indicated by the bracketing. Technically, we are dealing with analytic morphology in the partitive and non-analytic morphology in the genitive, following the terminology of Kaye (1995). Accordingly, the base forms a domain of its own in the partitive and behaves like an oxytone for the determination of overlength, while the genitive is a paroxyone and thus overlength is ruled out.

The same difference can be shown with words that are not related (inflectionally or otherwise). Paroxytone loans do not show Q3 consonants or vowels, cf. (21a–b) and footnote 16. Lack of Q3 cannot be blamed on their foreign origin, as the words in (21c–d), all of which loans, demonstrate.

It seems natural to assume that loan words entering the language as uninflected stems have no internal morphological structure. As such, we would expect them to conform to the patterns we find in simplex words. (21) differs from Table 12 in that the former compares unrelated lexical items, neither of which has any internal morphological structure, while the latter shows two forms that both have internal structure, but where the type of morphology differs (analytic vs. non-analytic). Both sets of data point in the same direction and show that the difference between oxytones/paroxytones is the relevant factor in the distribution of overlength, even if appearances are deceptive at times.

The English example in Table 12 is taken from Abercrombie (1964). Greater contains a suffix and … Grey to… consists of two words, with to acting like a clitic. Given the more independent status of to (as opposed to a suffix), it seems correct to treat Grey as an independent domain separate from following to, hence a Q3 vowel (diphthong in this case) is to be expected. This differs from the (non-analytic) comparative suffix -er which forms one single domain with the base it attaches to, giving rise to a paroxytone. That comparative -er is non-analytic and thus forms one domain with its base can be seen in the distribution of [ŋɡ], which English bars at the end of domains (long *[lɒŋɡ]). Given comparatives like long-er [ˈlɒŋɡə], in parallel with simplex finger [ˈfiŋɡə], we can conclude that the base -er attaches to does not form a domain of its own, making the suffix non-analytic and great-er one single domain.³⁵

Let us return to Danish for a last detail related to morphology. Differences in morphological structure and their effect on stød can also be seen in a productive process of stød addition under suffixation. As a result, even stød-less forms like ven [vɛn] ‘friend’ (cf. section 3.2) can receive stød. It is clear, however, that this depends on the exact type of suffixation; contrast the forms in (22).

There are two issues here: (i) Differences in which suffixes lead to stød addition and which do not. (ii) The formal mechanism underlying stød addition. As for (i), we can again capitalise on how loosely or tightly a suffix attaches to its base. As seen in Table 12, the definite article in (22b) attaches analytically, i.e. its base forms a domain of its own and, crucially, the base is an oxytone.³⁶ (22b) is then entirely parallel to the example ((mus)en) [muː^ʔsən] ‘mouse def.’ in Table 12. In contrast, the plural in (22c) seems to be non-analytic like the English comparative -er. As its base is a paroxytone, we do not expect stød.³⁷

As for (ii), I would like to suggest the following: In section 3.2 we saw that words like ven [vɛn] ‘friend’ lack a specifier (unlike pen [pɛn^ʔ] ‘pen’, with stød). If we assume that affixation of an analytic suffix (as in the definite form) requires a complete x-bar structure as a base (i.e. including a specifier), and that a base not meeting that requirement is modified accordingly, we automatically get the addition of stød. As a result, both vennen [ˈvɛn^ʔn̩] ‘friend def.’ and pennen [ˈpɛn^ʔn̩] ‘pen def.’ come out the same.

This can even be extended to other cases of stød addition as in sofa [ˈsoːfa] ‘sofa’ vs. sofaen [ˈsoːˌfæː^ʔn̩] ‘the sofa def.’ (Basbøll 2005: 318). Notice how the final unstressed syllable of the base not only acquires secondary stress, it is also lengthened and receives stød. In that way it is comparable to vowel-final oxytones (section 3.1), which makes sense under our assumption that affixation of an analytic suffix makes sure that we have a complete x-bar structure as the base. Both stød addition and vowel length fall out from this, since having a complete x-bar structure means having a specifier and thus a control relationship between the nuclear head and its complement, i.e. a long vowel the second half of which carries stød.

5.2 The mora

Our account so far has not made any reference to the notion of mora, a concept which has been alien to GP in all its incarnations: Harris (1994: 277 fn. 30) argues that moraic structure, in particular the difference between moraic and non-moraic segments, complicates the statement of phonotactic regularities, i.e. it is rather a hindrance than an advantage. Even for languages where the mora seems quintessential, alternatives have been offered which make do without it. For Japanese, both S. Yoshida (1990) and Y. Yoshida (1995) have argued that heavy syllables with two moras can be reinterpreted as a sequence of two light syllables (more precisely: two CV-pairs) without any loss of explanatory power; in fact, rather the opposite. If even the poster-child Japanese can do without the mora, then possibly Danish can, too. “[I]f the ultimate goal […] is to seek for a group of principles that make up Universal Phonology, a unit such as the mora, which is indispensable in some languages but completely irrelevant in other languages, is an unwelcome innovation.” (Yoshida 1990: 331).

For Danish, the mora seemed crucial as it allowed for a unification of two contexts: A long vowel is equivalent to a sequence of short vowel plus sonorant, cf. section 1. The question will then be, do we need recourse to the mora as an additional concept or are the notions we already have in our theory sufficient? If we do not need it, then the case for the mora becomes accordingly weaker. We have already seen that the mora is not sufficient to explain the distribution of stød. (It has nothing to say about the difference between oxytones and paroxytones, for example.) At the same time it does not even seem necessary, since our proposal about stød only refers to relationships between a nuclear head and its complement, which is what we also need in order to talk about length or clusters. This means that what the mora was supposed to capture can be adequately expressed in the vocabulary already in use in GP 2.0. Now, one could object (as a reviewer has done) that the mora also plays other roles in Danish, e.g. for word-minimality, syllable structure, or stress; so let us address those in turn.

For the purposes of stød we must of course make sure that only sonorants are treated as moraic, but not obstruents. This becomes troublesome when explaining word size minima in Danish: fib ‘goatee’, gik ‘went’ or bus ‘bus’ have a short vowel (one mora) and end in an obstruent, which ex hypothesi is not moraic. If we treat the final sonorant in stødless words like ven ‘friend’ (section 3.2) as extraprosodic, then those can be added to the list as well. All of this suggests that Danish allows monomoraic (content) words, which is also the conclusion of Basbøll (2005: 270ff). Yet when we look for monomoraic words that end in a vowel, we find that they are not content words, but function words (including adverbs like nu [nu] ‘now’ and reduced forms of modals like kan [ka] ‘be able to’). Both sets are treated as monomoraic, so the difference between them cannot be expressed in moraic terms. It can, however, be expressed in our terms: In words like nu ‘now’ the nuclear head has no complement whatsoever, in words like bus ‘bus’ (or bi ‘bee’) the nuclear head does have a complement. This also includes pen ‘pen’ (with stød) and ven ‘friend’ (without), both of which have a complement to the nuclear head. Reference to the complement (instead of the number of moras) draws the dividing line at exactly the point where it needs to be drawn.

What about syllable structure and the maximal size of a syllable? Let us note that marking the final mora as extraprosodic in a word like ven ‘friend’ succeeds in avoiding stød, but does not derive any other properties of the word, cf. the discussion at the end of section 3.2. In the same context we also noted that Basbøll’s rule which assigns a mora to the first consonant of the clusters in both falk ‘falcon’ and film ‘film’ manages to create a position for stød. One could argue that that rule helps maintain an upper limit of maximally two moras per syllable. But it only does so by brute force, i.e. by assuming that the second sonorant of the cluster in film ‘film’ simply does not get assigned a mora, even though a third mora would not be detrimental at all to an account that assigns stød to the second mora. Any third mora would be superfluous, but harmless. The mora is a rather abstract notion, then, a conclusion also reached in Grønnum & Basbøll (2001); one that does not translate easily into acoustic cues.

As for stress assignment, it is also unclear whether the mora actually does a lot of work. Danish is a Germanic language and stress usually marks the first syllable of the root. That stressed first root syllable could be monomoraic (suppe [ˈsɔbə] ‘soup’) or bimoraic (lampe [ˈlɑmbə] ‘lamp’). Also, like in most other Germanic languages, a fair number of loans has entered the language, and Basbøll (2005: 395–400) distinguishes between a French part of the lexicon (with final stress) and the rest. That rest gets assigned stress by two rules, replicated in (23) from Basbøll (2005: 397).

Note that rule (23a) refers to long vowels, which is different from a bimoraic syllable (which could also be a short vowel plus sonorant). Rule (23b) refers to a short vowel followed by any consonant. That consonant could be moraic (if a sonorant) or not (if an obstruent or lexically marked as non-moraic). Taken together, then, the mora does not feature in either rule.

In addition, there is an important proviso to the rules in (23) in that “[l]exemes with a stress placement different from the one predicted by the Default stress rule have underlying stress” (Basbøll 2005: 397). So not only does (23) not refer to moras, it can also be overridden when necessary. As Basbøll (2005: 397) himself points out: “The Default stress rule as given here cannot be falsified in any strict sense, since potential counter-examples can be given an appropriate underlying stress placement.” Note that I do not argue for or against the validity or usefulness of (23), but simply state that the mora seems orthogonal to it.

I conclude then that not much is lost for Danish if attention is directed away from the mora. The alternative outlined here helps us to make sense of stød, word minima, and syllable structure, and as for stress in Danish, the mora does not seem to be crucial to begin with.

5.3 Antepenultimate position

The article has dealt in detail with oxytones and paroxytones and tried to establish parallels in their behaviour across three different languages. The stød principle in (2) refers to odd-numbered syllables, and that includes antepenultimate position, i.e. proparoxytones, which we have not looked at so far. The question is, should they be subsumed under the same principles as other words? Fischer-Jørgensen (1989: 4) points out that “[t]risyllabic uninflected words are very rare” and that “[t]hey generally do not have stød”. This latter point changes once foreign words are taken in, such as kolera [ˈkoː^ʔləʁɑ] ‘cholera’. In addition, Basbøll (1988: 135) points out that stød is assigned in the (school) pronunciation of Latin and Greek words with antepenultimate stress, thus Latin insula [e^ʔnsula] ‘island’. So, proparoxytones should be considered if the entire lexicon is taken in, but the issue remains unclear with native words. Taking the simple way out and assuming that there are different strata of the lexicon would not help, because even if there are, words like kolera ‘cholera’ still need some representation. So let us explore likely contenders.

In section 4 I argued that paroxytones have their unstressed syllable embedded inside the projection of the stressed nucleus; more precisely in the specifier, recall mile [miːlə] ‘mile’ from (20b). Allowing proparoxytones to have both syllables embedded inside the (stressed) nucleus, say one in the complement and one in the specifier, makes two predictions: (i) Stød should be impossible (because the specifier is inaccessible for the nuclear head). (ii) Long vowels (with or without stød) in antepenultimate position should be impossible because the complement position that should provide the second half of the long vowel is needed for the middle syllable. Neither prediction is borne out and we have to reject the assumption that proparoxytones have both syllables embedded within the projection of a single nucleus.

The only alternative then seems to be that proparoxytones need to be broken down into smaller units, such as (ko-]) (lera). That would allow us to treat the first unit (ko-) in its own right and as an oxytone, with stød as expected.³⁸ It then remains to clarify what exactly those units are and what their internal structure is. If they are treated as feet, then the second foot (-lera) is somewhat unusual: It is hard to know which one of the two syllables should be the (more prominent) head position, if any. However, there is a certain similarity to the “weak foot” of Burzio (1994: 70), which shuns stress. If that is correct, then the lack of stress would also explain the lack of stød in the second foot.

It is reassuring for the comparative approach taken here that exactly the same issue arises in Estonian. The word muuseum ‘museum’ has initial stress and the vowel of the first syllable is in Q3. Again, this can be made sense of if we break down the word into smaller units, with muu forming a unit of its own. It would then be exactly identical to the word muu ‘other’, also with a Q3 vowel. That such smaller units (whether feet or something else) are important for the proper analysis of overlength has been argued for for a long time (Lehiste 1965; Prince 1980). What remains to be done is to integrate this thoroughly into GP 2.0, which will have to be the focus of future work.

5.4 The role of the specifier

Section 3.1 made the crucial assumption that a control relationship depends on the availability of a specifier. This has allowed us to make accurate predictions about the occurrence of stød in oxytones (why words with a long vowel or a sonorant-initial cluster take stød while those with a short vowel plus sonorant may or may not) and also predict the absence of stød in paroxytones.

Despite the usefulness of this link between specifier and control, the exact reason for the connection remains unclear, however. Why would a specifier have an effect on what can happen with the complement? One could make the (rather trivial) observation that a complement counts as more deeply embedded exactly because of the presence of a specifier. But that only says something about the geometry of the tree, not about a particular relationship (control) holding between two nodes.

What is somewhat reassuring is that the same phenomenon comes back elsewhere, viz. in consonants. Pöchtrager (2006) offered an analysis of the internal structure of consonants, and Pöchtrager (2021c) updated and slightly modified the account by looking at affricates and how they are set apart from other obstruents. Obstruents in this model are a projection of a consonantal head xO, which, like other heads, can project up to twice. A control relationship between head and complement encodes (complete) stopness, but such a control relationship is only possible (though not necessary) if the specifier is present. This allows for the three structures in (24), taken from (Pöchtrager 2021c: 8). The linear order of head and complement is immaterial here.

The position x₁ in all structures allows for the the encoding of the fortis/lenis contrast, as seen in section 4.1. A conceivable fourth possibility, i.e. a structure as in (24a) but with control is excluded since there is no specifier. And indeed, there is no further type of obstruent not already covered by one of the three types.

In this arrangement of structures, affricates take an intermediate position between fricatives and stops. This allows for a simple, formal characterisation of natural classes. Affricates are like fricatives in that neither one involves control (24a–b). At the same time, affricates are also like stops in that each involves two layers of projection of xO (24b–c), i.e. they are equal in size. Both groupings are relevant for phonological phenomena (Kehrein 2002; Lin 2011).

5.5 Sonorants and obstruents

GP has had a somewhat uneasy relationship with the distinction between sonorants (in particular sonorant consonants) and obstruents. Earlier versions of the theory had an element h which “maps onto the speech signal as aperiodic energy” (Harris 1994: 123) and characterised fricatives, affricates and (released) plosives, i.e. the class of obstruents. (Unreleased plosives pose an obvious problem since they are obstruents but lack h under that definition.) In the course of time, the set of elements was reduced quite dramatically, and in Kaye’s User Guide (Kaye 2000) we no longer find h. The definition of the element H, already responsible for voicelessness, aspiration and high tone since the early days of the theory, was extended in Backley (2011) to cover noise as well. However, Backley assumes that this element is not found in (English) lenis stops, and therefore H cannot be used to characterise the class of obstruents adequately. In GP 2.0 the sonorant/obstruent distinction is partially covered by two different kinds of consonantal heads (xO vs. xo), cf. footnote 23. But those different heads are also involved in the expression of other properties, such as coronality (Pöchtrager 2021c) and at present it remains somewhat unclear whether they provide a satisfactory characterisation of those two classes.

With a language like Danish one is paying the price for this negligence, because reference to the sonorant/obstruent divide seems crucial for a complete analysis of stød. In section 3.3 we assumed that obstruents cannot be controlled, a reinterpretation of the common stipulation that “obstruents are not moraic in Danish” in other accounts. However, by pulling together the results of sections 4.1 (on the representation of the fortis/lenis contrast) and 5.4 (on fricatives, affricates and stops) we are now able to express what the sonorant/obstruent distinction captures without reference to those notions, thus steering clear of any problems that remain in their (theory-internal) representation. In this section I will make a (still somewhat tentative) proposal how this could be achieved.³⁹

Since consonant-final oxytones with a long vowel have stød irrespective of the nature of the final consonant, we will only need to consider words with a short vowel. What we want to achieve is that control can target sonorants but not obstruents. What is interesting about Danish obstruents in final position is that plosives are all lenis (25a), while fricatives are fortis (25b).⁴⁰

As argued in section 4.1, lenis consonants contain an unused position, i.e. one that is not m-commanded by the consonantal head. In fortis consonants, however, the corresponding position is m-commanded by the head. Let us now assume that, counter to what was claimed in section 3.3, control can freely try to target sonorants and obstruents, instead of being restricted to sonorants. What would the consequence be? Take the fortis fricative at the end of tuf ‘tuff’ [tuf] (25b): Being a fricative, it contains two positions (a head and its sister); and since it is fortis the head m-commands its sister. All positions are used up, and since a position can be either controlled or m-commanded but not both, no control relationship (coming from the preceding nucleus) can be established. We expect that such words do not have stød, and indeed they do not.

Words ending in lenis stops (25a), on the other hand, do have an empty (thus controllable) position because they are lenis. But plosives already contain a control relationship by definition (section 5.4), and so the addition of another one coming from the preceding nuclear head would simply not change anything. The plosive stays a plosive.

Let us finally consider words ending in sonorants. For this we can go back to pen ‘pen’ [pɛn^ʔ], which we looked at in (12a) in section 3.2. There we assumed that the consonant can be controlled because it is a sonorant. According to the proposal made in this section control can be established because the consonant is lenis (like all sonorants in Danish) and therefore contains an empty position that can be controlled. Under either approach we correctly predict stød.

The alternative outlined in this section basically amounts to two claims. Firstly, the distinction between sonorants/obstruents is not the relevant distinction that we need to look at for Danish. Instead, what counts is whether a consonant contains an empty position or not. Under such a reinterpretation, Danish gets a little bit closer still to both Estonian and English, where the availability of empty positions was also crucial, but for the distribution of overlength. What was given as a difference between Danish versus English/Estonian in (8a) might actually be yet another parallel. The second claim is that control is the default, but that there are various factors that can block it: If there is no specifier as in ven ‘friend’ (section 3.2), if the specifier is not accessible as in paroxytones (section 4.1), or if there is no position that could be controlled (as in fortis fricatives). In all the other cases control is established, and that is why we get stød on sonorants, while in plosive-final words (25a) it just so happens that a control relationship between the nucleus and the final stop can be established, but that there is no audible effect. In this regard, there are similarities (in spirit, though not in theoretical machinery) to a recent proposal by Vazquez-Larruscaín (2021), who assumes that obstruents are moraic and hence potential targets for stød, but that stød is incompatible with obstruents and therefore fails to be realised in this context.

There are two implications of this proposal. Firstly, it casts even further doubt on the relevance of the mora. The sonorant/obstruent distinction formed the basis for deciding which consonants can count as moraic. Once that basis is gone, there is even less reason to uphold the claim that moraic structure is relevant. Secondly, in sections 3.2 and 3.3 we saw that for sonorant-final oxytones the specifier could be present in some words (pen ‘pen’ with stød) and absent in others (ven ‘friend’ without), while for obstruent-final oxytones it simply did not matter if the specifier was present. The reason for this discrepancy could lie in acquisition: Under the proposal made in this section, control could apply freely with both sonorants and obstruents, provided there is a specifier. In the case of pen and ven the child would have a clear indication for whether the specifier was present or absent: stød. In a word like hat ‘hat’ there could be a specifier and thus control, or no specifier or no control. In either case, there would be no stød. For the child, either option would be a possible representation.

Let me finally add that I see two potential problems for the proposal in this section, which might require a retreat to the more generally accepted reliance on sonorants and obstruents. For one thing, since the sonorant/obstruent divide is not exactly well-understood within GP, as we saw at the beginning of this section, it might be too rash to dismiss it out of hand. After all, we might just be lucky that the partitioning created by the fortis/lenis distinction in Danish coincides with that needed for stød. Secondly, final plosives as in hat ‘hat’ now involve two control relationships, one fully contained inside the consonant, and one from the nuclear head to the (specifier of the) consonant. Having two control relationships in the same consonant is a novelty in the theory, and as such its implications will need to be considered carefully. Both points, however, will have to await further developments in the theory of GP 2.0.