2.1.1 Descriptive Generalisations

Ukrainian has an interesting prosodic system because it combines free lexical stress with predictable grammatical stress, which enter into a complex interaction. Lexical stress in Ukrainian is weight-insensitive and there is no phonemic length. Ukrainian has a six-vowel system /i, ɨ,Footnote ² u, ɛ, ɔ, a/ (Toc’ka Reference Toc’ka and Bilodid1969). Primary (lexical) stress can appear on any syllable in a word, for example, [ˈdɔrɔɦɔ] ‘dear, adv.’ [dɔˈrɔɦa] ‘way, nom. sg.’, [dɔrɔˈɦa] ‘dear, nom. sg. fem’. Although the location of stress is largely unpredictable, there exist several morphologically conditioned accentual paradigms in Ukrainian. Similarly to the other East Slavic languages (Russian and Belarusian), stress in Ukrainian can be either fixed on one syllable or alternate between different syllables within inflectional paradigms (Stankiewicz Reference Stankiewicz1993), as illustrated by the stress patterns in the nominal stems in Table 1.

Table 1Stress patterns in nominal stems

Let us observe that stress can be fixed on the stem, as in [rɔˈdɨn+a] ‘family’, on the ending, as in [ʒɨtt^j+ˈa] ‘life’, or alternate between the stem and the ending in mobile stress patterns. In [t͡ʃɔlɔˈʋ^jik] ‘man’, for instance, the final syllable of the stem is stressed throughout the inflectional paradigm in the singular, whereas the inflectional ending is stressed in the plural. The opposite pattern is observed in [nɔʋɨn+ˈa] ‘news’, in which stress is located on the stem in the plural and, with the exception of the voc. sg. form [nɔˈʋɨn+ɔ], on the ending in the singular. Let us also note that, as in any system with lexical stress, there exist lexical items which exhibit variation in the location of the primary (lexical) stress, for example, [ˈpɔmɨlka] ~ [pɔˈmɨlka] ‘mistake, nom. sg.’, [ˈtakɔʒ] ~ [taˈkɔʒ] ‘also’, [ʋɛsˈn^janɨj] ~ [ʋɛsn^jaˈnɨj] ‘spring, adj. nom. sg.’.

In addition, both descriptive grammars and recent acoustic research point to the existence of secondary (rhythmic) stress in Ukrainian, which is assigned at the word’s edges, as well as on every other syllable, forming a predictable alternating pattern with lapses near lexical stress (Nakonečnyj Reference Nakonečnyj and Bilodid1969; Toc’ka Reference Toc’ka and Hryščenko2002; Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a, Reference Łukaszewicz and Mołczanow2018b). Let us point out that modern Ukrainian displays considerable dialectal diversity (Shevelov Reference Shevelov1979), which is particularly evident in the differences in the patterns of lexical stress placement. Yet, there is agreement in the literature that secondary stress is present both in the standard literary language (Nakonečnyj Reference Nakonečnyj and Bilodid1969), which is based on the south-eastern dialectal group, and in the standard Ukrainian spoken in the west of the country (Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a, Reference Łukaszewicz and Mołczanow2018b, Reference Łukaszewicz and Mołczanow2018c).Footnote ³

Data in (2) illustrate possible rhythmic patterns for words consisting of three to seven syllables (longer words are rare in Ukrainian).

1. (2) Rhythmic patterns in words of different length

   1. a. Three-syllable words

      ˈσσˌσ	[ˈrjiʃɛˌnnja] ‘decision, nom. sg.’
      σˈσσ	[t͡ʃaˈstɨna] ‘part, nom. sg.’
      ˌσσˈσ	[ˌmaɦaˈzɨn] ‘shop, nom. sg.’Footnote 4

   1. b. Four-syllable words

      ˈσσσˌσ	[ˈsprɔbuʋaˌtɨ] ‘try, inf.’
      σˈσσˌσ	[ʋaˈrɛnɨˌkɨ] ‘dumpling, nom. pl.’
      ˌσσˈσσ	[ˌkɔrɔˈlɛʋa] ‘queen, nom. sg.’
      ˌσσσˈσ	[ˌpɛrɛkɔˈnaʋ] ‘persuade, past. masc.’

   1. c. Five-syllable words

      ˈσσˌσσˌσ	[ˈʋɨkɔˌrɨstaˌnnja] ‘use, nom. sg.
      σˈσσσˌσ	[kɔmˈpanjijɛˌju] ‘company, instr. sg.’
      ˌσσˈσσˌσ	[ˌpɔpɛˈrɛdnjɔˌɦɔ] ‘previous, gen. sg. masc.’
      ˌσσσˈσσ	[ˌljitɛraˈtura] ‘literature, nom. sg.’
      ˌσσˌσσˈσ	[ˌunjiˌʋɛrsɨˈtɛt] ‘university, nom. sg.’

   1. d. Six-syllable words

      ˈσσσˌσσˌσ	[ˈbat͡ʃɨtɨˌmɛtɛˌsja] ‘see, 2nd pers. pl. refl. future’
      σˈσσˌσσˌσ	[ʋɨˈxɔdɨˌtɨmɛˌmɔ] ‘go out, 1st pers. pl. future’
      ˌσσˈσσσˌσ	[ˌnaɦɔˈlɔʃuʋaˌnnja] ‘accenting, nom. sg.’
      ˌσσσˈσσˌσ	[ˌzarɔzuˈmjiljiˌstju] ‘conceit, instr. sg.’
      ˌσσˌσσˈσσ	[ˌpɔdɔˌrɔʒuˈʋala] ‘travel, 3rd pers. sg. fem. past’
      ˌσσˌσσσˈσ	[ˌmunjiˌt͡sɨpaljiˈtɛt] ‘municipality, nom. sg.’

   1. e. Seven-syllable words

      ˈσσˌσσˌσσˌσ	[ˈʋɨbaˌlansuˌʋatɨˌsja] ‘balance out, inf. perf.’
      σˈσσσˌσσˌσ	[zaˈpamɔrɔˌt͡ʃɛnnjaˌmɨ] ‘dizziness, instr. pl.’
      ˌσσˈσσˌσσˌσ	[ˌpɛrɛˈʋɨʃt͡ʃuˌʋatɨˌmutj] ‘exceed, 3rd pers. pl. future’
      ˌσσσˈσσσˌσ	[ˌʋɨkɔrɨˈstɔʋuʋaˌnnja] ‘usage, nom. sg.’
      ˌσσˌσσˈσσˌσ	[ˌadmjiˌnjistraˈtɨʋnɔˌmu] ‘administrative, dat. sg. masc.’
      ˌσσˌσσσˈσσ	[ˌkapjiˌtaljizuˈʋatɨ] ‘capitalise, inf.’
      ˌσσˌσσˌσσˈσ	[ˌintɛrˌnat͡sjiˌɔnaˈljizm] ‘internationalism, nom. sg.’

These examples show that while lexical stress can appear on any syllable, the position of secondary stress is predictable. Initial and final syllables have secondary prominence when not immediately followed or preceded by lexical stress – for example, the initial syllable is stressed in ˌσσσˈσσ [ˌl^jitɛraˈtura] ‘literature, nom. sg.’ and the final syllable is stressed in σˈσσσˌσ [kɔmˈpan^jijɛˌju] ‘company, instr. sg.’. In contrast, the initial syllable in [kɔmˈpan^jijɛˌju] and the final syllable in [ˌl^jitɛraˈtura] remain unstressed because they are adjacent to lexical stress. Furthermore, word-medial rhythmic stress appears in longer words, in which lexical stress is removed from the left or the right word edge by four or more syllables, for example, ˌσσˌσσˈσσ [ˌpɔdɔˌrɔʒuˈʋala] ‘travel, 3rd pers. sg. fem. past’, σˈσσˌσσˌσ [ʋɨˈxɔdɨˌtɨmɛˌmɔ] ‘go out, 1st pers. pl. future’, with a lapse occurring next to lexical stress, for example, ˌσσˌσσσˈσσ [ˌmun^jiˌt͡sɨpal^jiˈtɛt] ‘municipality, nom. sg.’, ˈσσσˌσσˌσ [ˈbat͡ʃɨtɨˌmɛtɛˌs^ja] ‘see, 2nd pers. pl. refl. future ’.

It has been previously noted that Ukrainian is a highly inflectional language with complex morphology. Derived environments are notorious for their interaction with stress assignment in a number of languages. An illustrative example comes from English, in which secondary stress is lexicalised and its location is often unpredictable. For instance, the initial syllable is stressed in ˌcharacteˈristic because its derivational base is ˈcharacter, a word with initial primary stress. In contrast, the word Aˌmeriˈcana has secondary stress on the second syllable because it is derived from Aˈmerica, in which the second syllable carries metrical prominence (Chomsky & Halle Reference Chomsky and Halle1968; Hayes Reference Hayes1980; Halle & Vergnaud Reference Halle and Vergnaud1987). Unlike English, Ukrainian does not exhibit interactions between morphological structure and secondary stress placement (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2018b; Mołczanow & Łukaszewicz Reference Mołczanow and Łukaszewicz2021). The evidence provided in Mołczanow and Łukaszewicz (Reference Mołczanow and Łukaszewicz2021: 556–557) is based on the regular distribution of secondary prominence in unaccented stems and on alternations such as [xaˈraktɛr] ‘character, nom. sg.’ – [ˌxaraktɛˈrɨstɨˌka] ‘characteristics, nom. sg.’, in which the location of the lexical stress in the base [xaˈraktɛr] does not align with the position of the secondary stress in the derived form [ˌxaraktɛˈrɨstɨˌka]. It is also notable that, unlike primary stress, secondary stress is not marked in dictionaries of Ukrainian. Furthermore, native speakers do not have intuitions as to its presence or location within a word, which renders rhythmic stress in Ukrainian similar to languages such as Polish, in which the regular distribution of grammatical stress is independent of the morphological structure (Rubach & Booij Reference Rubach and Booij1985; Kraska-Szlenk Reference Kraska-Szlenk2003; Łukaszewicz Reference Łukaszewicz2018).

2.1.2 A Phonological Model of the Ukrainian Metrical System

As introduced in Section 1.2, the Ukrainian rhythmic pattern is reminiscent of typologically rare bidirectional stress systems with internal lapses (Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a, Reference Łukaszewicz and Mołczanow2018b, Reference Łukaszewicz and Mołczanow2019; Mołczanow & Łukaszewicz Reference Mołczanow and Łukaszewicz2021). In such systems, main stress is fixed with respect to the right or left edge of the word, while rhythmic stresses iterate from the opposite edge; compare Kager (Reference Kager2001) and Gordon (Reference Gordon2002). The iteration of (feet containing) rhythmic stress thus proceeds either from the word’s beginning rightwards (e.g. [(ˌσσ)(ˌσσ)σ(ˈσσ)], not *[σ(ˌσσ)(ˌσσ)(ˈσσ)], as in Polish; Rubach & Booij Reference Rubach and Booij1985; Kraska-Szlenk Reference Kraska-Szlenk2003; Łukaszewicz Reference Łukaszewicz2015, Reference Łukaszewicz2018; Łukaszewicz et al. Reference Łukaszewicz, Zajbt and Krawczyk2018, Reference Łukaszewicz, Zajbt and Mołczanow2020) or from the word’s end leftwards (e.g. [(ˈσσ)σ(ˌσσ)(ˌσσ)], not *[(ˈσσ)(ˌσσ)σ(ˌσσ)], as in Garawa; Furby (Reference Furby1974), cited, for example, in Gordon (Reference Gordon2002) and Kager (Reference Kager2005). Stress clashes are avoided – when there is an odd number of syllables between the word’s edge and the main stress position, a lapse (i.e. a sequence of two unstressed syllables) occurs in the vicinity of main stress.

Classical bidirectional stress systems such as Polish or Garawa are purely grammatical metrical systems – in such systems, (feet containing) primary and secondary stresses both occur at word edges. As a consequence, the only possibility admitted within a single system is that of secondary stresses iterating from one edge, which is the opposite edge with respect to the one where primary stress occurs (Łukaszewicz et al. submitted). Similarly to those previously known bidirectional systems, Ukrainian exhibits rhythmic stress propagation from the word’s edge towards the main stress position (Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a, Reference Łukaszewicz and Mołczanow2018b). However, unlike those systems, Ukrainian has free lexical stress, which can occur in any position in the word. As highlighted in Section 2.1.1, this gives rise to a large number of possible combinations of primary and secondary (rhythmic) prominences, depending on the position of lexical stress relative to the word edges. As a consequence, there can be simultaneously rightward and leftward rhythmic stress iteration in Ukrainian, starting off at both edges (Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a, Reference Łukaszewicz and Mołczanow2018b). In what follows, we discuss the challenge that this characteristic of the Ukrainian system poses to current metrical theories designed for simpler, purely grammatical stress systems (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2019; Mołczanow & Łukaszewicz Reference Mołczanow and Łukaszewicz2021). The discussion will focus on three- and six-syllable words – the former have the minimal length to accommodate two levels of stress; the latter have sufficient length to exhibit rhythmic stress iteration and a lapse at the peak, which makes Ukrainian a bidirectional stress system.

In order to accommodate rhythmic stress, the word minimally needs to consist of three syllables. In (3), we repeat for convenience all possible combinations of lexical and rhythmic stress on the basis of three-syllable words, illustrated earlier in (2a). Lexical stress falls on the first syllable in (3a), second syllable in (3b), and third syllable in (3c). In general, rhythmic stress is placed on the initial or final syllable of the word if at least one syllable intervenes between that syllable and the one carrying lexical stress. Thus, it is present in (3a) and (3c), in which the lexically stressed and the rhythmically stressed syllables occupy the opposite edges, but not in (3b), in which the lexically stressed syllable occurs in the middle of the word. The stress pattern in (3c) is a mirror image with respect to the one in (3a).

1. (3) Possible rhythmic stress patterns in three-syllable words

   a. [ˈσσˌσ]

   b. [σˈσσ]

   c. [ˌσσˈσ]

Three-syllable words are too short to accommodate rhythmic stress iteration, which can only be found in longer words. For rhythmic stress iteration to occur, at least four syllables should intervene between the word’s edge and the lexical stress position, which means that the minimal length of the word must be that of five syllables. However, the presence of iterative stress does not automatically indicate that the pattern is unidirectional or bidirectional. In ‘even-parity’ words – that is, words having an even number of syllables between the word’s edge and the lexical stress position, for example, [ˈσσˌσσˌσ] or [ˌσσˌσσˈσ], compare (2c) – the metrical structures are non-transparent with regard to the direction of rhythmic stress propagation: such structures may arise through rhythmic beats propagating from the lexical stress position towards the edge (as in a unidirectional pattern) or in the opposite direction (as in a bidirectional pattern), yielding practically the same results. A key argument for stress bidirectionality is then the position of a lapse in ‘odd-parity’ words. This can be illustrated by looking at possible combinations of lexical and rhythmic stress in six-syllable words in (4) (cf. (2d)). In bidirectional stress systems, the lapse is located near the peak, as schematised in (4a) and (4f). In those examples, the distance between the edge and the lexical stress position is that of five syllables, which allows us to infer both the iterative and bidirectional character of rhythmic stress in Ukrainian. In (4a), the structure is [ˈσσσˌσσˌσ], with a lapse located at the peak, not [ˈσσˌσσσˌσ], with a lapse occurring between rhythmic stresses, and also not *[ˈσσˌσσˌσσ] with no lapse at all and no rhythmic stress on the final syllable. The metrical structure in (4f), which is [ˌσσˌσσσˈσ], is a mirror image of the one in (4a); analogously to (4a), it reflects the bidirectional characteristics of the Ukrainian system.

1. (4) Possible rhythmic stress patterns in six-syllable words

   1. a. [ˈσσσˌσσˌσ]

   2. b. [σˈσσˌσσˌσ]

   3. c. [ˌσσˈσσσˌσ]

   4. d. [ˌσσσˈσσˌσ]

   5. e. [ˌσσˌσσˈσσ]

   6. f. [ˌσσˌσσσˈσ]

In what follows, we discuss the theoretical implications of the existence of mirror-image stress patterns such as [ˈσσˌσ] (3a) versus [ˌσσˈσ] (3c) and [ˈσσσˌσσˌσ] (4a) versus [ˌσσˌσσσˈσ] (4f) within a single stress system. In Section 2.2, we will present the results of recent acoustic studies which corroborate the bidirectional characteristics of the metrical system of Ukrainian, but also point to some additional adjustments affecting the phonetic manifestation of metrical stress. Specifically, it will be shown that vowels in pretonic positions (i.e. positions immediately preceding lexical stress) exhibit increased duration. The effect of pretonic lengthening interferes with the otherwise regular rhythmic stress pattern, causing it to disappear in the vicinity of lexical stress. We further argue in Section 3 of this Element that pretonic lengthening can be viewed as an extended lexical stress domain effect, formally modelled in terms of grid-based representations.

As briefly discussed in Section 1.2, contemporary metrical theories provide various tools for describing classical bidirectional stress systems with internal lapses (e.g. Rubach & Booij Reference Rubach and Booij1985; McCarthy & Prince Reference McCarthy, Prince, Booij and van Marle1993; van der Hulst Reference Hulst, Goedemans, van der Hulst and Visch1996, Reference Hulst2012, Reference Hulst and van der Hulst2014; Kager Reference Kager2001, Reference Kager2005; Gordon Reference Gordon2002; Hyde Reference 61Hyde2002, Reference Hyde2016; Alber Reference Alber2005). These tools differ in whether they are based on rules, output constraints, or parameters; they also differ in assumptions concerning the representation of stress – that is, whether it should be grid-based and/or foot-based. Most of the previous accounts are couched in the constraint-based framework of Optimality Theory (OT), regulating the positioning of stress in terms of alignment constraints. Alignment constraints require that the designated (left or right) edge of some prosodic domain coincide with the corresponding edge of some other prosodic or morphological domain (McCarthy & Prince Reference McCarthy, Prince, Booij and van Marle1993). They can be either categorical (Kager Reference Kager2001, Reference Kager2005) or gradient (McCarthy & Prince Reference McCarthy, Prince, Booij and van Marle1993; Alber Reference Alber2005).

The attraction of rhythmic stress to the word edges in three-syllable words in (3a) and (3c) can be modelled in a straightforward way in terms of a high-ranking categorical alignment constraint, Align Edges (Gordon Reference Gordon2002: 497). Assuming the grid-based approach of Gordon (Reference Gordon2002), Align Edges requires that the edges of level 0 of a prosodic word – that is, the level corresponding to syllable positions – be aligned with a grid mark on level 1 – that is, the level corresponding to rhythmic stress (5). Words having the structure (5a) or (5c) fully satisfy this constraint because both the initial and the final syllable align with grid marks on level 1 in those words, and, additionally, no violation of *Clash ensues. *Clash is based on a rhythmic principle proposed by Prince (Reference Prince1983), which prohibits adjacent stressed syllables within a given stress domain; with reference to the metrical grid, it can be formulated as ‘[a]djacent syllables carrying a level 1 grid mark are banned’ (Gordon Reference Gordon2002: 506). The grid marks on level 1 in lexically stressed syllables appear through extrapolation of level 2 – that is, the level corresponding to primary stress. Example (5b) violates Align Edges twice; however, it remains the optimal structure because of its stress clash avoidance, as enforced by the domination of *Clash. This analysis is summarised in Table 2. Following standard practice, underlying representations are given in slashes.

1. (5) Grid representations of three-syllable words differing in the position of lexical stress

   a. [ˈσσˌσ]	b. [σˈσσ]	c. [ˌσσˈσ]
   x .	x	. x	level 2 (primary stress)
   x . x	. x .	x . x	level 1 (secondary stress)
   σ σ σ	σ σ σ	σ σ σ	level 0 (syllable positions)
   [ˈdɔrɔˌɦɔ]	[dɔˈrɔɦa]	[ˌdɔrɔˈɦa]
   ‘expensive, adv.’	‘way, nom. sg.’	‘dear, nom. sg. fem.’

Table 2Grid-based approach with categorical alignment: three-syllable words

More problematic from the theoretical point of view is the accommodation of the mirror-image stress patterns in six-syllable words: [ˈσσσˌσσˌσ] (4a) versus [ˌσσˌσσσˈσ] (4f). Basically, there are two theoretical approaches which can be employed to guarantee the occurrence of a lapse near the peak in bidirectional stress systems: gradient alignment versus licencing. The former will have an effect of pushing rhythmic stresses towards the left or the right edge of the word; a by-product of this effect will be creating a lapse either to the left or to the right of primary stress in ‘odd-parity’ words, depending on the designated edge in the alignment constraint. The latter, by admitting marked structures such as lapses in the vicinity of certain prosodic positions, here primary stress, will have a general effect of repelling rhythmic stresses away from the lexical stress position. As we discuss in what follows, the limitations of the gradient alignment mechanism are immediately clear in a system where rhythmic stress propagation should occur in both directions simultaneously. This is so regardless of whether grid-only or foot-based representations are assumed. The licencing mechanism allows us to generate correct predictions for the rhythmic stress patterns in the Ukrainian system, but only when it operates on grid-based, not foot-based representations.

Gradient alignment constraints can be multiply violated, depending on the distance (the number of syllable units) separating the designated edges of two domains. In what follows, we illustrate the problem posed by the Ukrainian pattern, assuming a foot-based gradient alignment approach (McCarthy & Prince Reference McCarthy, Prince, Booij and van Marle1993; Alber Reference Alber2005), in which syllables are parsed into binary left-headed (trochaic) or right-headed (iambic) feet. The operational effect of gradient alignment is that all feet containing rhythmic stresses are pushed either to the left or to the right, depending on the mutual ranking of the alignment constraint Align-Ft-L (‘the left edge of every foot is aligned with the left edge of prosodic word’; McCarthy & Prince Reference McCarthy, Prince, Booij and van Marle1993) and Align-Ft-R (‘the right edge of every foot is aligned with the right edge of prosodic word’; McCarthy & Prince Reference McCarthy, Prince, Booij and van Marle1993). As shown in Table 3 (based on Mołczanow & Łukaszewicz Reference Mołczanow and Łukaszewicz2021: 559), if Align-Ft-L is ranked above Align-Ft-R, then secondary stress is assigned from the left word edge, correctly generating the rightward stress iteration in [ˌmun^jiˌt͡sɨpal^jˈtɛt] in (a) but incorrectly deriving penultimate secondary stress in *[ˈlaɦɔˌdɨtɨˌmɛtɛ] in (b). In turn, the correct form [ˈlaɦɔdɨˌtɨmɛˌtɛ] and the erroneous output *[muˌn^jit͡sɨˌpal^jiˈtɛt] are generated by the reverse ranking Align-Ft-R ≫ Align-Ft-L. An arbitrary parsing into trochaic rather than iambic feet is assumed in this analysis; also it is far from clear under what conditions unary feet would be allowed in Ukrainian. It is important to add that the gradient alignment mechanism fails to generate the rightward and leftward stress iteration simultaneously also when it operates in terms of prominence marks on the grid rather than in terms of feet. Thus, replacing Align-Ft-L and Align-Ft-R with Align (x1, L) and Align (x1, R), which require that every level 1 grid mark be aligned with the left/right edge of level 0 of grid marks in a prosodic word (see Gordon Reference Gordon2002), would essentially lead to the same directionality paradoxes. Let us also observe that, unlike in the simpler case of three-syllable words schematised in Table 2, the directionality paradox in the longer words in Table 3 cannot be resolved in terms of *Clash ≫ Align Edges, because this sub-hierarchy of constraints treats competing outputs, such as [(ˌσσ) (ˌσσ) σ (ˈσ)] vs. [(ˌσσ)σ(ˌσσ)(ˈσ)] as well as [(ˈσσ)σ(ˌσσ)(ˌσ)] versus [(ˈσσ)(ˌσσ)σ(ˌσ)] as faring equally well.

Table 3Foot-based approach with gradient alignment: Align-Ft-L ≫ Align-Ft-R

An alternative mechanism is that of licencing, which admits rhythmically marked entities (lapses) in a limited set of prosodic positions (the peak and the right edge of the prosodic domain); see Kager (Reference Kager2001, Reference Kager2005). This is achieved by a licencing rhythmic constraint, Lapse-at-Peak (‘Lapse must be adjacent to the peak’; Kager Reference Kager2001: 4). To generate edge-based stress, the model employs categorical constraints Align-Wd-L and Align-Wd-R (‘every prosodic word starts/ends with a foot’; Kager Reference Kager2001). There are two insurmountable problems that this model encounters. First, as it operates on feet, it faces the same problem of arbitrary foot assignment as the model based on gradient alignment (McCarthy & Prince Reference McCarthy, Prince, Booij and van Marle1993; Alber Reference Alber2005): the initial stress derives from locating a trochaic foot at a left word edge, whereas the final stress is modelled by building a unary foot at the right edge of the word. Like the model in Table 3, it can derive either word-initial or word-final secondary stress, but not both.Footnote ⁵ Table 4 serves to illustrate the point (based on Mołczanow & Łukaszewicz Reference Mołczanow and Łukaszewicz2021: 561). The correct output [(ˈlaɦɔ)dɨ(ˌtɨmɛ)(ˌtɛ)] in (bi) is suboptimal relative to the fully parsed candidate [(ˈlaɦɔ)(ˌdɨtɨ)(ˌmɛtɛ)] in (biii).

Table 4Foot-based approach with categorical alignment and licencing

It has been pointed out in Mołczanow and Łukaszewicz (Reference Mołczanow and Łukaszewicz2021) that it is possible to construct an alternative foot-based analysis if the increased duration of stressed syllables is encoded phonologically. In this model, bimoraic vowels in metrically strong positions are opposed to monomoraic unstressed vowels, and bimoraic feet are built for both lexically and rhythmically stressed syllables, as shown in Figure 1. Edge-based stress is derived by constructing bimoraic feet at both word edges, which is achieved by means of the constraints Align-Wd-L and Align-Wd-R, whereas bidirectional iterative stress is derived by the licencing constraint Lapse-at-Peak, as in the foot-based licencing approach with categorical alignment illustrated in Table 4.

Figure 1

Approach employing moraic feet.

Although this analysis can technically derive the Ukrainian pattern, it is problematic for several reasons. First, it assumes a two-way length contrast in vowels which does not express a lexical contrast and thus serves a diacritic purpose, its function being merely the identification of the location of secondary prominence. Another objection concerns the consequences of this assumption for the modelling of the phonological processes of Ukrainian unconnected to stress. In particular, Mołczanow and Łukaszewicz (Reference Mołczanow and Łukaszewicz2021) demonstrate that the phonological distinction in vocalic duration (one mora vs. two moras) complicates the analysis of glides and geminates in Ukrainian. As for the former, the glides [j] and [w] alternate with high vowels [i] and [u] at word boundaries – for example, [ˈʋ^jin iˈdɛ] ‘he goes’ – [ʋɔˈna ˈjdɛ] ‘she goes’, [iˈdut^j uˈt͡ʃɨtɨˌs^ja] ‘they go to study’ – [iˈdu ˈwt͡ʃɨtɨˌs^ja] ‘I go to study’ (Toc’ka Reference Toc’ka and Hryščenko2002). This process interacts with moraic structure because gliding, which is used to resolve vowel hiatus and thus improve syllable structure, consists in a loss of a mora. Mołczanow and Łukaszewicz (Reference Mołczanow and Łukaszewicz2021) argue that the analysis assuming bimoraic feet incorrectly predicts that the vowel would be deleted, not glided, when preceded by either lexically or rhythmically stressed syllable – for example, the model would generate an incorrect form *[ˈlɨt͡saˌr^ji ˈdut^j] instead of the attested [ˈlɨt͡saˌr^ji ˈjdut^j] ‘knights go’ (see Mołczanow & Łukaszewicz Reference Mołczanow and Łukaszewicz2021: 570–572 for further discussion).

Another argument against bimoraic feet adduced in Mołczanow and Łukaszewicz (Reference Mołczanow and Łukaszewicz2021) comes from the phonology of geminate consonants. Long (geminate) consonants contrast with single consonants in Ukrainian – for example, [ˈl^jut^j] ‘rage, nom. sg.’ – [ˈll^jut^j] ‘pour, 3rd pers. pl. pres.’, [suˈd^ji] ‘court, loc. sg.’ – [suˈdd^ji] ‘judge, gen. sg.’, [ˈsɨn^ju] ‘blue, adj. fem. acc. sg.’ – [ˈsɨnn^ju] ‘blue, noun instr. sg.’ (Toc’ka Reference Toc’ka and Bilodid1969; Bethin Reference Bethin1992; Loboda Reference Loboda and Ja2009). Geminates are standardly encoded in the underlying representation as moraic, whereas single consonants are underlyingly moraless (Hayes Reference Hayes1989). Assuming that stressed syllables are bimoraic and geminate consonants are moraic (as illustrated in Figure 2), the model predicts stressed vowels to be shorter before geminate consonants (Mołczanow & Łukaszewicz Reference Mołczanow and Łukaszewicz2021: 570).

Figure 2

Moraic representation of a word-medial.

(a)

singleton,

(b)

geminate,

(c)

cluster

Though shortening of vowels before geminates is not uncommon cross-linguistically (consider e.g. Italian; Krämer Reference Krämer2009), no such differences have been reported in the literature on Ukrainian and our preliminary study has not revealed any differences either. As illustrated in Figure 3, the duration of the vowel [u] is comparable in the words [ˈsudd^ji] ‘judge, nom. pl.’ and [ˈkurdɨ] ‘Kurd, nom. pl’ (102 ms vs. 101 ms, respectively).

Figure 3

An illustration of comparable vowel duration before.

(a)

a geminate and

(b)

a cluster

In sum, the Ukrainian data cannot be accounted for using a mechanism relying on feet. As argued extensively in Mołczanow and Łukaszewicz (Reference Mołczanow and Łukaszewicz2021), neither gradient alignment (McCarthy & Prince Reference McCarthy, Prince, Booij and van Marle1993) nor categorical alignment coupled with foot-based licencing constraints (Kager Reference Kager2001) can successfully derive the Ukrainian system, because these mechanisms would push all rhythmic stresses either to the left or to the right, independent of whether the assumed foot type is binary or ternary (Martínez-Paricio & Kager Reference Martínez-Paricio and Kager2015; see also Footnote fn. 2). Mołczanow and Łukaszewicz (Reference Mołczanow and Łukaszewicz2021) further argue that the Ukrainian data provide strong support for a grid-based representation, as advocated in Gordon (Reference Gordon2002). In this model, edge-based stress is generated by the constraint Align Edges (‘Every grid mark of level 1 is aligned with the {right, left} edge of level 0 of grid marks in a prosodic word’; Gordon Reference Gordon2002: 497). Align Edges thus aligns the initial and final syllables with a grid mark on a prosodic level corresponding to secondary stress, as illustrated in (6). (The same constraint was used in our analysis of the rhythmic stress pattern, summarised in Table 2.) The location of word-medial (iterative) rhythmic stresses is predicted by gradient alignment constraints Align (x1, L) and Align (x1, R) in Gordon’s (Reference Gordon2002) approach. As pointed out previously in this Element, although these constraints are defined in terms of a metrical grid, they lead to the same directionality paradoxes as foot-based gradient alignment because they enforce aligning the grid marks on level 1 with the left or right edge of the word, but not both. As such, they yield incorrect predictions for the rhythmic stress iteration patterns in Ukrainian and cannot predict the position of lapses in the examples in (6).

1. (6) Grid representations for six-syllable words with bidirectional rhythmic stress

   x	x	Level 2 (primary stress)
   x . x. . x	x . . x . x	Level 1 (secondary stress)
   x x x x x x	x x x x x x	Level 0 (syllable positions)
   ˌmunjiˌt͡sɨpaljiˈtɛt	ˈlaɦɔdɨˌtɨmɛˌtɛ

To derive both lapses in the vicinity of lexical stress, Mołczanow and Łukaszewicz (Reference Mołczanow and Łukaszewicz2021) employ the licencing constraint Lapse-at-Peak (‘Lapse must be adjacent to the peak’; Kager Reference Kager2001: 4), as in the foot-based approach with categorical alignment and licencing; cf. Table 4). Combining the grid-based constraint Align Edges with the licencing constraint Lapse-at-Peak allows for a successful generation of the Ukrainian pattern, as illustrated by the evaluation shown in Table 5 (Mołczanow & Łukaszewicz Reference Mołczanow and Łukaszewicz2021: 567).

Table 5A combination of the grid-based approach and the licencing approach

It is evident, then, that the metrical theory can in principle model the bidirectional iterative stress system of Ukrainian. However, as we will see in the remainder of this Element, this regular pattern of alternating rhythmic stresses is an idealisation which is not instantiated phonetically in an unambiguous way. Whereas the acoustic correlates of lexical stress are robust, the distinction between vowels carrying secondary stress and unstressed vowels is not always explicitly manifested in the acoustic signal. We will see that there exist significant phonetic differences between the stressed and unstressed vowels located to the left and to the right of lexical stress. Namely, syllables preceding lexical stress in ˌσσˈσ(σ) and ˌσσσˈσ(σ) show a gradual increase in duration from the left word edge towards lexical stress. This pattern of pretonic lengthening obliterates the duration-based expression of initial rhythmic stress. In what follows, we tackle the asymmetry between pretonic and posttonic positions in a series of acoustic studies based on words having different length. We investigate how the varying distance between the right/left word edge and lexical stress affects the phonetic manifestation of rhythmic stress and other prosodic phenomena. We also propose an extension of the model combining the grid-based approach and the licencing approach to account for the asymmetry between pretonic and posttonic position. Novel data are synthesised with those reported in previous studies to improve our understanding of the interaction between the lexical and grammatical stress domains, as well as the potential interaction between stress-related and other (e.g. positional) factors.

2.2.1 Lexical Stress

As demonstrated by previous findings (e.g. Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a, Reference Łukaszewicz and Mołczanow2018b, Reference Łukaszewicz and Mołczanow2018c), stress is manifested acoustically in terms of increased syllable/vowel duration in Ukrainian. Some authors single out intensity as a correlate of lexical stress in Ukrainian (Nakonečnyj Reference Nakonečnyj and Bilodid1969: 359; Brovčenko Reference Brovčenko1969; Loboda Reference Loboda and Ja2009: 21); however, acoustic measurements presented in Łukaszewicz and Mołczanow (Reference Łukaszewicz and Mołczanow2018c) demonstrate that intensity and F0 are not employed to cue word-level prominence. Numerous recent studies based on polysyllabic words of different length and with different primary stress location (e.g. Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a, Reference Łukaszewicz and Mołczanow2018b, Reference Łukaszewicz and Mołczanow2018c; Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2018, Reference Mołczanow, Łukaszewicz and Łukaszewicz2021) point to robust differences between lexically stressed syllables/vowels and those in metrically weak positions. Lexically stressed syllables are reported to be nearly 2 times longer than unstressed syllables in Łukaszewicz and Mołczanow’s (Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a) study, based on syllable duration measurements in five- and six-syllable words with lexical stress on the initial syllable, such as [ˈbat͡ʃɨˌtɨmɛˌtɛ] ‘see, 2nd pers. pl. future’ (p. 266). In another study (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2018b), based on words with lexical stress on the final syllable or near the end of the word – that is, on the fourth, fifth, and sixth syllables, as in [ˌʋɛlɔsɨˈpɛdnɨj] ‘bicycle, nom. sg. adj.’, [ˌɔrɦaˌnʲizuˈʋatɨ] ‘organise, inf.’, [ˌkapʲiˌtalʲizuˈʋatɨ] ‘capitalise, inf.’, lexically stressed syllables are 1.5 times longer than other syllables within a word (p. 380). In absolute terms, those stress-dependent differences are reported to be 86 ms for the low vowel /a/ and 49 ms for high vowels, on the basis of words with lexical stress on the fifth syllable (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2018c: 373). In a study of minimal pairs, which differ only in terms of the position of lexical stress – for example, [pɔˈpadaˌtɨ] ‘fall, inf. perf.’ – [ˌpɔpaˈdatɨ] ‘strike and hit the mark, inf. imperf.), the average difference between the vowels in the corresponding lexical versus unstressed position in the third syllable is 83 ms; the lexically stressed vowels turn out 2.3 times longer than the unstressed ones (Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2021: 11).

2.2.2 Rhythmic Stress

The presence of rhythmic stress has been reported in traditional descriptive grammars of Ukrainian (Broch Reference Broch1910; Lehr-Spławiński Reference Lehr-Spławiński1916; Ziłyński Reference Ziłyński1932; Bilodid Reference Bilodid1969); its acoustic correlates have been recently studied in a number of experiments (Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a et seq.). Similarly to lexical stress, rhythmic stress is expressed by increased duration. However, although rhythmically stressed and unstressed syllables differ in length, the difference between them is much smaller compared to the difference in the lexical stress contexts. In addition, rhythmic stress is an optional phenomenon, with different speakers showing different levels of rhythmicity (e.g. Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a; Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2021).

Studies of both the leftward and rightward stress iteration in Ukrainian have been conducted. The leftward rhythmic stress iteration has been investigated on the basis of words with lexical stress on the initial syllable, having the structure [ˈσσˌσσˌσ] or [ˈσσσˌσσˌσ] (Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a). The analysis of more than 2,100 syllable tokens from twelve speakers reveals consistent lengthening of the final syllable and optional lengthening of the third syllable from the end in such words. On the basis of segmentally identical syllables, a statistically significant increase of 16 ms is reported in the iterative stress position in comparison with the preceding unstressed syllable, which is part of a lapse in [ˈσσσˌσσˌσ] words. Similar results have been obtained for words with the rightward iteration. In Łukaszewicz & Mołczanow’s (Reference Łukaszewicz and Mołczanow2018b) study, based on acoustic measurements in more than 1,400 syllable tokens from sixteen speakers, the initial syllable is on average 30 ms longer than the second syllable in [ˌσσσˈσ(σ)], [ˌσσˌσσˈσ(σ)], and [ˌσσˌσσσˈσ(σ)] words. (Duration measurements were conducted on the basis of whole syllables in that study.) A significant increase in duration is also reported for the iterative position (the third syllable) in [ˌσσˌσσˈσ(σ)], and [ˌσσˌσσσˈσ(σ)] words, which turns out 21 ms longer than the preceding (i.e. second) metrically weak syllable. In another analysis based on segmentally identical syllables in words with potential stress iteration, the iterative position (third syllable) is about 16 ms longer than the preceding unstressed syllable, with a statistically significant effect of rhythmic stress (p. 379).

In sum, we can infer from the temporal patterns present in the acoustic speech signal that rhythmic stress propagation in Ukrainian proceeds as predicted for bidirectional systems – that is, from the word’s edge towards the main stress position, with lapses occurring near the peak. The presence of edge-based rhythmic stress propagation is illustrated in Figure 4, which depicts the metrical pattern in a word with lexical stress on the initial syllable, [ˈbat͡ʃɨtɨˌmɛtɛˌs^ja] ‘see, 2nd pers. refl. pl. future’. A conspicuous durational effect is seen in the lexically stressed syllable; also, the rhythmically stressed syllables exhibit longer vowels compared to those in adjacent unstressed syllables. This example clearly demonstrates the leftward direction of rhythmic stress propagation – the lapse formed by the sequence -t͡ʃɨtɨ- is clearly located at the peak.

Figure 4

Leftward rhythmic stress iteration.

Figure 5 illustrates the metrical patterns in words with lexical stress on the fifth (a), and sixth syllables (b). Both in [ˌkataˌl^jizuˈʋatɨ] ‘catalyse, inf.’ (a) and [ˌtɛlɛˌfɔnʲizuˈʋatɨ] ‘to set up a telephone connection, inf.’ (b), the lexically stressed vowel in the syllable -ʋa- is clearly the longest of all. In accordance with the bidirectional system’s characteristics, here we expect rhythmic stress iteration in the reversed direction – from the word’s beginning rightwards, which is indeed the case. In both examples, the vowel in the initial (rhythmically stressed) syllable is longer than the vowel in the second (unstressed) syllable. The third (rhythmically stressed) syllable is slightly enhanced in comparison with the preceding syllable. Altogether, the expected [ˌσσˌσ-] pattern appears across the first three syllables in those words. However, there also seems to be an extra domain of temporal enhancement in the syllables preceding lexical stress, visible in Figure 5, which we address in Section 2.2.3.

Figure 5

Rightward rhythmic stress iteration – durational enhancement of vowels in the rhythmically stressed initial and third syllables; pretonic lengthening of the vowel in the fourth syllable in (a) and the fourth and fifth syllables in (b).

2.2.3 Pretonic Lengthening

We can infer from both Figure 4 and Figure 5 that rhythmic stress applies at the left/right edge and iterates towards the position of main stress; the rightward pattern [ˌσσˌσ-] thus seems to be a mirror image of the leftward pattern [-ˌσσˌσ]. However, by comparing the two figures, we may also observe that this symmetrical bidirectional characteristic of the Ukrainian system is not fully reified on the physical level. There is no perfect symmetry in the temporal patterns to the immediate left and to the immediate right of lexical stress. In Figure 5, there seems to be increased duration in the pretonic syllable relative to the rhythmically stressed vowels in the initial and third syllables. No such duration enhancement is seen in the posttonic syllable in Figure 4 – the vowel in the posttonic position seems to be conspicuously shorter than the rhythmically stressed vowels in the antepenultimate and final syllables.

The presence of an extra domain of temporal enhancement in the syllable immediately preceding the position of lexical stress was observed in previous studies of the Ukrainian metrical system; the phenomenon has been referred to as ‘pretonic lengthening’ (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2018b, Reference Łukaszewicz and Mołczanow2018c; Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2019b). Comparisons of vocalic duration in different prosodic positions in words with lexical stress on the fifth syllable (i.e. words having the structure [ˌσσˌσσˈσ(σ)]) showed that vowels are on average 14 ms longer in the pretonic position than in the unstressed (second) position (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2018c). Acoustic measurements demonstrate that pretonic lengthening is consistently present across various types of words – that is, also in words where no rhythmic stress iteration is expected. In a recent systematic study of the pretonic lengthening effect in Ukrainian (Łukaszewicz et al. submitted), based on words with lexical stress on the fourth syllable (i.e. words having the structure [ˌσσσˈσ(σ)]), pretonic vowels exceed in length both the vowels in the rhythmically stressed (initial) and the unstressed (second) position. The statistically significant difference between the vowel /a/ in the pretonic and the initial position amounts to 10 ms. As we will see in Sections 2.2.4 and 2.3.2, an increase in duration is also observed in the pretonic syllable in shorter quadri- and tri-syllabic words with lexical stress on the second or third syllable.

Given that lexical and rhythmic stress are both expressed in terms of increased duration in Ukrainian, the existence of pretonic lengthening, which is yet another kind of temporal adjustment in that language, poses an additional descriptive and theoretical challenge. From the descriptive point of view, little is known about the scope of this effect and how it depends on the distance between the beginning of the word and the lexical stress position; another question is that of how duration enhancement interacts with vowel quality (phonetic reduction) in pretonic positions. On the theoretical side, Łukaszewicz and Mołczanow (Reference Łukaszewicz and Mołczanow2018b) suggest that the lexical stress domain extends beyond the lexically stressed syllable in Ukrainian, which may hinder the expression of the alternating rhythmic pattern in the vicinity to the left of lexical stress. If pretonic lengthening is a lexical domain effect, it needs to be clarified how it can interact with rhythmic constraints such as Lapse-at-Peak. It also seems necessary to place the Ukrainian pattern within a broader context of pretonic lengthening effects occurring in other languages, especially those belonging to the East Slavic group.

A subtle increase in vowel duration in the pretonic relative to the pre-pretonic position, similar to the one reported for Ukrainian, has been detected in Romance languages such as European Portuguese, Romanian, and Spanish (Chitoran & Hualde Reference Chitoran and Hualde2007), as well as Modern Hebrew (Cohen et al. Reference Cohen, Silber-Varod and Amir2018). A more conspicuous pretonic lengthening effect has been reported for Cordoban Spanish (Lang-Rigal Reference Lang-Rigal2014; Lenardón Reference Lenardón2017) as well as some East Slavic dialects (Bethin Reference Bethin2006); in both, the pretonic syllable can exceed the lexically stressed syllable in length. Pretonic lengthening may represent a gradient phonetic effect – for example, the strength of this effect may decrease with distance from the lexically stressed vowel (see Cohen et al. Reference Cohen, Silber-Varod and Amir2018: 12). In some languages, the extra duration present in the pretonic position has been reported to cause emergence of certain phonological patterns; compare the phonologisation of iV sequences in Spanish as diphthongs or hiatus (Chitoran & Hualde Reference Chitoran and Hualde2007: 59).

Pretonic lengthening has been widely documented in East Slavic. In Standard Russian, ‘a vowel in a pretonic syllable is longer than a vowel in an unaccented syllable by a quarter to almost half (1.25 to 1.4 approx.)’ (Jones Reference Jones1923/69: 216). This difference has been corroborated by instrumental data reported in Vysotskij (Reference Vysotskij, Azarx, Bromlej and Bulatova1973: 38), with a 22 ms difference in vocalic duration detected between the first and the second pretonic positions. In East Slavic dialects reported in Vysotskij (Reference Vysotskij, Azarx, Bromlej and Bulatova1973), there seems to be a special connection between the duration of the immediately pretonic vowel and that of the lexically stressed (tonic) vowel. Correlation analyses conducted on the basis of Vysotskij’s data corroborate the observation that the pretonic and tonic syllables constitute a close-knit unit across East Slavic dialects (r (13) = 0.841, p < 0.001), while a rather loose relationship (no significant correlation) is observed between pre-pretonic and pretonic or pre-pretonic and tonic vowels (Łukaszewicz et al. submitted). Pretonic lengthening is important from the point of view of the degree of vowel reduction, which is a phonological process in Standard Russian. As we show in Section 2.2.5, Ukrainian is different from Standard Russian not only in terms of temporal patterns (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2018b: 381), but also in terms of how duration adjustments correspond to vowel quality (formant undershoot).

Notably, no similar effect has been reported for the immediately posttonic positions in East Slavic. In this Element, we widen the focus to include both the pretonic and the posttonic positions, supplementing the description by new empirical data from Ukrainian. Posttonic lengthening has not been previously reported for Ukrainian, and its absence, confirmed by the current findings, points to an asymmetrical temporal pattern in syllables located next to lexical stress. A preliminary study based on intrinsic comparisons in three-syllable words having the structure [ˈσσˌσ] and the same vowel category in the posttonic versus final positions – compare /a/ in [ˈʋɨpaˌla] ‘fall out, 3rd pers. sg. fem. past ’ – demonstrates that the vowel in the posttonic (metrically weak) syllable is conspicuously shorter than the same vowel in the final (metrically strong) syllable; see Figure 6 (Łukaszewicz & Mołczanow 2024). The lengthening of the final syllable cannot simply be a boundary effect in Ukrainian – as illustrated in Section 2.2.4, stress-induced differences are found in extrinsic comparisons of the final syllable in minimal pairs having the structure [ˌσσˈσσ]/[σˈσσˌσ].

Figure 6

Durational enhancement of the final (metrically strong) vowel relative to the posttonic position.

We return to pretonic lengthening in Section 3, in which we argue that the scope of this effect is important from the point of view of interaction between the lexical and grammatical stress domains. Specifically, we suggest that lexical stress domain extends leftwards to up to three preceding syllables. As this extension is realised in terms of a gradual increase in duration, pretonic lengthening interferes with the duration-based expression of rhythmic stress (see Section 3.2 for further discussion).

In Section 2.2.4, we consider the confounding effect of word boundaries on the temporal expression of metrical prominence. Specifically, we ask whether the increase in duration observed in initial and final positions in Ukrainian cues rhythmic stress or signals word edges.

2.2.4 Word Boundary Effects

The experiments involving words of five or more syllables have revealed that both primary and secondary stress are cued by increased duration (Łukaszewicz & Mołczanow Reference Łukaszewicz, Mołczanow, Czaplicki, Łukaszewicz and Opalińska2018a, Reference Łukaszewicz and Mołczanow2018b, Reference Łukaszewicz and Mołczanow2018c). Duration is a cross-linguistically common correlate of metrical prominence, but it is also a well-known multipurpose phonetic cue. Factors such as word length, segmental structure, phrasal stress, or boundary effects can be confounding factors as far as the expression of word-level prominence is concerned (see e.g. Turk & Shattuck-Hufnagel Reference Turk and Shattuck-Hufnagel2000, Reference Turk and Shattuck-Hufnagel2007; Plag et al. Reference Plag, Kunter and Schramm2011; White & Turk Reference White and Turk2010; Vogel et al. Reference Vogel, Athanasopoulou, Pincus, Heinz, Goedemans and van der Hulst2016). Furthermore, observed duration adjustments can manifest multiple mechanisms operating simultaneously. An illustrative example is provided by lengthening patterns in English phrases such as tuna#choir versus tune#acquire. The word-final [ə] in tuna#choir is longer than the word-initial [ə] in the segmentally identical phrase tune#acquire, whereas the [uː] of the syllable tun is longer in the latter example. These temporal patterns can be caused by word-final lengthening (Beckman & Edwards Reference Beckman, Edwards, Kingston and Beckman1990) and other mechanisms, such as asymmetric polysyllabic shortening (Lindblom & Rapp Reference Lindblom and Rapp1972) and syllable ratio equalisation (Abercrombie Reference Abercrombie1965/71); see Turk and Shattuck-Hufnagel (Reference Turk and Shattuck-Hufnagel2000: 401) for further discussion.

As discussed previously, Ukrainian has rhythmic stress which is located, depending on the word length, at both or one of the word edges, and is expressed by prolonged vowel duration. However, given that speakers use duration adjustment mechanisms for multiple prosodic purposes, a question arises whether the increased duration at word edges in Ukrainian cues prosodic prominence or signals word boundaries.

To answer this question, Mołczanow et al. (Reference Mołczanow, Łukaszewicz and Łukaszewicz2018, Reference Mołczanow, Łukaszewicz and Łukaszewicz2021) investigated segmentally identical word pairs differing only in the position of lexical stress and rhythmic structure – for example, [pɔˈpadaˌtɨ] ‘fall, inf. perf.’ – [ˌpɔpaˈdatɨ] ‘strike and hit the mark, inf. imperf.’ (cf. 7a). This design made it possible to empirically distinguish between the effects of metrical prominence and lengthening at the word edges, simultaneously controlling for the potential confounding influence of polysyllabic shortening and intrinsic segmental length. The following extrinsic comparisons were performed (7b):

1. 1. a.

      σ1 ˈσ2 σ3 ˌσ4	e.g.	[pɔˈʋɔdɨˌtɨ] ‘behave, inf.’
      ˌσ1 σ2 ˈσ3 σ4	[ˌpɔʋɔˈdɨtɨ] ‘lead, inf. perf.’

   1. b.

      σ1: pretonic – secondary	[pɔ] – [ˌpɔ]
      σ2: tonic – pretonic	[ˈʋɔ] – [ʋɔ]
      σ3: unstressed – tonic	[dɨ] – [ˈdɨ]
      σ4: secondary – unstressed	[ˌtɨ] – [tɨ]

The use of segmentally identical minimal pairs ensured that any observed temporal differences reflected differences in prosodic prominence. Fourteen speakers were audio-recorded reading test words which were placed in the frame [skaˈʒɨ … ˈdruɦɨj ˈraz] ‘Say (2nd pers. sg. imp.) … for the second time.’ The statistical analysis was based on the duration measurements of seven minimal pairs (4,128 vowels and consonants in total).

Overall, the results point to the existence of edge-based prominence independent of boundary strengthening. As illustrated in Figure 7, the word-final [ɨ] is visibly shorter in the metrically weak position in [ˌpɔʋɔˈdɨtɨ] ‘lead, inf. perf.’ (a) than in the metrically strong position in [pɔˈʋɔdɨˌtɨ] ‘behave, inf.’ (b). Additionally, the intrinsic comparison of the posttonic (metrically weak) and final (metrically strong) [ɨ] in [pɔˈʋɔdɨˌtɨ] ‘behave, inf.’ (right panel) points to increased duration in the latter. The pattern is statistically robust (Łukaszewicz & Mołczanow 2024).

Figure 7

Durational enhancement of the final metrically strong vowel (right panel) relative to the final metrically weak vowel

(left panel).

As for the initial position, the measurements revealed the effect of pretonic lengthening. In Figure 7, the pretonic [ɔ] is visibly longer than the rhythmically stressed [ɔ], in the case of the intrinsic comparison of the two vowels in [ˌpɔʋɔˈdɨtɨ] ‘lead, inf. perf.’ (panel (a)) as well as the extrinsic comparison of the vowel [ɔ] in the initial syllables of [ˌpɔʋɔˈdɨtɨ] ‘lead, inf. perf.’ (the rhythmic stress condition; panel (a)) and [pɔˈʋɔdɨˌtɨ] ‘behave, inf.’ (the pretonic condition; panel (b)). Duration measurements conducted for the whole data set revealed a small but statistically significant difference of 7.5 ms between the vowel in the rhythmically weak pretonic position and the vowel in the rhythmically stressed position.

In sum, the comparison of temporal patterns in segmentally identical syllables indicates that word-final rhythmic stress and pretonic lengthening are separate duration-based mechanisms independent of temporal adjustments associated with word boundaries. As we will see in Section 2.3.1, this result is confirmed by extrinsic comparisons of identical syllables in trisyllabic words.

2.2.5 Vowel Reduction

This section presents the results of our previous research on the relation between duration and vowel quality vis-à-vis the metrical structure in Ukrainian. It is well known that duration may interact with vowel formants to signal metrical prominence. As word stress is inextricably related to the phenomenon of vowel reduction, a comprehensive account of a prosodic system cannot dispense with the study of the effect of metrical prominence on the expression of vocalic contrasts. Vowel reduction can be categorical (i.e. leading to a loss of lexical contrast) or phonetic, typically resulting in non-categorical (gradient) shrinkage of the vocalic space. Ukrainian does not have phonological reduction, unlike, for example, typologically close Belarusian, which displays categorical neutralisation of lexical distinctions in unstressed positions (Toc’ka Reference Toc’ka and Bilodid1969; Czekman and Smułkowa Reference Czekman and Smułkowa1988). This is illustrated by the alternation [o] – [a] in Belarusian in (8a) and its absence in Ukrainian in (8b):

1. 1. a.

      [ˈkɔzɨ]

      –

      [kaˈza]

      Belarusian

   1. b.

      [ˈkɔzɨ]	–	[kɔˈza]	Ukrainian
      ‘she-goat, nom. pl.’			‘id., nom. sg.’

Phonetic reduction, in turn, is widely attested in unstressed positions in a variety of languages and may either accompany phonological reduction or occur in its absence. Phonetic reduction usually consists in the reduction in duration, spectral reduction, or both. This type of reduction has been reported for many languages – for example, Swedish (Lindblom Reference Lindblom1963), Dutch (Beinum & Jeannette Reference Beinum and Jeannette1980), English (Moon & Lindblom Reference Moon and Lindblom1994), and Polish (Nowak Reference Nowak2006, Strycharczuk et al. Reference Strycharczuk, Ćavar and Coretta2021).

Phonetic vowel reduction has been standardly described in terms of gestural undershoot attributed to decreased duration in prosodically weak contexts (Lindblom Reference Lindblom1963; Flemming Reference Flemming, Hayes, Kirchner and Steriade2004; Barnes Reference Barnes2006). In the classical vowel reduction model of Lindblom (Reference Lindblom1963), the first vowel formant (F1) is shown to be a function of the decreasing vowel duration in unstressed vowels in Swedish. Subsequent studies have found that the compression of vowel space can also be caused by shorter segment durations associated with faster speaking rates (e.g. Miller Reference Miller, Eimas and Miller1981; Flege Reference Flege1988; Agwuele et al. Reference Agwuele, Sussman and Lindblom2008, among many others). Interestingly, other studies have shown that the effect of temporal reduction on vowel quality is not automatic, in that reduced duration can be dissociated from formant undershoot on a language-specific basis (Delattre Reference Delattre1965; Fourakis Reference Fourakis1991; Beckman et al. Reference Beckman, Edwards, Fletcher, Docherty and Ladd1992; Barnes Reference Barnes2006; Nadeu Reference Nadeu2014, and others). For instance, Barnes (Reference Barnes2006) reveals a strong correlation between F1 and duration in the second pretonic but not in the pretonic position in Russian. Barnes (Reference Barnes2006) interprets this finding – that is, duration-dependent reduction in the second pretonic position versus duration-independent reduction in the pretonic position – in terms of structural differences: reduction in the first pretonic position is categorical (phonological), whereas reduction in the second pretonic position is gradient (phonetic).

Vowel neutralisations in Ukrainian are non-categorical and consist in centralisation and vowel undershoot (Toc’ka Reference Toc’ka1973: 186; Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2019b; Łukaszewicz et al. submitted). An experimental study by Toc’ka (Reference Toc’ka1973) indicates that vowel quality may play a role in expressing secondary stress. Based on data collected from five speakers coming from central Ukraine, Toc’ka (Reference Toc’ka1973) reports that the distinctive vowel quality is maintained in some unstressed positions. Specifically, the measures of formant values of unstressed vowels show that qualitative reduction is suspended in positions removed by one or two syllables from the main stress. Toc’ka (Reference Toc’ka1973) finds qualitative differences in unstressed positions only for the vowels [a], [u], and [ɛ], and she does not relate the presence of vocalic undershoot to any rhythmic pattern. The presence of phonetic vowel reduction has been detected in more recent acoustic studies (Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2019b; Łukaszewicz et al. submitted) which conducted formant measurements of the vowel [a] in all positions preceding lexical stress.Footnote ⁶ The analysis of acoustic data reveals subtle lengthening of the pretonic vowel and formant undershoot across the lexically unstressed syllables. Interestingly, these findings indicate that the relationship between temporal and spectral parameters is not the same in the metrically strong and weak positions.

The measurements of the formant structure of the vowel [a] were conducted based on pentasyllabic (and quadrisyllabic) words with lexical stress falling on the fourth syllable – that is, words having the structure [ˌσ₁σ₂σ₃ˈσ₄(σ₅)]. While a small progressive increase in vowel duration was observed across the three positions preceding lexical stress, only the pretonic position (σ₃) was significantly different, and the initial (σ₁) and second (σ₂) positions were comparable in length. Interestingly, a significant positive correlation between F1 and duration was detected for the second unstressed vowel (σ₂) (r(291) = 0.19) and the pretonic vowel (σ₃) (r(286) = 0.46) but not for the initial (rhythmic) vowel (r(289) = – 0.075); see Figure 8). Similarly to the initial (rhythmic) position, vowels in the lexically stressed (tonic) positions (σ₄) did not display a correlation between F1 and duration. We have tentatively concluded that this stability of F1 targets in metrically strong positions (i.e. the positions of rhythmic and lexical stress) might serve as another cue to metrical prominence (Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2019b; Łukaszewicz et al. submitted). Alternatively, as we point out in Łukaszewicz et al. (submitted), duration-independent stable F1 targets may also point to phonologisation of vowel reduction in the initial position.

Figure 8

The relationship between normalised F1 and duration in [ˌσσσˈσ(σ)] words, divided by position.

We return to the issue of vowel reduction in Section 2.3.3, where we present new data drawn from duration and format measurements of vowels in shorter (trisyllabic) words. These new findings show that the relationship between F1 and duration is more complex than suggested by the results of previous studies discussed in this section and may also depend on such factors as word length or the relative position of lexical stress with respect to the word’s left versus right edge.

2.2.6 Interim Summary

In sum, previous research on Ukrainian points to a rather complex relationship between metrical phonology and phonetics, with some non-obvious surface-level effects resulting from the interaction of various prosodic factors manifested in terms of temporal enhancement. Acoustic measurements in polysyllabic words, such as those in Figure 4 and Figure 5, suggest some interesting asymmetry on the phonetic level: the syllables immediately to the left of the lexically stressed position show a subtle lengthening effect, while those to the right do not. In Section 2.3, we look at temporal patterns in three-syllable words in Ukrainian. The point of interest is whether three-syllable words having the ‘mirror-image’ metrical structures, [ˈσσˌσ] versus [ˌσσˈσ], exhibit a degree of (a)symmetry in the leftward versus rightward pattern on the phonetic level, comparable to that occurring in the ‘mirror-image’ six-syllable words, [ˈσσσˌσσˌσ] and [ˌσσˌσσσˈσ]. Does the pretonic position differ significantly from the posttonic one in such short words? Moreover, considering the relatively small two-syllable distance between the word’s beginning and lexical stress in words having the structure [ˌσσˈσ], we expect either the predicted rightward rhythmic pattern or pretonic lengthening to occur, but not both. Do then the temporal patterns across the first two syllables in [ˌσσˈσ] words resemble the initial rhythmic [ˌσσ-] pattern of [ˌσσˌσσσˈσ] words, or rather show the gradual ‘pretonic lengthening’ effect in the vicinity of lexical stress? Which of the two competing phenomena, rhythmic stress or pretonic lengthening, prevails in such words? We also tackle the question of the relationship between duration and formant structure in different prosodic positions in those words.

2.3.1 Methods

Ten native speakers of Ukrainian (9F, 1M; aged M = 48) took part in the experiment. To minimise dialectal variation, we selected participants who came from western Ukraine (Lviv, Lutsk, Ivano-Frankivsk, and Rivne regions). Seven participants were recorded in Ukraine and three in Warsaw in Poland. The participants recorded in Ukraine were monolingual; the participants recorded in Poland reported some knowledge of Polish but used Ukrainian in everyday speech.

The recordings were performed using a Tascam Dr-100mkIII portable recorder, set at a sampling rate of 44.1 kHz, and an AT897 microphone. Participants were audio-recorded reading sentences containing target words in three repetitions. The words put in a frame were presented on a computer monitor; the list was randomised to avoid order effects. Apart from target items, twenty filler words were used. Lexical stress was marked orthographically to facilitate the identification of words. We obtained 1,080 tokens in total (10 participants * 9 stress/position conditions * 4 segmental types * 3 repetitions). Target words all appeared in the same frame: [ˈskaʒɛˌtɛ … ˈdruɦɨj ˈraz] ‘You (pl.) will say … for the second time’. Twenty-one tokens (1.9% of data) were rejected during analysis because of speech dysfluencies.

Segmentation was done manually using a high-resolution waveform editor (Sound Forge Pro v. 11.0); vowel boundaries were marked based on the dynamics of changes in the shape of the waveform, the visual inspection of the spectrogram in Praat, and auditory perception. Measurements were conducted in Praat (v. 6.2.09; Boersma & Weenink Reference Boersma and Weenink2022); duration values were obtained using a script. Raw duration values, expressed in [ms], were used to calculate by speaker z-scores in order to make the data more comparable.

2.3.2 Temporal Patterns

We performed two kinds of statistical analysis: (i) an overall analysis testing the effect of stress on duration across all tokens, and (ii) planned comparisons targeting selected prosodic and positional effects which could be tested on the basis of subsets of data. For statistical analyses, we used linear mixed effects models, built in SPSS (v. 29).

The overall analysis included standardised duration (z-scores) as the dependent variable and ‘stress’ as well as ‘trial’ as fixed effects. The ‘stress’ condition had five levels: initial rhythmic, pretonic, lexical (tonic), posttonic, and final rhythmic; the trial effect had three levels (corresponding to the number of repetitions in the experiment). To account for the repeated measures (identical segmental contexts) occurring in the experiment, we added ‘sequence’ as a random effect – the model included the sequence-specific intercept and slope for the fixed effect of stress. Individual differences in speech rates were controlled in terms of by-speaker z-scores; however, there still might be individual differences related to the expression of stress. To control for such effects, we included by-speaker random slopes for the fixed effect of stress in our model.

Significant results were obtained for both ‘stress’ and ‘trial’ conditions. The model had a marginal R² of 0.86 (reflecting the proportion of variance explained by fixed factors alone), and a conditional R² of 0.88 (reflecting the proportion of variance explained by both fixed and random factors). The estimated means for particular stress conditions are depicted in Figure 9. The final rhythmic syllable, which was the reference level in the analysis, turned out significantly different from all other ‘stress’ positions, except the pretonic one; initial rhythmic: β₁ = −0.206, SE = 0.056, t = −3.715, p < 0.001; pretonic: β₂ = −0.068, SE = 0.051, t = −1.347, p = 0.188; lexical: β₃ = 1.826, SE = 0.049, t = 37.166, p < 0.001; posttonic: β₄ = −0.205, SE = 0.051, t = −4.041, p < 0.001. As anticipated, the most conspicuous temporal enhancement was found in the lexical stress position. Also, the ‘final rhythmic’ vowel turns out significantly longer than the ‘posttonic’ vowel in this analysis. This is an important result because it corroborates the presence of rhythmic stress in Ukrainian. A similar effect of final rhythmic stress was reported in Mołczanow et al. (Reference Mołczanow, Łukaszewicz and Łukaszewicz2018). Additional paired comparisons reveal a significant, but very small difference of 0.138 (z-scores), p < 0.05, between the pretonic vowel and the one in the initial rhythmic condition, pointing to a subtle pretonic lengthening effect. In addition, a comparison between the pretonic and posttonic conditions reveals that the pretonic vowel is longer than the posttonic one; the difference is small (0.137 z-duration), but statistically significant (p < 0.01). This suggests a rightward–leftward asymmetry in temporal patterns, similar to the one occurring in the vicinity of lexical stress in longer words (recall the discussion in Section 2.3.1).

(a)

Duration (z-scores) across the five stress conditions: 1 – initial rhythmic, 2 – pretonic, 3 – lexical stress, 4 – posttonic, 5 – final rhythmic;

(b)

the enlarged fragment.

Regarding the trial effect, the third trial was shorter than the first one; β = 0.086, SE = 0.026, t = 3.263, p < 0.001. The effect was significant but, again, very small.

As we can see in Figure 9, the resultant pattern across the syllables preceding the lexically stressed position is clearly not a mirror image of the pattern occurring across the syllables following lexical stress. It seems, then, that in three-syllable words, the leftward alternating rhythm – that is, the one propagating from the end of the word – appears as predicted by the metrical theory. However, the rightward one (i.e. the one propagating from the beginning of the word) is not reified in such words, as pretonic lengthening supersedes it.

We also conducted four additional analyses to test whether

1. – any positional effects exist independently of stress,

2. – whether the pretonic and posttonic conditions are significantly different from each other independently of the word position,

3. – whether pretonic versus initial rhythmic conditions, as well as posttonic versus final rhythmic conditions are significantly different independently of position.

For the purpose of the first analysis, we used a subset of data containing only lexically stressed vowels. We tested the effect of position, initial (the first syllable in the word), medial (the second syllable in the word), final (the third syllable in the word), while keeping the stress condition constant. The linear mixed effects model included ‘position’ and ‘trial’ as the fixed effects; the random structure was analogous to the one in our general model, the only difference being that the random slopes were used for the fixed effect of ‘position’, not for the fixed effect of ‘stress’. We obtained a significant effect of ‘trial’, but not that of ‘position’. The third syllable is slightly longer than the first one, the difference being close to the threshold of significance: β = −0.285, SE = 0.1, t = −2.108 (p = 0.05). The statistical results thus point to a potential gradual and subtle lengthening effect across the entire word.

In the second analysis, we compared the pretonic and posttonic conditions in exactly the same position within the word, which was the medial (second) syllable; compare [ˈσ σ ˌσ] (posttonic) and [ˌσ σ ˈσ] (pretonic). (Because of convergence problems we had to remove the sequence-specific slopes in this analysis.) Of particular interest to us here is whether the pretonic and posttonic conditions remain significantly different from each other when the word position is kept constant. This expectation is borne out. The pretonic condition turns out significantly different from the posttonic condition, which is the reference category in our linear mixed effects analysis: β = 0.224, SE = 0.05, t = 4.394, p < 0.001. We conclude that the pretonic vowel is longer than the posttonic one. There was no significant effect of trial in that analysis.

Finally, we test whether rhythmic stress exists as a significant effect independently of the initial/final position. This is an important question because in three-syllable words, rhythmic stress can appear only at word edges; thus, hypothetically, it could simply be a boundary strengthening effect unconnected with stress. We conducted two separate analyses for the initial and final syllables, containing the relevant stress conditions. In both analyses, the models converged with the fully specified random structure. We did not obtain a significant result for the difference between the initial rhythmic condition and the pretonic condition within the subset of data limited to the first syllable in the word (p = 0.085). However, the analysis of potential stress effects in the third syllable yielded significant results. The posttonic (unstressed) condition turns out significantly shorter from the final rhythmic condition, which is the reference category (β = −0.157, SE = 0.051, t = −3.106, p < 0.05).

To wind up, both the overall analysis as well as additional detailed statistical analyses point to phonetic asymmetry in durational patterns in three-syllable words. It is noteworthy that the present measurements are in principle consistent with the description of Toc’ka (Reference Toc’ka1973: 172), who reports the following relative vowel durations in three-syllable words (vowel length has been represented on a scale from 0.75 to 2, where 2 stands for maximal duration of stressed vowels): 2 – 1 – 1.75, 1 – 2 – 1.5, 0.75 – 1 – 2. Similarly to the results obtained in the current study, this description reveals an asymmetric temporal pattern in [ˌσ σ ˈσ] vs. [ˈσ σ ˌσ] words, with a duration increase in final rhythmically stressed syllables (2 – 1 – 1.75) and a gradual increase in duration across pretonic syllables in words with rhythmic stress on the initial syllable (0.75 – 1 – 2). These duration patterns show that the words which are expected to be mirror images of each other from the point of view of metrical theory – compare [ˌσ σ ˈσ] and [ˈσ σ ˌσ] – are not symmetrical on the phonetic level. While the final rhythmic prominence is seen in [ˈσ σ ˌσ] words, no initial rhythmic prominence is found in [ˌσ σ ˈσ] words. Instead, it is a gradual lengthening effect across the syllables preceding lexical stress that prevails in such words. This agrees with the pretonic lengthening pattern reported earlier for longer words, in which the otherwise regular alternation of rhythmic beats was found to disappear in the vicinity of lexical stress (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2018b). If, as suggested in previous work (Łukaszewicz & Mołczanow Reference Łukaszewicz and Mołczanow2018b; Łukaszewicz et al. submitted), pretonic lengthening is viewed as the lexical stress domain extension, the Ukrainian data can shed light on the interaction between lexical and grammatical stress domains, and the extent of application of rhythmic stress.

2.3.3 Vowel Reduction (F1 Undershoot)

The relationship between duration and vowel quality vis-à-vis the metrical structure in Ukrainian has been tested thus far only on the basis of [ˌσσσˈσ(σ)] words (as presented in Section 2.2.5). As the scope of previous studies (Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2019b; Łukaszewicz et al. submitted) was limited to metrical positions occurring to the left of lexical stress, little is known about formant undershoot in posttonic positions and its relation to metrical structure in Ukrainian. Here we present novel data on F1/duration patterns in three-syllable words, using the same data set which was analysed in Section 2.3.2. The measured segment is the vowel [a] occurring in nine different stress/position conditions, as schematised and illustrated earlier in (9).

To test for the presence of vowel undershoot, we measured F1 in the vowel [a] using the Burg LPC algorithm in Praat (v. 6.2.09; Boersma & Weenink Reference Boersma and Weenink2022). Measurements were conducted at acoustic midpoints using a Praat script, with the ceiling of the formant search range being 5,000 Hz for male speakers and 5,500 Hz for female speakers. The data were balanced with respect to the places of articulation of the flanking consonants, which allowed us to minimise the effect of asymmetrical consonantal contexts. In order to ensure data comparability across speakers, formant frequencies in [Hz] were converted to a normalised acoustic space by calculating by speaker z-scores (cf. Lobanov Reference Lobanov1971).

Two kinds of statistical analyses in terms of linear mixed effects models were performed. The first set of analyses was designed to test whether there would be a significant effect of stress on F1. As F1 correlates negatively with vowel height, we expect the vowel [a] to show lower F1 in metrically weak positions relative to metrically strong positions; lack of reduction is expected especially in the lexical stress position (Mołczanow et al. Reference Mołczanow, Łukaszewicz and Łukaszewicz2019b; Łukaszewicz et al. submitted). The second set of analyses was implemented to examine the relationship between two continuous parameters, F1 and duration, depending on stress and position. The point of interest here is whether the stress-induced duration decrease in Ukrainian goes hand in hand with an automatic reduction in vowel quality (F1 undershoot). A preliminary analysis over the aggregated data from all nine stress/position conditions points to a strong positive correlation between F1 and duration; r(1,059) = 0.8, p < 0.001. Because the relationship between F1 and duration is clearly non-linear (as demonstrated in Figure 10, panel (a)), in this analysis the duration values were transformed using a logarithm (a constant was first added to ensure that all duration z-scores would end up above zero). The result of this transformation is visible in panel (b). This preliminary analysis does not inform us whether there is an independent effect of stress on F1 after the effect of duration has been accounted for, which is the problem we address in the second set of analyses.

Figure 10

F1 (z-scores) versus duration (z-scores) –.

(a)

raw and

(b)

log, depending on the stress condition: 1 – initial rhythmic, 2 – pretonic, 3 – lexical stress, 4 – posttonic, 5 – final rhythmic

In the first set of analyses, we built a linear mixed effects model with F1 as the dependent variable, and ‘stress’ and ‘trial’ as fixed factors. Analogously to the model described in Section 2.3.2, the ‘stress’ condition had five levels (initial rhythmic, pretonic, lexical (tonic), posttonic, final rhythmic); the trial effect had three levels (reflecting the number of repetitions in the experiment). To account for the repeated measures (identical segmental contexts) occurring in the experiment, we added ‘sequence’ as a random effect – the model included sequence-specific intercepts and slopes for the fixed effect of ‘stress’. Individual differences in F1 were controlled in terms of z-scores, which made the random effect of ‘speaker’ redundant; however, by-speaker random slopes for the fixed effect of ‘stress’ were included to account for potential differences in the degree of reduction related to stress.

The effect of stress was significant, but that of trial was not. The final rhythmic vowel, which is the reference level in the analysis, turns out to be significantly different only from the lexically stressed vowel (β = 1.735, SE = 0.191, t = 9.062, p < 0.001). This points to reduced vowel quality across all lexically unstressed positions. As anticipated, in paired comparisons the lexical stress level is significantly different from all other stress levels. The biggest difference in F1 values is found between the lexical stress position and the initial rhythmic stress (1.905, SE = 0.191, p < 0.001). There is also a statistically significant difference between the initial rhythmically stressed and pretonic vowel (−0.504, SE = 0.192, p < 0.05). Figure 11 illustrates the estimated marginal means for standardised F1 depending on the level of the ‘stress’ condition.

Figure 11

F1 (z-scores) at acoustic midpoints across the five stress conditions: 1 – initial rhythmic, 2 – pretonic, 3 – lexical stress, 4 – posttonic, 5 – final rhythmic.

This model achieves a marginal R² of 0.62, which reflects the proportion of the variance for F1 explained by the fixed effect of stress. This proportion is smaller than the proportion of the variance for duration explained in the analogous model in Section 2.3.2, which had a marginal R² of 0.86 (the effect of ‘trial’ is negligible in both models). The linear mixed effects model with duration as the dependent variable wins over the analogous model with F1 as the dependent variable also in terms of −2log likelihood, a goodness-of-fit criterion; it also fares better in terms the Bayesian Information Criterion (BIC), which assesses the trade-off between goodness of fit and the number of parameters used, to prevent the risk of overfitting. In model selection, models with lower −2log likelihood and lower BIC indices are preferred. A comparison of the two models along those two criteria reveals much smaller indices in the duration-based model than in the analogous F1-based model (the duration-based model: −2log likelihood = 800, BIC = 877 vs. the F1-based model: −2log likelihood = 1,698, BIC = 1,775). Next we address the relationship between duration and F1 in more detail.

In order to test whether there is an independent effect of stress on F1 after the effect of duration has been accounted for, we built a baseline model with F1 as the dependent variable, which included the fixed factor of ‘trial’, duration as well as by-speaker slopes and by-sequence random intercepts and slopes for duration, and then compared it to models augmented in an up-step fashion, first to additionally include (i) the fixed effect of stress as well as by-speaker slopes and by-sequence random intercepts and slopes for stress, and then (ii) also the stress*duration interaction term (cf. Strycharczuk et al. Reference Strycharczuk, Ćavar and Coretta2021). The stress-based models were compared against the baseline model in terms of goodness of fit (likelihood ratios) and variance explained (marginal R²). There were statistically significant differences between the baseline and stress-based models in terms of the likelihood ratios: χ²(6) = 155.14, p < 0.001 (baseline vs. model i), χ²(4) = 22.32, p < 0.001 (model i vs. model ii); also increases in R² were detectable: 0.63 (baseline) < 0.66 (model i) < 0.67 (model ii).

Apart from the overall analysis, additional statistical analyses were conducted, focusing on F1 patterns occurring in selected portions of the data set. All initial models included fully specified random effects (by-speaker and by-sequence intercepts and slopes) for the relevant fixed effects (position or stress depending on the analysis); however, not all models converged, in which case the random structure was reduced. We first used a linear mixed effects model to test whether F1 is affected by the position within the word – initial, medial, or final. We used a subset of data containing only lexically stressed vowels. (Recall that lexical stress was the only stress level represented across all three positions within the word.) The third position, which was the reference position in the analysis, turns out to be different from the other two positions at the significance level of α = 0.05; compare the difference between the first and the third positions: β = 0.209, SE = 0.075, t = 2.770, p < 0.01; the difference between the second and the third positions: β = 0.179, SE = 0.076, t = 2.364, p < 0.05. Comparing this result with the one obtained for duration in Section 2.3.2, we can observe that the vowel in the final syllable is slightly reduced in terms of quality, but not in terms of length, in comparison with vowels in the preceding syllables.

The analyses divided by position additionally reveal some non-automatic relationship between F1 and duration. There is a statistically significant difference in the initial position between the initial rhythmic and pretonic levels, amounting to β = −0.481, SE = 0.085, t = −5.672, p < 0.001. Thus there is more reduction in the initial rhythmic than pretonic vowel in the first syllable of the word, although no significant difference in duration is reported for exactly the same subset of data. In the second position, the difference between the pretonic and posttonic levels is also significant: β = 0.452, SE = 0.16, t = 2.761, p < 0.05. This result points to a less reduced quality in the pretonic vowel, which is accompanied by a relatively increased length of that vowel (as revealed by the analysis described in Section 2.3.2). In the third syllable, there is no significant difference in F1 between the posttonic and the final rhythmic position. However, there is a significant difference between those two positions in terms of duration – as the analysis in Section 2.3.2 shows, the final rhythmic vowel is longer.

Synthesising the present and previous results on vowel formant stability vis-à-vis varying duration points to the existence of vowel undershoot in Ukrainian, but also reveals the complexity of that relation, possibly involving such mediating factors as metrical stress, word position, word length, and the distance between lexical stress and edge(s) of the word. Hopefully, this study is a step towards a better understanding of those intricacies, with the non-automatic relationship between F1 and duration to be addressed in more detail in future research.

2.3.4 Other Parameters

Measurements of other parameters which are standardly associated with prominence – that is, pitch and intensity – were also conducted (e.g. Lehiste Reference Lehiste1970). A Praat script was used to extract peak intensity (Intensity_max), peak F0 (F0_max), and F0 slope. To reflect the well-known non-linearity of human perception, in the case of intensity and pitch, measurements are expressed using a logarithmic rather than linear scale. Intensity was measured in decibels [dB]. F0 was originally measured in Hertz [Hz], with the autocorrelation algorithm and different range settings for male (75–300 Hz) and female speakers (100–500 Hz). Next, the F0 maximum and minimum values were transformed to semitones [ST] relative to the lower limit of the measurement range, using the following formula: 12*(log₂(F0_max/min_i/F0_threshold)), where F0_max/min_i is the ith measurement of the F0 maximum (or minimum) and F0_threshold equals 75 Hz for male speakers and 100 Hz for female speakers. Because the differences in perceived prominence may also be related to differences in pitch changes (e.g. rising vs. falling pitch; see Hermes & Rump Reference Hermes and Rump1994), F0 slope was calculated in accordance with the standard formula, whereby the difference between the standardised F0 maximum and minimum values is divided by the interval between the time points at which those F0 values were measured: F0_slope = (STF0_max-STF0_min)/(max_time-min_time). Therefore, the F0 slope is measured in semitones per second [ST/s].

Separate statistical analyses were conducted for peak intensity (Intensity_max), peak F0 (F0_max), and F0 slope as dependent variables, using linear mixed effects models. The independent factors in all analyses were the same as in the previous analyses involving duration and F1 – that is, ‘stress’ and ‘trial’. The random effects included speaker- and sequence-specific intercepts and slopes.

In the statistical analysis with intensity as the dependent factor, both ‘stress’ and ‘trial’ emerge as significant effects. The final rhythmic position (the reference level in the analysis) is not significantly different from the posttonic position; however, it is significantly different from the lexical stress, pretonic, and initial rhythmic positions; the difference between lexical stress and final rhythmic: β = 1.718, SE = 0.256, t = 6.703, p < 0.001; the difference between pretonic and final rhythmic: β = 1.524, SE = 0.271, t = 5.63, p < 0.001; the difference between initial rhythmic and final rhythmic: β = 1.145, SE = 0.313, t = 3.659, p < 0.001. Paired comparisons across the five ‘stress’ levels further confirm that the major observed effect is a significant abrupt decline of 1.7 dB between the lexical stress and the posttonic position. There also seems to be a gradual increase in intensity across the first three syllables, with the initial rhythmic position being significantly different from the lexical stress position (−0.5 dB), but not from the pretonic position. The results are presented in Figure 12 (panel (a)).

Figure 12

Estimated mean values of.

(a)

maximum intensity,

(b)

maximum standardised F0,

(c)

F0 slope,

(d)

F0 range in trisyllabic words, divided by the stress condition: 1 – initial rhythmic, 2 – pretonic, 3 – lexical stress, 4 – posttonic, 5 – final rhythmic

Analogous statistical analyses were performed for the maximum F0 and the F0 slope. (In the case of the latter parameter, a simpler intercept-only random structure was used.) No significant effect of ‘stress’ was obtained for the maximum F0; see Figure 12 (panel (b)). For the F0 slope, all estimated marginal means show negative values, pointing to the presence of a falling F0 pattern within a vocalic interval across all five stress levels; see Figure 12 (panel (c)). Relevant from the point of view of metrical prominence marking is the value of F0 slope in the lexical stress position, which is conspicuously different from the values of that parameter in neighbouring positions, pretonic and posttonic. In paired comparisons, there are significant differences between the pretonic and lexical stress positions (−37.133 ST/s, p < 0.001) as well as the lexical stress and posttonic positions (29.969 ST/s, p < 0.001), but no significant difference between the initial rhythmic and pretonic vowels, nor between the posttonic and final rhythmic vowels. The much flatter slope in the lexical stress position relative to other positions may be due to the longer duration interval in that position, rather than a smaller F0 range. An additional linear mixed effects analysis involving the F0 range (= STF0_max-STF0_min) demonstrates a significantly greater F0 decrease within the lexical stress position (EM = 3.824) in comparison with the other positions (initial rhythmic: EM = 2.382 ST; pretonic: EM = 2.543 ST; posttonic: EM = 2.385 ST; final rhythmic: M = 2.574 ST; EMs stand for ‘estimated marginal means’); see Figure 12 (panel (d)). There are no significant effects on F0 parameters connected with initial or final rhythmic stress.