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date: 16 October 2017

Metrical Structure and Stress

Summary and Keywords

Metrical structure refers to the phonological representations capturing the prominence relationships between syllables, usually manifested phonetically as differences in levels of stress. There is considerable diversity in the range of stress systems found cross-linguistically, although attested patterns represent a small subset of those that are logically possible. Stress systems may be broadly divided into two groups, based on whether they are sensitive to the internal structure, or weight, of syllables or not, with further subdivisions based on the number of stresses per word and the location of those stresses. An ongoing debate in metrical stress theory concerns the role of constituency in characterizing stress patterns. Certain approaches capture stress directly in terms of a metrical grid in which more prominent syllables are associated with a greater number of grid marks than less prominent syllables. Others assume the foot as a constituent, where theories differ in the inventory of feet they assume. Support for foot-based theories of stress comes from segmental alternations that are explicable with reference to the foot but do not readily emerge in an apodal framework. Computational tools, increasingly, are being incorporated in the evaluation of phonological theories, including metrical stress theories. Computer-generated factorial typologies provide a rigorous means for determining the fit between the empirical coverage afforded by metrical theories and the typology of attested stress systems. Computational simulations also enable assessment of the learnability of metrical representations within different theories.

Keywords: metrical structure, stress, foot, weight, lapse, clash, binary, ternary, learnability

Metrical structure refers to the phonological representations capturing the prominence relationships between syllables. The conception of metrical structure as a relational property (Liberman, 1975), rather than a phonological feature parallel to other segmental features, as in the Sound Pattern of English (SPE; Chomsky & Halle, 1968), is a definitional characteristic of modern metrical stress theory. Although metrical structure is inherently abstract, metrical prominence is typically reflected along one or more physical dimensions, including increased intensity, longer duration, salient pitch events, and hyperarticulation. Syllables associated with these prominent properties are characteristically assumed to carry stress.

There are several threads of research relevant to the study of metrical structure. These may be broadly bifurcated into two groups, one dealing with establishment of the cross-linguistic range of variation in stress systems and the other concerned with the development of formal theories that are both learnable and capable of modeling all the stress systems attested in languages of the world.

1. Typology of Stress Patterns

There is an extensive literature on the typology of stress systems. The seminal survey of stress patterns by Hyman (1977) identifies five locations for stress cross-linguistically: the initial syllable, the peninitial (second) syllable, the antepenultimate (third from the end) syllable, the penultimate (second-to-last) syllable, and the final syllable. Examples of one of these stress patterns, involving final stress, are provided by Kulina (Dienst, 2014) (1). Following International Phonetic Alphabet conventions, primary stress throughout the paper is marked with ˈ and secondary stress with ˌ.

(1) Final stress in Kulina (Dienst, 2014)

iˈma

‘story’

bo̜taˈni

‘stingray’

t͡sʰikaˈta

‘sour’

Other cross-linguistic surveys of stress systems include Gordon (2002), Goedemans (2010), and Goedemans and van der Hulst (2013a,b), the last two of which are part of the World Atlas of Language Structures (Dryer & Haspelmath, 2013) survey of linguistic structures and include a map depicting the geographic distribution of stress systems. Van der Hulst, Goedemans, and van Zanten (2010) is a comprehensive geographically organized volume providing an overview of stress patterns found throughout the world. The StressTyp2 database (Goedemans, Heinz, & van der Hulst, 2015) is a searchable online database containing descriptions of stress for over 750 languages.

These surveys indicate a rich array of stress patterns in languages of the world. In addition to languages with a single stress in one of the five locations identified by Hyman (1977), some languages have a stress at or near both edges of a word. For example, primary stress in Chimalapa Zoque (Knudson, 1975) falls on the penultimate syllable and secondary stress on the initial syllable (2).

(2) Initial and penultimate stress in Chimalapa Zoque (Knudson, 1975)

ˈminpa

‘he comes’

ˌminˈkeʔtpa

‘he is coming again’

ˌminsukˈkeʔtpa

‘they are coming again’

1.1 Binary Stress

Stress may also follow a rhythmic pattern, most commonly involving a “binary” alternation between stressed and unstressed syllables. For example, in Maranungku (Tryon, 1970), primary stress falls on the first syllable, and secondary stress falls on odd-numbered syllables after the primary one (3).

(3) Left-edge oriented binary stress in Maranungku (Tryon, 1970)

ˈmæræˌpæt

‘beard’

ˈjaŋarˌmata

‘the Pleiades’

ˈŋaltiˌritiˌri

‘tongue’

Binary stress patterns differ based on the direction at which the alternating stress pattern originates and whether the pattern begins with a stressed or unstressed syllable, yielding a four-way typology: stress on odd-numbered syllables counting from the left (as in Maranungku), stress on even-numbered syllables from the left, for example in Osage (Altshuler, 2009), stress on odd-numbered syllables from the right, as in Urubú Kaapor (Kakumasu, 1986), and stress on even-numbered syllables from the right, as in Warao (Osborn, 1966). Urubú Kaapor (Kakumasu, 1986), which is the mirror image of Maranungku, provides an example of a binary stress system oriented toward the right edge (4).

(4) Right-edge oriented binary stress in Urubú Kaapor (Kakumasu, 1986)

tatˈta

‘fire’

ˌwaɾuˈwa

‘glass, mirror’

aˌɾlasˈha

‘deer’

A nearly universal feature of languages with rhythmic stress is that the stress closest to the edge at which the alternating stress pattern originates is the primary one, suggesting that primary stress serves as the anchor point for secondary stress (van der Hulst, 1984, 1997). Thus, in stress systems counting from the left edge, the leftmost stress is the primary one, while in systems counting from the right edge, the rightmost stress is the main one. For example, the rightmost stress in the right-edge-oriented system of Urubú Kaapor (Kakumasu, 1986) is the primary one, whereas the leftmost stress in the left-edge-oriented system of Maranungku (Tryon, 1970) is the main one.

1.2 Lapse and Clash

Purely binary stress systems avoid both sequences of stressed syllables, termed “stress clashes,” and sequences of unstressed syllables, termed “lapses.” Lapse and clash avoidance conflict with each other in “bidirectional” systems involving stress oriented toward both edges of a word. For example, South Conchucos Quechua (Hintz, 2006) stresses the first syllable plus even-numbered syllables counting from the right edge (5).

(5) Bidirectional stress in South Conchucos Quechuas (Hintz, 2006)

ˌimaˈkuna

‘things’

ˌtuˌʃukuˈnaqḁ

‘dancers’

ˌwaˌraːkaˌmunqaˈnanqa

‘I crunch up my own (e.g., prey) with teeth’

In South Conchucos words consisting of an odd-number of syllables, there is a stress clash between the first two syllables. Garrwa (Furby, 1974) deviates from South Conchucos in suppressing the stress on the second syllable in odd parity words, resulting in a stress lapse rather than a clash (6); compare South Conchucos Quechua ˌtuˌʃukuˈnaqḁ ‘dancers’ with Garrwa ˈnariŋinˌmukuˌnʲinaˌmira ‘at your own many’.

(6) Bidirectional stress in Garrwa (Furby, 1974)

ˈpunʲala

‘white’

ˈwatʲimˌpaŋu

‘armpit’

ˈnariŋinˌmukuˌnʲinaˌmira

‘at your own many’

Rhythmic principles also play a role in stress at the phrase level. The English rhythm rule involves a reversal of primary and secondary stress in a word followed by another word in which the leftmost stress is the primary one. For example, although the word ˌfourˈteen has primary stress on the final syllable and secondary stress on the first syllable when uttered in isolation or at the end of a sentence, the two stresses are characteristically reversed in the phrases ˈfourˌteen ˈcows and ˈfourˌteen ˈalliˌgators before the primary stress in the following noun. The reversal in the stress pattern of the first word creates separation between the primary stresses of the two words in the phrase.

Kager (2007) observes certain asymmetries in the location of stress lapses and clashes. He finds that stress clashes in languages like South Conchucos Quechua, combining binary stress plus a fixed stress at the opposite edge, involve two secondary stresses rather than a primary stress plus a secondary stress. He also finds that languages like Garrwa that combine binary and fixed stress but favor stress lapses over clashes position the lapse immediately adjacent to the primary stress. Languages that contradict this pattern in positioning a lapse adjacent to a secondary stress, such as Indonesian, are claimed by Alber (2005) to have borrowed the stress patterns intact in loan words.

1.3 Quantity-Sensitive Stress

In addition to the “quantity-insensitive” languages considered thus far, in which stress is positioned on the basis of distance from a word edge and/or rhythmic principles, there are many languages in which stress is sensitive to the internal structure, or weight, of syllables. In these “quantity-sensitive” (or “weight-sensitive”) systems, stress preferentially is attracted to certain “heavy” syllable types. For example, in Yana (Sapir & Swadesh, 1960), stress is pulled from its default position on the first syllable of a word (7a) to the first heavy syllable to the right of the initial syllable (7b), where heavy syllables are those containing either a long vowel (CVV) or coda consonant (CVC).

(7) Quantity-sensitive stress in Yana (Sapir & Swadesh, 1960)

a.

ˈp’udiwi

‘women’

b.

siˈbumk’ai

‘sandstone’

ʦiniˈjaː

‘no’

Quantity-sensitivity stress comes in several guises sensitive to a number of different dimensions. One of these is weight criterion, i.e. which syllables count as heavy. In Yana, both CVV and CVC are heavy, but in other languages, for example in Aguacatec (McArthur & McArthur, 1956), only CVV is heavy, while in still others, weight is a function of vowel quality, where central vowels such as schwa are lighter than full, non-central vowels and, among the full vowels, lower vowel qualities are heavier than high vowels (see de Lacy, 2002; Goedemans & van der Hulst, 2013c,d; Gordon, 2006; Kenstowicz, 1997 for surveys of weight-sensitive stress). Stress systems also differ in whether weight is relevant for primary stress, as in Vach Ostyak (Gulya, 1966), secondary stress, as in Koya (Tyler, 1969), or both primary and secondary stress, as in Malayalam (Mohanan, 1986).

In many languages with rhythmic stress, heavy syllables interrupt the rhythmic pattern by attracting stress. For example, Chickasaw (Gordon & Munro, 2007; Munro & Ulrich, 1984) places stress on even-numbered syllables in words containing only light (CV) syllables (8a). This pattern is interrupted, however, by heavy (CVV and CVC) syllables, which attract stress and trigger a restart of the alternating stress pattern (8b). (see section 3.2 “Iambic/Trochaic Law” for more on Chickasaw).

(8) Quantity-sensitive stress in Chickasaw (Gordon & Munro, 2007; Munro & Ulrich, 1984)

a.

ʧiˌpisaˈli

‘I look at you’

aˌsabiˈka

‘I am sick’

b.

ˌoktaˌpaˈtok

‘It was blocked’

ʧiˌkiˈlaː

‘You’re burning’

ˌaːˌʧomˈpaːt

‘store’ (subject)

Another type of weight-sensitive stress system involves a single stress per word falling on either the first or the last (parameterized on a language-specific basis) heavy syllable and on either the first or last (also parameterized) syllable in the default case involving a word with only light syllables. These systems, termed “unbounded” since stress can potentially fall on any syllable depending on weight conditions, may be divided into two sub-classes based on whether the stress is attracted to the same edge both in words with and words without heavy syllables (“default-to-same”), as in Yana (see above), or is attracted to a different edge in the two cases (“default-to-opposite”). Kʷak’ʷala (Bach, 1975; Boas, 1947; Shaw, 2009; Wilson, 1986) instantiates the latter pattern: stress falls on the leftmost full vowel (excluding those followed by a coda glottal stop) or schwa followed by a sonorant coda) (9a), otherwise on the rightmost syllable (9b).

(9) Unbounded quantity-sensitive stress in Kʷak’ʷala (Bach, 1975; Boas, 1947; Shaw, 2009; Wilson, 1986)

a.

ˈkʷakʷ’ala

‘Kʷak’ʷala’

səˈbaju

‘searchlight’

ɬəˈnəmdi

‘red elderberry plant’

b.

ʣəˈɢʷəd

‘coal’

ʦəɢəɬˈm’əs

‘thimbleberry plant’

2. The Foot in Metrical Structure

A major area of research in metrical stress theory is concerned with the role of constituency in capturing prominence relations. One type of theory assumes that prominence is encoded directly in a metrical grid without any reference to constituents smaller than the word (Gordon, 2002; Prince, 1983; Selkirk, 1984). In grid-based theories, prominence is a function of the number of grid marks dominating a syllable: syllables projecting a greater number of grid marks are more prominent than those projecting fewer. Another type of theory assumes that sequences of stressed and unstressed syllables are grouped into feet, which are parameterized according to the ordering of the syllables (e.g., Halle, 1990; Halle & Idsardi, 1995; Halle & Vergnaud, 1987; Hayes, 1980, 1995; Idsardi, 1992; Liberman & Prince, 1977). Trochaic feet consist of a stressed syllable followed by an unstressed one, whereas iambic feet consist of an unstressed syllable followed by a stressed one. Grid-based and foot-based representations of the English word alligator are given in (10).

(10) Grid-based (on left) and foot-based (on right) metrical representations of alligator

Level 3 (Primary stress)

x

Word level

(x        )

Level 2 (Secondary stress)

x .

x .

Foot level

(x .)(x . )

ˈal liˌga tor

ˈal liˌga tor

All five positions for stress observed cross-linguistically may be captured using feet. Initial and penultimate stress reflect trochaic feet at the left and right edge, respectively, of the word, #(ˈσσ‎‎)… and …(ˈσσ‎‎)#, whereas peninitial and final stress manifest iambic feet, left and right-aligned, respectively, #(σˈσ‎‎)… and …(σˈσ‎‎)#. Antepenultimate stress is typically analyzed using a trochaic foot constructed over the antepenultimate and penultimate syllables with the final syllable being prosodically inert, …(ˈσσ‎‎)σ‎‎# (see below on extrametricality).

In a foot-based theory of stress, binary stress patterns reflect foot structure constructed over the entire word. Thus, stress on odd-numbered syllables counting from the left edge, as in Maranungku, is attributed to trochaic feet constructed from left to right, (ˈσσ‎‎)(ˈσσ‎‎)(ˈσσ‎‎), while stress on odd-numbered syllables counting from the right, as in Urubú-Kaapor, is attributed to a right-to-left iambic parse, (σˈσ‎‎)(σˈσ‎‎)(σˈσ‎‎).

Both grid-based and foot-based theories of stress assume that syllable weight is encoded in terms of mora count: heavy syllables project two moras and light syllables project one. In grid-based theories, heavy syllables (in addition to light syllables that occur in metrically prominent positions) project an additional grid mark. In foot-based theories, feet are binary at the level of the mora in weight-sensitive stress systems: feet thus consist of either a single heavy (bimoraic) syllable or two light (monomoraic) syllables, (σμσμ‎‎) or (σμμ‎‎). Apodal and podal representations of weight-sensitive stress in Chickasaw are provided in (11).

(11) Grid-based (on left) and foot-based (on right) representations of Chickasaw stress

Metrical Structure and Stress

3. Stress Asymmetries

3.1 Final Stress Avoidance

There are a number of asymmetries in the distribution of stress systems based on position and syllable weight. One concerns a distinction between the left and right edges of the word in their resistance to stress. Although both the final and the penultimate syllable are common docking sites for right-edge oriented stress, only the initial syllable is a popular location for left-edge oriented stress. Furthermore, antepenultimate stress is attested, albeit rarely, while its left-edge counterpart, third syllable stress appears to be virtually unattested, although there are at least a few languages with lexically marked stress that limit stress to a three-syllable window at the left edge (Kager, 2012). These asymmetries are attributed to a stronger avoidance of peripheral stress at the right edge than the left edge of a word. Penultimate stress and antepenultimate stress can thus be viewed as stress retraction effects at the right periphery with less common analogs at the left edge; the rarity of peninitial stress compared to penultimate stress and third syllable stress relative to antepenultimate stress.

A further manifestation of the left vs. right edge asymmetry is found in binary stress systems. Many languages with a left-to-right system suspend the alternating stress pattern in order to avoid final stress. For example, Pite Saami (Wilbur, 2014) stresses odd-numbered non-final syllables (12).

(12) Binary stress on odd-numbered non-final syllables in Pite Saami (Wilbur, 2014)

ˈkole

‘fish (nom.pl.)’

ˈbetnaka

‘dog (nom.pl.)’

ˈsaːlpmaˌkirrje

‘psalm book’

ˈkuhkaˌjolkikijt

‘long leg (acc.pl.)’

The right-to-left edge counterpart to the Pite Sami pattern, in which the initial syllable is unstressed even when it falls in a metrically prominent position, is unattested.

Finally, many languages employ stricter weight criteria in final relative to non-final syllables. For example, a CVC penult attracts stress in Palestinian Arabic (see Watson, 2002 for an overview of Arabic stress) (13a), but it takes two coda consonants (CVCC) for a syllable to attract stress in final position (13b).

(13) Final vs. non-final weight asymmetries in Palestinian Arabic (Watson, 2002)

a.

ka.ˈtab.na

‘we wrote’

b.

da.ˈrast

‘I studied’

ˈka.tab not *ka.ˈtab

‘he wrote’

Metrical stress theory handles final stress avoidance through the mechanism of extrametricality (Hayes, 1982), according to which final elements may be prosodically inert on a language-specific basis. Antepenultimate stress is assumed (in theories employing binary feet) to reflect a final extrametrical syllable in conjunction with a trochaic foot at the right edge of a word, as in (ˈσσ‎‎)<σ‎‎> (where extrametrical elements are surrounded by < >). Because extrametricality is typically stipulated to be limited to final position (but see Buckley, 1994, 2014 for a case of initial extrametricality in Kashaya Pomo), the left edge analog to antepenultimate stress, third syllable stress, is excluded.

Extrametricality can apply to prosodic units both smaller and larger than the syllable. The weight distinction between final light CVC and non-final heavy CVC in Palestinian Arabic discussed above emerges if one treats final consonants as extrametrical. The final syllable in (ˈkata) is light and rejects stress because the final consonant is extrametrical. This contrasts with ka(ˈtab)na, in which the penult is heavy because the consonant /b/occurs in non-final position and is thus not extrametrical. Final CVCC is heavy because extrametricality is limited to peripheral elements, meaning that the second-to-last consonant is shielded from extrametrical status, as in da(ˈras)<t>. Hayes (1995) analyzes several languages in which stress falls to the left of the penult in certain word shapes in terms of foot extrametricality (see Hyde, 2011 for an overview of extrametricality).

3.2 Iambic/Trochaic Law

Languages with iambic and trochaic stress systems conspicuously diverge in their weight patterns. The former overwhelmingly tend to be quantity-sensitive, while the latter may be quantity-sensitive or not (Hayes, 1985, 1995). In response to this distinction, Hayes (1995) proposes an asymmetric foot inventory in which iambs may only be weight-sensitive, but trochees may be either weight-sensitive (termed “moraic trochees”) or not (termed “syllabic trochees”). In keeping with their bias in favor of quantity-sensitivity, iambic languages tend to display lengthening of stressed syllables, resulting in a light-heavy foot. For example, the iambic stress language Chickasaw (see section 1.3 “Quantity-Sensitive Stress”) has a process of vowel lengthening that targets stressed non-final open syllables (Gordon & Munro, 2007; Munro & Ulrich, 1984), as in ʧipisalitok/ ‘I looked at you’ → (ʧiˈpiˑ)(saˈliˑ)(ˈtok). In contrast, lengthening of stressed vowels in trochaic systems appears to be far less widespread. In fact, an a priori unintuitive process of shortening of stressed vowels is found in some languages with trochaic stress. For example, in Fijian (Schütz, 1985), a long stressed vowel in the penult is shortened before a final short unstressed vowel, the result being a trochaic foot consisting of two light syllables, as in /m͡bŋgu/‘my grandmother’ → (ˈm͡bu.ŋgu). On the basis of this asymmetry between iambic and trochaic systems in their relationship between stress and lengthening, Prince (1990) suggests that the ideal iamb is durationally unbalanced, that is, it has a light-heavy profile, whereas the canonical trochee is balanced, consisting of two light syllables. The fundamental distinction between iambic and trochaic stress systems in their duration patterns provides one of the strongest pieces of evidence for the foot as a prosodic constituent.

4. Segmental Diagnostics of Foot Structure

Besides the iambic/trochaic law, other phonetic evidence for foot structure has been gleaned from segmental alternations that depend on metrical structure distinct from stress. One language displaying such evidence for foot structure is Chugach Alutiiq (Leer, 1985), in which consonants that are foot-initial, according to Hayes’ (1995) weak local parsing analysis (see section 5. “Ternary Stress”), are strengthened relative to their counterparts that appear in other contexts. For example, the strengthened consonant (in bold) occurs in the onset of the pretonic syllable in ˈanʧiquˈkut, ‘we’ll go out’, analyzed by Hayes (1995) as the first syllable in a disyllabic foot comprising the pretonic and the tonic syllable, (ˈan)ʧi(quˈkut). An advantage of this analysis is that it assumes that fortition occurs in foot-initial position in keeping with a common cross-linguistic pattern of domain-initial fortition. In contrast to a foot-based analysis, fortition in a grid-based theory would have to be described as pretonic, a position that that is not a cross-linguistically natural one for strengthening.

Vaysman (2009) presents data from a number of Uralic languages displaying segmental alternations that are not only difficult to analyze in terms of stress but that actually conflict with metrical structure diagnosed by stress. For example, Eastern Mari has an alternation between schwa and full (non-schwa) vowels, whereby underlying schwa surfaces as a full vowel in word-final position under conditions that Vaysman (2009) argues are metrically governed. Schwa strengthens to a full vowel in final position of a foot (14), where disyllabic feet are parsed from left-to-right, and the quality of the full vowel resulting from fortition is determined by orthogonal processes of palatal and rounding harmony.

(14) Metrically-governed vowel alternations in Eastern Mari (Vaysman, 2009)

(ˈtaŋ-se)

‘the one who is a friend’

(okˈsa)-sə

‘the one that is money’

(peˈle)(dəʃ-se)

‘the one that is a flower’

(puʃaŋ)(gə-ˈna)-sə

‘the one that is our tree’

As these forms show, the metrical structure diagnosed by schwa fortition is orthogonal to the stress system, which positions stress on the rightmost full vowel (in monomorphemic roots) and otherwise on the initial syllable in non-derived words containing only schwa. Crucially, underlying schwa that strengthens in final position does not count as a full vowel for stress, an observation that demonstrates that that the schwa vs. full vowel alternations are due to fortition rather than lenition, (ˈtaŋ-se) not *(taŋ-ˈse) from/taŋsə/. Gordon (2011) and Hermans (2011) discuss other languages displaying a lack of convergence between metrical structure diagnosed by stress and metrical structure diagnosed by segmental alternations.

5. Ternary Stress

Although most languages with rhythmic prominence stress every second syllable, there are a few that stress every third syllable. One of these is Cayuvava (Key, 1961, 1967), which stresses every third syllable counting from the right edge (15).

(15) Ternary stress in Cayuvava (Key, 1961, 1967)

ikiˌtapareˈrepeha

‘the water is clean’

ˌʧa.adiˌroboβuˈruruʧ‎‎e

‘ninety-nine (first digit)’

meˌdaruʧeˌʧe.iroˈhi.iɲ

‘fifteen each (second digit)’

Ternary stress systems present a challenge to metrical stress theory since they appear to require constituents consisting of three syllables. To admit trisyllabic feet into the inventory of feet entails a considerable expansion of the theory beyond the core iambic and trochaic feet. Responses to the challenge of ternarity vary. Halle and Vergnaud (1987) and Levin (1988) handle Cayuvava by admitting one type of ternary foot into the universal inventory of feet, an amphibrach consisting of a stressed syllable in the middle flanked by an unstressed syllable on either side, as in (σˈσσ‎‎). In conjunction with extrametricality of the final syllable, the ternary pattern of Cayuvava is derived through a right-to-left parse into feet, for example (meˌdaru)(ʧeˌʧe.i)(roˈhi.i)<ɲe>.

The amphibrachic analysis does not, however, readily extend to other ternary systems in which each stressed syllable is not necessarily adjacent to an unstressed syllable on either side. For example, stress in Chugach Alutiiq (Leer, 1985) falls on the second syllable and on every third syllable thereafter in words consisting of light syllables (those other than CVV and initial CVC): aˈtuˑquniˈki ‘if he (refl.) uses them’, piˈsuˑqutaˈquˑni ‘if he (refl.) is going to hunt’ (where stress is indicated uniformly as primary stress, since it is unclear which stress is most prominent). Note that Chugach Alutiiq, like Chickasaw, displays iambic lengthening in non-final open syllables. A sequence of unstressed syllables at the end of a word, however, is avoided by stressing a final syllable immediately preceded by an unstressed syllable, resulting in a binary interval at the right edge: maˈŋaχ‎‎suquˈtaˑquˈni ‘if he (refl.) is going to hunt porpoise’.

Hayes (1995) accounts for ternary stress intervals in Chugach Alutiiq and elsewhere by introducing the possibility of “weak local parsing,” whereby a light syllable is skipped on a language-specific basis in the metrical parse if there is sufficient material remaining to construct a well-formed binary foot, as in (maˈŋaχ‎‎)su(quˈtaˑ)(quˈni). Although it introduces a novel mode of parsing, Hayes’ account has the advantage of limiting the inventory of feet to trochees and iambs. As Elenbaas and Kager (1999), Gordon (2002), and Kager (2007) show, the constraint against skipping more than one syllable follows naturally from an anti-lapse prohibition against sequences of more than two unstressed syllables.

Another means for accounting for ternarity is to assume internally layered feet consisting of a strong branch and a weak branch (e.g., Blevins & Harrison, 1999; Buckley, 2014; Dresher & Lahiri, 1990; Ito & Mester, 2003; Kager, 2012). In this approach, the strong branch (i.e., the head) of a foot consists, on a language-specific basis, of either a single heavy syllable or two light syllables, as in ([σμσμ‎‎]σ‎‎) or ([σμμ‎‎]σ‎‎) (where the foot head is surrounded by brackets). Ternary stress of the Cayuvava type can be captured if one assumes that two syllables, the stressed one plus the immediately following one, comprise the head of the foot, while the syllable after the immediately posttonic one constitutes the weak branch of the foot, for example me([ˌdaru]ʧe)([ˌʧe.i]ro)([ˈhi.i]ɲe).

Hyde (2002) offers a different account of ternarity within a theory that assumes a greater separation of prominence, or grid marks, and foot structure than in traditional foot-based metrical theories assuming a one-to-one mapping between stress and feet. While prohibiting trisyllabic or internally layered feet, Hyde’s account assumes that all types of stress systems exhaustively parse words into feet, which consist of either two syllables or, in the case of a stray syllable that cannot be parsed together with an adjacent syllable, a single syllable. Hyde’s account is unique in allowing for the possibility of feet lacking a prominent syllable and the possibility of a single syllable belonging to two feet. Headless feet arise in single-stress systems, which under his theory exhaustively parse words into feet, only one of which has a head. Ternary feet occur in languages in which a syllable is shared between two feet. Binary feet, in contrast, occur when there is a “default” one-to-one mapping between feet and stress. Representations of binary stress (odd-numbered from left-to-right, as in Maranungku), single stress (final syllable, as in Kulina), and ternary stress (every third syllable from the end, as in Cayuvava) are provided in (16). Stressed syllables carry a grid mark, strong syllables (foot heads) are associated with a vertical line and weak syllables are associated with a diagonal line.

(16) Metrical representations in Hyde (2002)

Metrical Structure and Stress

The representations of single stress in Kulina and ternarity in Cayuvava illustrate the possibility of feet lacking a grid mark (i.e., stress). In the case of Kulina, this is due to a requirement that any grid marks be aligned with the right edge of a word. In Cayuvava, a language-specific prohibition against final grid marks (essentially a right-edge extrameticality condition) produces the final stressless foot.

6. Computational Evaluation of Metrical Stress Theory

6.1 Factorial Typology

Because the typology of stress patterns is relatively well documented, metrical stress theory has served as the test case in computational simulations belonging to two research programs. The first of these, concerned with the evaluation of the generative capacity of theories, has burgeoned in response to incarnations of metrical stress theory couched within the constraint-based framework of Optimality Theory (Prince & Smolensky, 1993). By permuting the rankings of a set of metrical constraints, it is possible to generate a factorial typology of stress patterns generated by a theory and compare the predicted patterns with the typology of attested patterns. Both grid-based and foot-based representations are found in the Optimality Theory literature on stress. Working within a grid-based metrical framework, Gordon (2002) submits a set of 12 constraints designed to generate all attested weight-insensitive stress systems to the factorial typology module of OTSoft (Hayes, Tesar, & Zuraw, 2000). His constraints fall into several categories, which are described for expository purposes here in terms of stress rather than relationships between grid marks and their proximity to domain edges. Three alignment constraints capture the attraction of stress by edges by penalizing forms with non-final stresses (Align-Right), those with non-initial stresses (Align-Left) and those in which either the first and last syllable are unstressed (Align-Edges). Alignment constraints specific to primary stress (Alight-Left-Main and Align-Right-Main) evaluate the proximity of the main stress to word edges. Competing with the alignment constraints are constraints against stresses lapses of two consecutive unstressed syllables (*Lapse), highly ranked in binary stress patterns, or three consecutive unstressed syllables (*Extended Lapse), highly ranked in ternary systems. In addition, Gordon posits three edge-specific anti-lapse constraints (*Lapse Left, *Lapse Right, and *Extended Lapse Right), which work in concert with a alignment constraint referring to the opposite edge to yield penultimate (second-to-last syllable), peninitial (second syllable), and antepenultimate (third-to-last syllable) stress. For example, ranking *Lapse Right above Align-Left above, in turn, Align Right, produces penultimate stress by requiring that stress fall as far to the left in a word without leaving a sequence of unstressed syllable at the right edge. Finally, an anti-clash constraint (*Clash) penalizes adjacent stressed syllables, while a Nonfinality constraint bans final stress, thereby accounting for the Pite Saami type pattern characterized by stresses on alternating syllables except the final one.

Of the nearly 11 trillion logically possible stress systems encompassing words ranging from one to eight syllables in length, Gordon’s constraint set generates only 79 systems including all those identified in his typological survey of quantity-insensitive stress. His account also generates several apparently unattested patterns, where most of these involve combinations of elements that are attested in isolation; for example peninitial plus final stress. Compositional patterns of this type are plausibly viewed as accidental gaps in the inventory of stress systems currently documented rather than as pathologic predictions of the theory.

Kager (2012) builds on both the stress typology database and the research program employing computer generated factorial typologies in his examination of window effects, in which the location of stress varies within a certain number of syllables near a word edge. Spanish, for example, limits stress to a three-syllable window at the right edge of a word, where the location of stress within this window is lexically determined but falls on the penultimate syllable in the majority of words. Kager (2012) expands the typology of stress locations to include the possibility, as in Choguita Rarámuri (Caballero, 2008, 2011), of lexical marking of stress within a three syllable window at the left edge. Third syllable stress represents a novel pattern not among the five stress locations (initial, peninitial, antepenultimate, penultimate, and final) identified in Hyman’s (1977) survey. Third syllable stress requires an expansion of the theoretical apparatus to include either, in a foot-based theory, initial extrametricality, or, in a grid-based framework, a constraint banning a stress lapse of greater than two syllables at the left edge of a word, i.e. *Extended Lapse Left). Incorporating a novel constraint to account for the newly discovered three-syllable left edge window as well as a faithfulness constraint requiring preservation of lexically marked stress, Kager (2012) computes the factorial typology for window-sensitive stress systems generated by constraint-based implementations of three metrical representations: a traditional foot-based theory employing binary feet, a foot-based theory using internally layered feet, and a grid-based analysis. He finds that a theory employing internally layered feet (see section 5. “Ternary Stress”) offers the best typological coverage of the three accounts, both generating all the attested window-delimited patterns and largely avoiding pathologic overgeneration of unattested patterns. In particular, the internally layered foot theory succeeds where the other theories fail in excluding unattested patterns instantiating the “midpoint pathology,” whereby words of a particular length (but not all lengths) display attraction of stress to the middle of the word in order to minimize lapses of unstressed or unfooted syllables at both edges.

An interesting result of Kager’s cross-theory evaluation of factorial typology is that the introduction of the faithfulness constraint to lexical stress triggers the midpoint pathology in Gordon’s (2002) grid-based analysis, which had been successful as long as it contained only output-sensitive metrical well-formedness constraints. The midpoint pathology emerges when two highly ranked anti-lapse constraints oriented toward different edges exert a tug-of-war resulting in a stress near the middle of relatively short words, in which both anti-lapse constraints can be satisfied. However, when one of the anti-lapse constraints cannot be satisfied in longer words, one must kowtow to faithfulness. For example, *Extended Lapse Left and *Extended Lapse Right are satisfied by a stress on any syllable in a two-syllable (σˈσ‎‎ or σˈσ‎‎,),or three-syllable (σˈσσ‎‎ or σσˈσ‎‎ or ˈσσσ‎‎) word, by stress on either the second or third syllable in a four-syllable word (σˈσσσ‎‎ or σσˈσσ‎‎), and by stress on the third syllable in a five syllable word (σσˈσσσ‎‎). In words longer than five syllables, however, it is impossible to satisfy both anti-lapse constraints, meaning that a lower ranked faithfulness constraint requiring that a lexically marked stress surface has the opportunity to spring into action to determine which syllable is stressed within the window referred to by the highest ranked anti-lapse constraint. A six-syllable word with lexical stress on the second syllable would thus wind up with second-syllable stress (σˈσσσσσ‎‎), in contrast to a five-syllable word with third-syllable stress (σσˈσσσ‎‎). The result is an unattested type of system with window-delimited stress in short words but lexically marked stress in longer words.

6.2 Learnability of Metrical Stress Theories

Another prominent computational research program involving metrical stress theory employs computer simulations to model learnability. Stress is particularly probative in diagnosing the efficacy of a learning algorithm since many types of stress systems are non-local in requiring evaluation of strings of non-adjacent syllables.

Working within a foot-based theory, Dresher and Kaye (1990) develop a cue-based learning algorithm employing eleven binary parameters, each of which has a default setting that can be switched in the face of input data that is incompatible with the default. Some of their parameters are sensitive to directionality, including the direction of the parse into feet (left vs. right), the headedness of the foot (left-strong, i.e., trochaic, vs. right-strong, i.e., iambic), and the orientation of the main stress (left or right edge). Other parameters determine whether footing is iterative or not (i.e., whether stress follows a rhythmic alternating pattern, as in Maranungku and Urubú Kaapor), and whether feet are confined to a two syllable window (bounded) at the word-edge or whether they can occur word-internally, as in unbounded systems in which heavy syllables can occur in any position (e.g., Yana or Kʷak’ʷala). Further parameters concern whether weight is relevant or not in the calculation of stress and, if so, the weight criterion (only CVV heavy vs. both CVV and CVC heavy). A further parameter, set to “yes” in a language with lengthening of stressed vowels like Chickasaw determines whether stressed syllables are obligatorily heavy. Another parameter captures the divergence between languages in whether they tolerate stress clashes or not. Finally, a parameter specifies whether there are extrametrical elements and a sub-parameter determines whether, if present, they occur at the left or right edge.

Because their learner is a deterministic one with irrevocable parameter settings, they opt for a batch learner in which all the data is provided before any parameters are set, as opposed to an incremental one in which hypotheses are constructed and revised online, with continued exposure to data. Gillis, Durieux, and Daelemans (1995) run a simulation using Dresher and Kaye’s model, feeding the learner a corpus of data consisting of all logically possible strings, ranging from one to four syllables, and employing ten of the eleven parameters in the model (excluding one dealing with the option of de-stressing in clash). Cross-classification of the ten parameters yields 216 stress systems, including both weight-sensitive and weight-insensitive patterns, since two of the parameters are sensitive to syllable weight (weight-sensitive vs. weight-insensitive, CVC heavy vs. CVC light). The 216 stress systems do not match the complete typology of attested patterns, although the mismatch is at least partially attributed to the less extensive typological knowledge of stress systems at the time of Dresher and Kaye’s work. Gillis et al.’s simulation results in a generation rate of 80% of the 216 targeted systems, a success rate that would potentially rise if strings longer than four syllables were included in the learning corpus.

Working within a constraint-based paradigm, Hayes and Wilson (2008) employ a maximum entropy model of phonotactic learning, in which constraints are weighted in their relative strength rather than operating within a strict dominance hierarchy, as in Classical Optimality Theory of the type used in the computer-generated factorial typologies of Gordon (2002) and Kager (2012). They test their learner against two classes of stress systems: default-to-opposite weight-sensitive (as in Kʷak’ʷala) and weight-insensitive systems. In the first simulation, Hayes and Wilson’s (2008) constraint set, designed to capture default-to-opposite stress systems, correctly assigns perfect grammaticality scores to attested patterns, while heavily penalizing illicit forms. In the second test, their model discovers a set of six constraints capable of generating the 33 quantity-insensitive stress systems in Gordon’s (2002) typology. In a final test, their model successfully generates the weight-sensitive stress system (as well as other phonotactic features) of Wargamay.

A key feature of the metrical theory adopted by Hayes and Wilson (2008), which differentiates it from the Dresher and Kaye (1990) model, is its employment of a grid-based rather than a foot-based approach to stress, thereby bypassing the additional complexity inherent in acquiring the hidden structure implicit in a foot-based theory. Whereas a language learner can hear stresses, foot structure must be inferred through comparison of different word structures, any one of which may be compatible with multiple foot parses. For example, the Maranungku pattern involving stress on odd-numbered syllables could reflect the following foot structures in a four-syllable word even imposing a binary cap on foot size: (ˈσσ‎‎)(ˈσσ‎‎), (ˈσ‎‎)(σˈσ‎‎)σ□□‎‎(ˈσσ‎‎)(ˈσ‎‎)σ‎‎, (ˈσ‎‎)σ‎‎(ˈσ‎‎)σ‎‎ (see Tesar, 2004, 2007; Tesar & Smolensky, 2000, for approaches to the acquisition of hidden metrical structure; see also Heinz, 2009 for a learning algorithm that departs from grid-based and foot-based theories in representing stress systems as regular sets generated by finite-state acceptors).

7. Metrical Stress Theories: Conclusions

The last 40 years have witnessed important advances in both the typological knowledge of stress systems and in the theories designed to model them. Stress systems vary along a number of dimensions, including the number of stresses per stress domain, the role of rhythm, and sensitivity to syllable weight. A prominent debate in metrical stress theory centers on the role of the foot as a prosodic constituent. Although stress patterns themselves appear amenable to grid-based theories of stress that do not appeal to the foot, various segmental alternations provide evidence for a constituent larger than a syllable but smaller than a word, that is, a foot. Computational implementations of metrical stress theories have increasingly been employed in the evaluation of the predictive capacity of theories and their learnability.

Further Reading

De Lacy, P. (2002). The interaction of tone and stress in Optimality Theory. Phonology, 19, 1–32.Find this resource:

Dresher, B. E., & Kaye, J. (1990). A computational learning model for metrical phonology. Cognition, 34, 137–195.Find this resource:

Elenbaas, N., & Kager, R. (1999). Ternary rhythm and the lapse constraint. Phonology, 16, 273–329.Find this resource:

Gillis, S., Durieux, G., & Daelemans, W. (1995). A computational model of P&P: Dresher and Kaye (1990) revisited. In M. Verrips & F. Wijnen (Eds.), Approaches to parameter setting (pp. 135–173). Amsterdam: University of Amsterdam.Find this resource:

Goedemans, R., Heinz, J., & van der Hulst, H. (2015). StressTyp2.Find this resource:

Gordon, M. (2002). A factorial typology of quantity insensitive stress. Natural Language and Linguistic Theory, 20, 491–552.Find this resource:

Gordon, M. (2006). Syllable weight: phonetics, phonology, typology. New York: Routledge.Find this resource:

Halle, M., & Idsardi, W. (1995). Stress and metrical structure. In J. Goldsmith (Ed.), The Handbook of Phonological Theory (pp. 403–443). Oxford: Basil Blackwell.Find this resource:

Halle, M., & Vergnaud, J.-R. (1987). An Essay on Stress. Cambridge, MA: MIT Press.Find this resource:

Hayes, B. (1982). Extrametricality and English stress. Linguistic Inquiry, 13, 227–296.Find this resource:

Hayes, B. (1985). Iambic and trochaic rhythm in stress rules. Berkeley Linguistics Society, 13, 429–446.Find this resource:

Hayes, B. (1995). Metrical stress theory: Principles and case studies. Chicago, IL: University of Chicago Press.Find this resource:

Heinz, J. (2009). On the role of locality in learning stress patterns. Phonology, 26, 303–351.Find this resource:

Hyde, B. (2002). A restrictive theory of metrical stress. Phonology, 19, 313–359.Find this resource:

Hyde, B. (2011). Extrametricality and nonfinality. In M. van Oostendorp, C. Ewen, E. Hume, & K. Rice (Eds.), The Blackwell companion to phonology (Vol. 2, pp. 1027–1051). West Sussex, U.K.: Wiley-Blackwell.Find this resource:

Idsardi, W. (1992). The computation of prosody (PhD Diss.). Cambridge: Massachusetts Institute of Technology.Find this resource:

Kager, R. (2007). Feet and metrical stress. In P. De Lacy (Ed.), The Cambridge handbook of phonology (pp. 195–227). Cambridge, U.K.: Cambridge University Press.Find this resource:

Kager, R. (2012). Stress in windows: Language typology and factorial typology. Lingua, 122, 1454–1493.Find this resource:

Kenstowicz, M. (1997). Quality-sensitive stress. Rivista di Linguistica, 9(1), 157–187.Find this resource:

Liberman, M. (1975). The intonational system of English (PhD Diss.). Cambridge: Massachusetts Institute of Technology.Find this resource:

Liberman, M., & Prince, A. (1977). On stress and linguistic rhythm. Linguistic Inquiry, 8, 249–336Find this resource:

Prince, A. (1983). Relating to the grid. Linguistic Inquiry, 14, 19–100.Find this resource:

Prince, A. (1990). Quantitative consequences of rhythmic organization. Parasession on Syllable in Phonetics and Phonology, Chicago Linguistic Society, 26, 355–398.Find this resource:

Rice, C. (2011). Ternary rhythm. In M. van Oostendorp, C. Ewen, E. Hume, & K. Rice (Eds.), The Blackwell companion to phonology (Vol. 2, pp. 1228–1244). West Sussex, U.K.: Wiley-Blackwell.Find this resource:

Selkirk, E. (1984). Phonology and syntax: The relation between sound and structure. Cambridge, MA: MIT Press.Find this resource:

Tesar, B. (2007). Learnability. In P. De Lacy (Ed.), The Cambridge handbook of phonology (pp. 555–574). Cambridge, U.K.: Cambridge University Press.Find this resource:

Tesar, B., & Smolensky, P. (2000). Learnability in optimality theory. Cambridge, MA: MIT Press.Find this resource:

Van der Hulst, H., Goedemans, R., & van Zanten, E. (Eds.). (2010). A survey of word accentual patterns in the languages of the world. New York: Mouton de Gruyter.Find this resource:

Vaysman, O. (2009). Segmental alternations and metrical theory (PhD Diss.). Cambridge: Massachusetts Institute of Technology.Find this resource:

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