24.961 Stress-3 Stress in Windows [1] Kager (2012): many languages restrict stress/accent to a window of two or three syllables at the right or left edge of the word. R. Kager / Lingua 122 (2012) 1454--1493 R. Kager / Lingua 122 (2012) 1454--1493 1461 1461 Elías-Ulloa thesepatterns patternsusing using a strictly disyllabic adjusting the weight of an initialsyllable closed syllable Elías-Ulloa(2005) (2005)analyzes analyzes these a strictly disyllabic foot,foot, adjusting the weight of an initial closed preceding another to(LˈH) (LˈH)bybymeans means Weight-to-Stress and Grouping Harmony 1990). This weight preceding anotherclosed closedsyllable syllable to of of Weight-to-Stress and Grouping Harmony (Prince,(Prince, 1990). This weight • right edge: Aklan binary, by Modern Greek, Italian, Spanish ternary adjustment isisindependently suffixal allomorphy is sensitive to odd/even parity treating count, treating adjustment independently supported supported by a asuffixal allomorphy thatthat is sensitive to odd/even parity count, closed closed syllables as light odd positions (see 2009 forfor an an analysis). Assuming that the disyllabic foot-based analysis analysis is syllables light ininodd positions (seeVaysman, Vaysman, 2009 analysis). Assuming that the disyllabic foot-based is • asleft edge: Onati Basque binary, Choguita Raramuri ternary correct and alsothat thatititcan canbe be generalized generalized totoCapanahua, these languages no longer constitute evidence for a mixed correct and also Capanahua, these languages no longer constitute evidence for adefault. mixed default. •thethe accent location in in window is determined by syllable weight, lexical encoding, as asspurious. thirdS/I S/I language Mathimathi (Hercus, 1969), quantity-sensitivity is likelyis tolikely be well spurious. ForFor third language in StressTyp, StressTyp, Mathimathi (Hercus, 1969), quantity-sensitivity to be Goedemans(1997) (1997)shows shows that that Mathimathi stress is is entirely morphologically governed; the appearance of typologically Goedemans Mathimathi stress entirely morphologically governed; the appearance of typologically distance from word edge uncommonquantity quantitycriteria criteria is is due processes targeting stemsstems of specific lengths.lengths. uncommon due to tohistorical historicalphonological phonological processes targeting of specific All three P/U languages listed in StressTyp areor Austronesian: Javanese, Malay, and Ngada, and their status in stress • accent may be realized by stress pitch and hence is a n abstract quantity All three P/U languages listed in StressTyp are Austronesian: Javanese, Malay, and Ngada, and their status in stress typology is problematic. For Javanese, the status of word stress is controversial and descriptions are not uniform (Horne, typology ismaximal problematic. For Javanese, the status ofbword stress controversial and not uniform2002) (Horne, • Poedjosoedarmo, window three syllables ut found toisbe at descriptions both edges are (cf. Gordon 1961; 1982;is Ras, 1985). In the Indonesian spoken bysymmetric native speakers of Javanese, no systematic 1961; Poedjosoedarmo, 1982; Ras, 1985). the Indonesian spoken speakers of Javanese, no the systematic phonetic correlates of stress have been found.InMoreover, stress seems notby to native be perceived by Javanese listeners: • correlates final syllable canhave be obligatorily unstressedstress but not thenot initial syllable phonetic of contours stress been seems to be perceived(Goedemans by Javanese the manipulation of pitch of final and found. prefinalMoreover, syllables failed to result in different perceptions andlisteners: van manipulation of pitch contours final the andsituation prefinalappears syllables result in different perceptions (Goedemans Zanten, 2007). For varieties of of Malay, to failed be no to less complex (van Zanten et al., 2003; Roosman, and van Zanten, 2007). varieties Malay, the situation appears to be no lessamong complex (van Zanten al., 2003; Roosman, 2006; ZuraidahFor et al., 2008). of Finally, Ngadˈa is most probably miscategorized P/U systems since et schwa does not [2] examples occur in the final according to Arndt (1933). For probably these reasons, it seems rather premature to claim the existence 2006; Zuraidah etsyllable al., 2008). Finally, Ngadˈa is most miscategorized among P/U systems since schwaofdoes not P/Uin systems with mixedaccording defaults. Into sum, the(1933). evidence forthese opposite defaults in the form of S/I and P/U systems rather occur the final syllable Arndt For reasons, it seems rather premature to claim is the existence of Macedonian: antepenult stress withforthe exceptional lexical stress in with loanwords No compelling arguments theevidence existencefor of stress windows P/Uweak. systems with mixed defaults.remain In sum, opposite defaults innon-uniform the form ofdefault S/I andsystems. P/U systems is rather consider languages have for hierarchies for intrinsic prominence (e.g. a non-uniform syllable weightdefault scale).systems. Weight weak.Finally, No compelling argumentsthat remain the existence of stress windows with hierarchies are well-known for that unbounded stress languages (such as Kelkhar's Hindi Kashmiri; Prince and Weight Finally, vodéničar consider languages have hierarchies for intrinsic prominence (e.g. syllable weight scale). ‘miller’ vodeníčar-ot ‘miller def.aand Smolensky, 1993). In case a weight scale system also imposes a stress window, the primary stress falls on the heaviest hierarchies are well-known for unbounded stress languages (such as Kelkhar's Hindi and Kashmiri; Prince and syllable occurring within the window -- a weight peak. In case there is not a single weight peak, but two or three peaks konzumátor ‘consumer’ konzumatór-i-te ‘consumers def.’ Smolensky, 1993). In case a weight scale system also imposes a stress window, the primary stress falls on the heaviest compete for attracting stress, the choice among these is made per default, similarly to languages with a binary weight syllable occurring within Pirahã the window a weight peak. In case not three a single weight peak,in but twostress or three contrast. For example, (Muran;-- Everett and Everett, 1984)there has aisfinal syllable window which is peaks compete for attracting the choice is made per default, similarly to languages with a binary weight predictable according stress, to a syllable weight among hierarchythese in (15): contrast. For example, Pirahã (Muran; Everett and Everett, 1984) has a final three syllable window in which stress is Piraha (Everett & Everett 1984) predictable according syllable in (15): G = voiced) (15) CVV > GVV to > a VV > CVweight > GVhierarchy (C = voiceless; 1 (15) 2 3 4 5 CVV > GVV > VV > CV > GV (C = voiceless; G = voiced) Stress falls on 1 2 the heaviest 3 of the 4 last three 5 syllables in the word. In the representations below, the stress window has been marked by square brackets. Stress falls on the heaviest of the last three syllables in the word. In the representations below, the stress window has (16) a. 4-4-[3-2-1] ko.so.ii.gai.ˈtai ‘eyebrow’ been marked by square brackets. b. 4-[1-4-4] ʔi.ˈtii.ʔi.si ‘fish’ (16) c. 1-1-[1-4-3] a. d. 4-4-[3-2-1] 1-[1-5-5] b. e. 4-[1-4-4] 4-[1-4-3] c. f. 1-1-[1-4-3] 4-[5-5-2] d. g. 1-[1-5-5] 4-[4-2-4] e. 4-[1-4-3] Inf.case4-[5-5-2] the heaviest g. 4-[4-2-4] (17) ʔoo.hoi.ˈhoi.hi.ai ‘caterpillar’ ko.so.ii.gai.ˈtai ‘eyebrow’ pii.ˈhoa.bi.gi ‘frog’ ʔi.ˈtii.ʔi.si ‘fish’fuel’ ʔi.ˈsii.ho.ai ‘liquid ʔoo.hoi.ˈhoi.hi.ai ‘caterpillar’ ʔo.ga.ba.ˈgai ‘want’ pii.ˈhoa.bi.gi ‘frog’ ʔa.pa.ˈbaa.si ‘square’ ʔi.ˈsii.ho.ai ‘liquid fuel’ syllable in the word falls outside the window, it fails to attract the primary stress: ʔo.ga.ba.ˈgai ‘want’ ʔa.pa.ˈbaa.si ‘square’ a. 1-1-5-[4-3-4] pia.hao.gi.so.ˈai.pi ‘cooking banana’ b. 1-[2-4-3] poo.ˈgai.hi.ai ‘banana’ In case the heaviest syllable in the word falls outside the window, it fails to attract the primary stress: c. 1-[3-5-5] kao.ˈai.bo.gi ‘jungle spirits’ (17) a. 1-1-5-[4-3-4] pia.hao.gi.so.ˈai.pi ‘cooking banana’ c. 1-[3-5-5] kao.ˈai.bo.gi ‘jungle spirits’ The default stress position in Pirahã is rightmost. This is evidenced by windows that contain more than a single b. syllable 1-[2-4-3] ‘banana’ heaviest (i.e. a tie),poo.ˈgai.hi.ai in which case the rightmost of these is stressed. (18) a. [2-1-1] bai.toi.ˈsai ‘wildcat’ b. [1-1-1] pao.hoa.ˈhai ‘anaconda’ This is evidenced by windows that contain more than a single The default stress position in Pirahã is rightmost. 5-[1-5-1] ‘pig’rightmost of these is stressed. heaviest c. syllable (i.e. a tie),ba.hoi.ga.ˈtoi in which case the d. 1-[2-5-2] kao.bii.ga.ˈbai ‘almost falling’ 4-1-5-[3-4-3] bai.toi.ˈsai ka.pii.ga.ii.to.ˈii ‘pencil’ (18) a. e. [2-1-1] ‘wildcat’ 4-4-[3-3-3] ʔo.ho.aa.aa.ˈaa ‘searching intensely’ b. f. [1-1-1] pao.hoa.ˈhai ‘anaconda’ [4-4-4] ko.ʔo.ˈpa ‘stomach’ c. g. 5-[1-5-1] ba.hoi.ga.ˈtoi ‘pig’ h. [5-5-5] gi.go.ˈgi ‘what about you’ d. 1-[2-5-2] kao.bii.ga.ˈbai ‘almost falling’ e. 4-1-5-[3-4-3] ka.pii.ga.ii.to.ˈii ‘pencil’ Kager, René. “Stress in Windows: Language Typology and Factorial Typology.” Lingua 122, no. 13 f. 4-4-[3-3-3] ʔo.ho.aa.aa.ˈaa ‘searching intensely’ (2012): 1454–93. © Elsevier. All rights reserved. This content is excluded from our Creative g. [4-4-4] ko.ʔo.ˈpa ‘stomach’ Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. h. [5-5-5] gi.go.ˈgi ‘what about you’ 1 words longer than two syllables (30f). (30) a. b. c. d. la.ˈqa.na me.ˈloo.ni ˈpaa.wits.ja ˈsip.mas.mi ‘squirrel’ ‘musk melon’ ‘duck’ ‘silver bracelet’ d. e. f. ˈtaa.vo ˈko.ho ˈsi.kis.ve ‘cottontail’ ‘wood’ ‘car’ Azkoita Basque (Hualde 1998) Two more examples of initial two syllable window systems that impose final unstressability are Oñati Basque, which has lexical pitch accent (Hualde, 1999), and Aranda (Australian; Strehlow, 1942; Davis, 1988), which is based on syllable - stress rightmost syllable in trisyllabic window at left edge of word except that wordweight (the presence of syllable onsets). Turningfinal now syllable to initial three syllable windows constrained by non-finality, we already discussed a mixed lexical accent is not stressed plus syllable weight system, that of Terêna, in section 2. An example of a purely accentual system is Azkoitia Basque (Hualde, accent in words longer than two syllables: /gizon/ ‘man’ ‘the man-ABS’ (31) a. gi.ˈzo.na c. /alargun/ ‘widow’ gi.zo.ˈnai ‘the man-DAT’ a.lar.ˈgu.ne ‘the widow-ABS’ gi.zo.ˈna.na ‘the man-GEN+ABS’ a.lar.ˈgu.nei ‘the widow-DAT’ gi.zo.ˈna.kin ‘the man-COM’ a.lar.ˈgu.ne.na ‘the widow-GEN+ABS’ a.lar.ˈgu.ne.kin ‘the widow-COM’ gi.zo.'nan.tsa.ko ‘the man-BEN’ ‘the widow-BEN’ a.lar.'gu.nen.tsa.ko Kager, René. “Stress in Windows: Language Typology and Factorial Typology.” Lingua 122, no. 13 b. /on/ ‘good’ (2012): 1454–93. © Elsevier. All rights reserved. This content is excluded from our Creative ABS’ ˈo.na For more information, ‘the good Commons license. see onehttp://ocw.mit.edu/help/faq-fair-use/. ... [3]Observe analytical to define two and over three-syllable window (/ˈo.na/ ‘the good one’, */o.ˈna/). that options strict non-finality has priority (default) non-initiality ‘‘The accentual pattern of bisyllabic forms such as óna ‘the good one’ shows that when the application of both •extrametricality binary feet conditions plus extrametricality edge syllable, constraints lapses, layered would make ofthe whole domainrhythmic unaccentuable, initial on extrametricality is revoked. Expressed in below) terms of ranked constraints, nonfinality is ranked above noninitiality.’’ (Hualde, 1998:108) feet (see • problem noted by Green & Kenstowicz (1995) for foot-binarity plus extrametricality: That is, on an analysis that attributes default third syllable stress to initial extrametricality (rendering the initial syllable unparsable), and final unstressability to final extrametricality (unparsability), the former the latter. This extrametricality must be “revoked” in case final syllable is strongest inmust wordoverrule in Piraha: ranking similarly applies to Hopi seen above, on the analysis that second syllable stress is due to initial unparsability. (‘pii.ai).ia ‘scissors’ but ?o.gi.’ai ‘big’ • same problem for OT: Non-Finality » Align-Ft-Right fails to license stress on ?o.gi.’ai • Green (1995) proposes Lapse constraint: *adjacent unstressed syllables not separated by 1476 a foot boundary: *(ss)ss#, *#ss(ss) • R. Kager / Lingua 122 (2012) 1454--1493 pathological pattern: in words(Eisner of two or1997, three syllables, stress is free to fall on any syllable, whereas in longer words, stress is entails midpoint pathology Hyde 2008) restricted to fall on a non-peripheral syllable. (49), a candidate with1454--1493 a right-aligned iamb satisfies LAPSE/PARSE-2, hence 1476 R. In Kager / Lingua 122 (2012) thedetermines Lapse constraint prevents lexical from drifting far from the lexical-accent the outcome because FAITHstress -ACCENT dominates thetoo default constraints. pathological pattern: in words of two or three syllables, stress is free to fall on any syllable, whereas in longer words, stress is edge of the word so that it remains within the window (49) Free stress in three syllable forms restricted to lexical fall on a non-peripheral syllable. In (49), a candidate with a right-aligned iamb satisfies LAPSE/PARSE-2, hence but determines as the word longer, stressFwill be drawn to the the middle ofconstraints. the word lexical- accent thegets outcome because AITH-A CCENT dominates default FAITH L APSE / FT= ALIGN / / to avoid a lapse on each edge word -2 of the PARSE ACCENT TROCHEE WORD-L (49) *! (' ) - [TD$INLE] no language attested has this bizarre system *! * ( ' ) * *! (' ) Free lexical stress in three syllable forms * * ( ' ) [TD$INLE] FAITH FT= ALIGN L APSE / / / -2 ACCENTof LAPSE -L since any candidate with a strictly PARSE TROCHEE WORD In longer forms of four (or more) syllables, violation /PARSE-2 will be minimal: ) one more violation of LAPSE/P*!ARSE-2 than a candidate with a non-aligned foot, an ˈinternalˈ window aligned foot('incurs *! that heads a * non-peripheral foot. emerges that stress to fall on any syllable ( restricts ' ) In longer forms of LAPSE/PARSE-2 will be minimal: since any candidate with a strictly *! * (' )of four (or more) syllables, violation (50) aligned foot incurs ( ' ) one more violation of LAPSE/PARSE-2 than a*candidate with* a non-aligned foot, an ˈinternalˈ window emerges that restricts stress to fall on any syllable that heads a non-peripheral foot. Peripheral unstressability in four-syllable form: default overrules peripheral accent (50) Peripheral unstressability in four-syllable form: default overrules peripheral accent FAITH FT= ALIGNL APSE/ / / FAITH L APSE/ FT= ALIGN/ / ACCENT PARSE-2 TROCHEE WORD -L [TD$INLE] PARSE-2 ACCENT TROCHEE WORD -L *! * (' ) *! * (' ) *! * * ( ' ) *! * * ( ' ) * * (' ) [TD$INLE] * * (' ) * *! * ( ' ) * *! * ( ' ) *! * * (' ) *! * * (' ) (51) Non-peripheral * * ( ' ) stressability*!in four-syllable form * * *! ( ' ) L APSETypology / AITHFactorial FT= LinguaA122, LIGNno. - 13 Fand / / Windows: Language Kager, René. “Stress in Typology.” PinARSE ACCENT TROCHEE WORD-L -2 This (2012):Non-peripheral 1454–93. © Elsevier. All rights reserved. content from our Creative (51) stressability four-syllable form is excluded * Commons license. see http://ocw.mit.edu/help/faq-fair-use/. (' For ) more information, *! L APSE F*T= ALIGN FAITH *! / * (/ ' ) / [TD$INLE] PARSE-2 ACCENT TROCHEE WORD *! * -L 2 extrametricality-based models with binary feet cannot account for stress windows naturally leads to a shift in the attention to different mechanisms: anti-lapse constraints and ternary foot models, which will be discussed in sections 4.2 and 4.3, respectively. 4.2. Symmetrical anti-lapse constraints [4] grid-only with anti-lapse constraints also faces this problem (Gordon 2002) A second model is based on symmetrical anti-lapse constraints. Anti-lapse (58) a. x xxxx# extended lapse b. x xxx# lapse c. constraints ban sequences of unstressed 1983; Selkirk, 1984). In an edge-based model, that target lapses specifically in word 2002). Below, three configurations of grids x xx# no lapse Kager, René. “Stress in Windows: Language Typology and Factorial Typology.” Lingua 122, no. 13 (2012): 1454–93. © Elsevier. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. A final three syllable window system has a high-ranked constraint banning extended lapse at the right edge, while a Final three-syllable window: » Faith-Accent » Align-maximal window for the symmetrical final two syllable window systems bans regular lapse at *Extended-Lapse-R the right edge. To account size of three syllables,Head-L anti-lapse constraints that target extended lapses must be assumed for both edges. The specific implementation of this mechanism will be a pure grid (PG) model, adapted from Gordon (2002). Gordonˈs initial three-syllable window: *Extended-Lapse-L » Faith-Accent » Alignoriginal set was simplified by eliminating constraints that are exclusively relevant for iterative stress. The resulting model has the following constraint set. Head-R - 1480 R. Kager (2012)too 1454--1493 Extended-Lapse keeps stress/ Lingua from 122 drifting far away from edge and then Faith orwhile Head-alignment in the stress window extended lapse constraints, in words of three locates syllablesstress long, placing on any syllable will satisfy both anti-lapse constraints simultaneously. This predicts window systems in which stress is free to fall on any syllable in a three syllable word, on the second or third in Lapse four syllable words,are but top-ranked may only occur onthe the best third window syllable inisfive syllable words. This Problem: when both Extended constraints then one in window pattern is a specimen of ˈMidpoint Pathologyˈ (Eisner, 1997; Hyde, 2008:4), ˈa collection of situations where an the middle of a word with five syllables object is drawn toward a medial position in a formˈ. (61) Window reduced in words of length 4 and 5 syllables / ' [TD$INLE] *! ' ' / ' ' ' *** ** * *E XTENDED *E XTENDED FAITH -A CCENT A LIGN -HEAD-L APSE-L -L APSE-R R *! *! ' * *! * *! ' / ' *E XTENDED *E XTENDED FAITH -A CCENT A LIGN -HEAD-L APSE-R R -L APSE-L / *! *! * * * * **** *** ** * Kager, René. “Stress in Windows: Typology.” Lingua 122,the no.two 13 high-ranking anti-lapse Strikingly, words longer than fiveLanguage syllablesTypology regain and theirFactorial accentual freedom: since (2012): 1454–93. © Elsevier. rights reserved. This content excluded from ourjumps Creative CCENT into activity again. This restores constraints can no longer both beAll satisfied, one must give way,isand FAITH-A Commons morewindow: information, see http://ocw.mit.edu/help/faq-fair-use/. the initial three license. syllableFor stress (62) Window- regained in words of words length 6a syllables in four-syllable lexical accent on the second syllable can survive [TD$INLE] / *E XTENDED -A CCENT A LIGN -HEAD *E XTENDED FAITH since/ both extended lapse constraints are satisfied; but when the word is five ' syllables there is an extended so a violation occurs * lapse on the *! right and ***** -L APSE-L -L APSE-R R * **** satisfies both - ' the candidate with accent placed in the middle of word *! *** *! ** *! *! But ' the window is regained when the word is longer*than five syllables since *! *! ' ' - extended lapse constraints *! ' * now among the competing candidates every word will violate one or the other of of the Extended Lapse constraints and hence is patterns a tie that will be The factorial typology constraint set for pure grids contains 254there window in which stress in five syllable words is fixed on theresolved middle syllable, with shorter words and/or longer words obeying a window. Among these, 175 show fixed by the lower-ranked faithfulness or alignment constraints midpoint stress in five syllable words, while shorter and longer words have accentual freedom within a window (of two or three syllables, in initial or final position). The most severe cases are of the following kind: an (initial or final) window of two syllables is imposed on longer words, i.e. a window size defeated by the fixed midpoint stress in five syllable forms.6 Additional pathological window patterns arise by specific interactions of anti-lapse constraints targeting lapses of different 3 which words sizes. For example, the high-ranked combination *LAPSE-L » *EXTENDED-LAPSE-R generates a window system in of all lengths are subject to an initial two syllable domain, except that four syllable words have fixed stress on the antepenult. Table (42) displays window reductions for all logically possible combinations of anti-lapse constraints for words of lengths of two to seven syllables. The stress windows are indicated by square brackets. In each cell, the stress patterns are listed that *! ' * Strikingly, words longer than five syllables regain their accentual freedom: since the two high-ranking anti-lapse constraints can no longer both be satisfied, one must give way, and FAITH-ACCENT jumps into activity again. This restores the initial three syllable stress window: / (62) ' [TD$INLE] *E XTENDED *E XTENDED -L APSE-L -L APSE-R / ' ' ' ' * * * *! *! *! ' FAITH -A CCENT A LIGN -HEADR *! *! *! *! *! ***** **** *** ** * Kager, René. “Stress in Windows: Language Typology and Factorial Typology.” Lingua 122, no. 13 (2012): 1454–93. © Elsevier. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. The factorial typology of the constraint set for pure grids contains 254 window patterns in which stress in five syllable words is fixed on the middle syllable, with shorter words and/or longer words obeying a window. Among these, 175 show fixed midpoint stress in five syllable words, while shorter and longer words have accentual freedom within a window (of two or three Thus, free-ranking of natural constraints predicts an unattested stress system in the typology. syllables, in initial or final position). The most severe cases are of the following kind: an (initial or final) window of two syllables is imposed on longer words, i.e. a window size defeated by the fixed midpoint stress in five syllable forms.6 [5] The problem is not just limited to lexical can arise more generally in any system Additional pathological window patterns arise byaccent specificbut interactions of anti-lapse constraints targeting lapses of different sizes. For example, the high-ranked combination *L APSE-L » *EXTENDED-LAPSE-R generates a window system in which words where the two opposite-edge lapse constraints dominate alignment (Stanton 2014); stress is of all lengths are subject to an initial two syllable domain, except that four syllable words have fixed stress on the antepenult. drawn middle ofwindow word just in case remove lapses at both edges; but inconstraints longer words thisof lengths of Tableto (42) displays reductions foritallcan logically possible combinations of anti-lapse for words two to seven syllables. The stress windows are indicated by square brackets. In each cell, the stress patterns are listed that is not possible and so the default edge orientation will reassert itself arise under a specific ranking of a pair of anti-lapse constraints. This ranking has anti-lapse constraint in the vertical dimension as the higher-ranked one, and the anti-lapse constraint in the horizontal dimension as the lower-ranked one: *Lapse-L » *Lapse-R » Align-L 6 Ss sSs Ssss Sssss Ss Sss sSss ssSss Ssssss To be sure, window systems are attested in which the degree of accentual freedom is correlated with syllable number, without showing Midpoint Pathology. For example, the pitch accent in Kyungsang Korean (Kenstowicz and Sohn, 2001) is restricted by a final two syllable window in words*Extended-Lapse-L of two or three syllables, whereas accent is fixed on the »penult in words of four or more syllables. This is not a case of Midpoint Pathology, » *Extended-Lapse-R Align-L as five syllable words are not accented on the middle syllables; moreover, longer words (exceeding four syllables) do not regain accentual freedom. Thanks to an anonymous reviewer for pointing this out. [6] Kager’s suggested solution is to represent the two and three-syllable windows with a weakly1482 / Lingua 122foot (2012) 1454--1493 layered foot: a ternary foot withR.a Kager single binary inside. Nonfinality is restricted to final (64) unstressability. Shapes of the Weakly Layered foot [TD$INLE] head + adjunct adjunct + head no adjunct binary head, trochee ([' ] ) ( [' ]) ([' ]) binarywhen head, iamb Layered A stress window occurs a Weakly ([ foot ' ] is ) obligatorily ( [ aligned ' ]) with a domain ([ ' ])edge. A two syllable window unary head results when the adjunct is disallowed, and hence, aligned with both ([' the ] ) head is doubly ( [' ]) ([' ])foot edges. (65) Two syllable windows: adjunct disallowed Kager, René. “Stress in Windows: Language a. final window b. initial windowTypology and Factorial Typology.” Lingua 122, no. 13 rights reserved. This content is excluded from our Creative U ([σ (2012): ˈσ]) # 1454–93. ([ˈσ])©#Elsevier. I #All([ˈσ σ]) # ([ˈσ]) Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. P ([ˈσ σ]) # S # ([σ ˈσ]) Observe that the contrast of peripheral versus non-peripheral stress may arise either by manipulating the head's Gen is “hard-wired” only allowversus a single “adjunct” syllable either athe left orof a DPS dominance (trochaic versus iambic), or itstosize (binary unary). Technically, thison involves ranking constraint above a right foot form constraint. edge of foot and the internal “head” foot is restricted to two syllables (cf. foot A three syllable window emerges when an adjunct is allowed in the weakly layered foot, so that the head may be misbinarity) aligned with one (but not both) foot edges. As compared to two syllable windows, the number of representational possibilities for- non-peripheral increases. Forateach stress position, four representational options amounts tostress binary feet with mostnon-peripheral one recursion occur, as shown below. - (66) Ito & Mester (2012) propose similar restrictions on the depth of recursion in phrasal Three syllable windows: adjunct allowed phonology a. final window U ([ˈσ]) # ([σ ˈσ])set: # Kager’s (2012) constraint P A ([ˈσ σ]) # ([ˈσ σ] σ) b. I S T initial window # ([ˈσ]) # ([σ ˈσ]) # (σ [σ ˈσ]) ([σ ˈσ] σ) # (σ [σ ˈσ]) # (σ [ˈσ σ]) # (σ [ˈσ]) ([ˈσ] σ) 4 # ([ˈσ σ]) # (σ [ˈσ σ]) # ([ˈσ σ] σ) # ([σ ˈσ] σ) # ([ˈσ] σ) # (σ [ˈσ]) Observe that the three-way stress contrast is representationally encoded as variation in four aspects of foot form: head dominance, head size, head alignment, and foot size. Evidently, foot form variation is not random, but under control of constraint interaction. Crucially, a weakly layered foot model of stress windows should not be combined with extrametricality (of the final syllable unparsability type) as this would incorrectly predict four syllable window systems. (See Everett, 1988:233 for a similar argument based on Pirahã.) However, non-finality can be assumed as an unstressability requirement. The following constraint set will be assumed: (67) Constraint set for the Weakly Layered Model a. b. c. d. e. f. g. h. i. j. HD-BIN ALIGN-HD-L ALIGN-HD-R HD=TROCHEE HD=IAMB PARSE-SYL ALIGN-WORD-L ALIGN-WORD-R NON-FINALITY FAITH-ACCENT Heads are binary under syllabic or moraic analysis. Heads are left-aligned with feet. Heads are right-aligned with feet. Heads begin with strong syllable. Heads begin with weak syllable. Syllables are parsed by feet. Words are left-aligned with a foot. Words are right-aligned with a foot. Stress must not fall on the final syllable. A lexical accent should be realized as primary stress. HD-BIN is the counterpart of FT-BIN in the binary model, and it is evaluated analogously. Analogously to assumptions Kager, for René. Windows: Typology and violates Factorial H Typology.” Lingua 122, 13 . The Weakly Layered made earlier the“Stress binaryinfoot model,Language a monosyllabic head D=IAMB, but not H D=Tno. ROCHEE (2012): 1454–93. © Elsevier. All rights reserved. This content is excluded from our Creative Model has no constraints requiring peripheral syllables to be non-parsed by a foot, as in the binary foot model; the only Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. constraint referring to the final syllable requires its unstressability: NON-FINALITY. To determine the side of the adjunct with respect to the head, a pair of head-to-foot alignment constraints (67b--c) are assumed. In case both constraints are high-ranked, the adjunct is suppressed, in which case the size of the foot equals the size of its head (i.e. maximally two - no lapse and clash constraints - word-to-foot alignment constraints keep main stress foot at an edge while separate constraints on foot form locate the stressed syllable within this maximally trisyllabic foot domain; in the “foot-free” model all constraints are constraints on stress since there is no foot or grouping by hypothesis - the mid-point pathology does not arise in Kager’s model since no consistent ranking of the constraint set will produce this syndrome: to get third-syllable stress in a five syllable word with lexical accent, the constraints defining the default must dominate Faith for lexical stress; but then they will also override lexical stress within the window; if Faith for lexical accent is top ranked then lexical accent can surface independent of the window [6] Stanton (2014) - over-generation in the typology of grammars predicted with lapse constraints does not automatically entail weakly layered feet or more generally metrical grouping - the evidence needed to motivate the ranking with both lapse constraints undominated does not appear in the data readily available to the learner - thus, such grammars are theoretically possible but not reachable for learnability reasons (a familiar argument form; cf. Lightfoot’s 1979 Degree-0 learnability) - to learn the ranking where Extended Lapse constraints are top-ranked, long words (six or seven syllables) are needed and they will be much less frequent in most (nonagglutinating) languages compared to shorter words - for binary-lapse dominant constraints the long-word argument does not hold and the claim is that it is difficult to infer the appropriate ranking change (aka the “credit” problem) with the Gradual Learning Algorithm - other pathologies: given Kager’s 2001 constraints licensing lapses at the stress peak, a possible ranking will shift location of main stress in odd-parity words to license a lapse. But this is also not attested. (not clear if this bears on the grouping question) 5 Norwegian University Science Technology & Utrecht University Non-intervention constraints and theand binary-to-ternary rhythmic continuum VioletaofMartínez-Paricio & René Kager ! !" ! VioletaofMartínez-Paricio & René Kager Norwegian University Science and Technology & Utrecht University Norwegian of Science andhead Technology & UtrechtatUniversity 1. Introduction The IL foot respects locality,University due to adjacency of the and its dependent both levels of structure. Ternary rhythm the dependents phenomenon being((10)0) placed and rhythmically on every syllableadjacent or mora. 1. Introduction Although the top is level ofof thestress IL dactyl anapest (0(01)) arethird not linearly [7] weakly-layered feet have been proposed for ternary stress rhythms (Kager & Martinez-Paricio paradigm caseisisthe Cayuvava (Key 1961, 1967), stress occurs third Introduction Ternary rhythm phenomenon stress being placed rhythmically onevery everyto third syllablecounting orfoot. mora. toA1. the head syllable, what matters for of locality is thatwhere the dependents are on adjacent thesyllable innermost 2014) 1 backward from the word end: Ternary rhythm isisthe phenomenon of1961, stress being where placed rhythmically on every every third or mora. A paradigm case Cayuvava 1967), stress occurs on syllable counting The IL foot is equally local in its(Key vertical dimension: an upper bound of two layersthird of structure. classical grammar: dactyl (Sss) anapest (ssS) amphibrach (sSs) A paradigm casetheis word Cayuvava backward from end:1 (Key 1961, 1967), where stress occurs on every third syllable counting Since headedness varies at two levels, four IL feet‘inside arise: of a dactyl (1) 3n !"#$"#$%&$'(&$)*$+* cow’ ((10)0), two amphibrachs ((01)0) and 1 backward from the word end: Cayuvava (dactyl) ((Ss)s) (0(10)) (0(01)). Importantly, all four typesof arecow’ typologically attested. The dactyl ((10)0) (1) and 3nan anapest !"#$"#$%&$'(&$)*$+* ‘inside 3n+1 ma.!ra.ha.ha.'e.i.ki ‘their blankets’ occurs Tripura !"#$"#$%&$'(&$)*$+* Bangla and Cayuvava:5 ‘inside of cow’ (1) in 3n 3n+1 ma.!ra.ha.ha.'e.i.ki ‘their blankets’ 3n+2 i.ki.!ta.pa.re.'re.pe.ha ‘the water is clean’ (8) The dactylma.!ra.ha.ha.'e.i.ki ((10)0) in Tripura Bangla and Cayuvava 3n+1 ‘their blankets’ 3n+2 i.ki.!ta.pa.re.'re.pe.ha ‘the water is clean’ 3n+1 ((#bi.$%&.s'&.na 3n ((()*+)*&+,-&+..#/-+$0&+10& Another 3n+2 classicali.ki.!ta.pa.re.'re.pe.ha example is Chugach Alutiiq ‘the Yupik (Leer 1985a,b,c), where stress falls on every water is clean’ syllable inclassical position 3n!1 (e.g.is"Chugach as3n+1 on the ma.(((ra.ha).ha).((#e.i).ki) final syllable of words of length Another example Alutiiq Yupik (Leer 1985a,b,c), where stress3n+1. falls 2on every 2, "5), as well 3n+2 ((#2'.ma).l!).((s'.na) 2 Chugach Alutiq (amphibrach) (sS)s)well as on Another classical example is "Chugach Yupik (Leersyllable 1985a,b,c), where stress 3n+1. falls on every syllable in position 3n!1 (e.g. the final of words of length 2, "5), as Alutiiq (2) 3n+2 ((#o.nu).k'&.(((ro.ni).j'&" ta.'qa.ma.lu.'ni ‘apparently getting done’ 3n " 3n+2 i.ki.(((ta.pa).re).((#re.pe).ha) syllable in position 3n!1 (e.g. "2, "5), as well as on the final syllable of words of length 3n+1.2 (2) 3n+2 ta.'qa.ma.lu.'ni ‘apparently getting done’ ‘he stopped eating Chugach 3n Alutiiq a.'ku.tar.tu.'nir.tuq instantiates the ‘left-branching’ amphibrach ((01)0),akutaq’ to be supported in §4. (2) 3n+2 ta.'qa.ma.lu.'ni ‘apparently getting done’ 3n a.'ku.tar.tu.'nir.tuq ‘hehestopped akutaq’ .)eating is going to hunt porpoise’ 3n+1 ma.',ar.su.qu.'ta.qu.'ni (REFL (9) The left-branching amphibrach ((01)0) in‘if Chugach Alutiiq 3n a.'ku.tar.tu.'nir.tuq ‘he stopped eating akutaq’ 3n+1 ma.',ar.su.qu.'ta.qu.'ni ‘if he (REFL.) is going to hunt porpoise’ 3n+2 ((ta.#qa).ma).(lu.#ni) A third example is Tripura Bangla (Das 2001), where falls on alltosyllables in position 3n+1 (e.g. is going hunt porpoise’ 3n+1 ma.',ar.su.qu.'ta.qu.'ni ‘if he stress (REFL.) 3n ((a.#ku).tar).((tu.#nir).tuq) Bangla (dactyl) ((Ss)s) "A1, third "4),Tripla except thatisfinal syllables are(Das always unstressed. Bangla 2001), where stress falls on all syllables in position 3n+1 (e.g. example Tripura A example is Tripura Banglaare (Das 2001), where stress falls on all syllables in position 3n+1 (e.g. "1,third "4),3n+1 except((ma.#3ar).su).(qu.#ta).(qu.#ni) that final syllables always unstressed. (3) 3n+2 '-..ma.l!.!s..na ‘criticism’ "1, "4), except that final syllables are always unstressed. (3)anapest 3n+2 '-..ma.l!.!s..na ‘criticism’ The (0(01)) matches the /accentual of Winnebago (Miner 1979, 1981).6 However, 3n 'o.nu.k..!ro.ni.j./ // distribution ‘imitable’ (3) that binary 3n+2 and '-..ma.l!.!s..na ‘criticism’ note ternary alternation both occur, and the conditioning factors are poorly understood 3n 'o.nu.k..!ro.ni.j.// // ‘imitable’ 3n+1 'o.no.nu.!da.)o.ni.j. ‘unintelligible’ (cf. Hale & Eagle 1980, Hayes 3nWhite'o.nu.k..!ro.ni.j./ / 1995:350). // ‘imitable’ 3n+1 'o.no.nu.!da.)o.ni.j. ‘unintelligible’ Winnebago (anapest) (s(sS)) Ternarity has been reported for a handful of other languages: Estonian (Hint 1973), possibly Finnish 3n+1 'o.no.nu.!da.)o.ni.j. ‘unintelligible’ (10) The anapest (0(01)) in Winnebago 3 non-stress languages with (Carlson Sentani (Cowan and of Winnebago (Miner 1979). Ternarity1978), has been reported for 1965) a handful other languages: EstonianTwo (Hint 1973), possibly Finnish 3n+1 (hi.(d4o.#wi)).re ‘fall in’ 3 ternary groupings arereported Gilbertese &ofWinnebago Harrison 1999) andEstonian Irabu Ryukyuan (Shimoji 2009). Ternarity has been for (Blevins a1965) handful other languages: (Hintnon-stress 1973), possibly Finnish Two languages with (Carlson 1978), Sentani (Cowan and (Miner 1979). 3n+2 (ho.(ki.#wa)).(ro.#ke) ‘swing (noun)’ 3 Two non-stress languages with (Carlson 1978), Sentani (Cowan 1965) and&Winnebago (Miner ternary groupings are Gilbertese Harrison 1999) and1979). Irabu (Shimoji 2009).Local The dominant metrical analysis of(Blevins ternary rhythm involves binary feet Ryukyuan and underparsing (Weak ternary3ngroupings are Gilbertese (Blevins & Harrison 1999) and Irabu Ryukyuan (Shimoji 2009). ‘swing (verb intr.)’ Parsing; WLP; (ho.(ki.#wa)).(ro.(ro.#ke)) Hayes 1995). WLP a parsing mechanism derivational theory(Weak (WLP-DT) The dominant metrical analysis of as ternary rhythm involves in binary feet andmetrical underparsing Local isThe well-constrained (by 1995). virtue of locality) and typologically it hastheory been(Weak shown that dominant analysis of ternary rhythm involvessuccessful, binary feethowever and metrical underparsing Local Parsing; WLP;metrical Hayes WLP as a parsing mechanism in derivational (WLP-DT) [8]WLP; feet as contexts for segmental (cf. Kenstowicz 1993, Vaysman 2008, Davis 2009, WLP analyses couched in Optimality suffer from severe shortcomings, to two Parsing; Hayes WLP asTheory a phonology parsing mechanism in derivational metrical theory (WLP-DT) is well-constrained (by1995). virtue of locality) and (WLP-OT) typologically successful, however it has been due shown that and many more) constraint types:couched Gradient and Rhythmic Licensing. Asfrom we will explain, these problems is well-constrained (by virtue of locality) and typologically successful, however it has been shown that WLP analyses inAlignment Optimality Theory (WLP-OT) suffer severe shortcomings, due to can two be grouped under two headings: theoretical (non-locality) and typological anddefined under-generation). - couched Davis & Alignment Cho (2003) distribution aspiration in English can be asdue foot-initial WLP analyses in Optimality Theory (WLP-OT) suffer from shortcomings, to two 4 ofLicensing. constraint types: Gradient and Rhythmic As we severe will(over explain, these problems can o(t áto)), (Mèdi)(t er(ránne))an, if a foot-initial adjunct postulated: (p and constraint Alignment and isRhythmic Licensing. As we will(over explain, problems can be groupedtypes: underGradient two headings: theoretical (non-locality) typological andthese under-generation). h h h (T àta)(ma(góuchi)) be grouped under two headings: theoretical (non-locality) and typological (over and under-generation). 1 h - Onset in the adjunct? athómathon, authómatha, octophus 1 1 6 shown (57),arewhere wepreferred provide the tonal patterns two arise wordsonly withtoheavy These ternaryinfeet overall to binary feet; theoflatter satisfysyllables. exhaustivity andwords avoid have similar length (both trisyllabic) andsupporting stress occurs exactlybased the same syllables (i.e. the first unary feet (46). Here we are provide evidence thison proposal on the distribution of tones. and differthe in tonal their patterns tonal melodies: (57a) syllable bears a reports low tone, Thethird). data inStill, (56) they illustrates in wordsinwith all the lightsecond syllables. Leer (1985c) that whereas thecan second syllable (57b)different does not. syllables exhibit one ofinthree tonal patterns: they can bear a high tone (H), a low tone (L) or, under specific circumstances, do not words receive a particular tone; pitch of these syllables depends (57) Tone patterns in Chugach Alutiiq light andPortuguese heavythe syllables Kenstowicz & Sandalo (2014:with in Brazilian intensity/duration measures of on tones neighboring (Leer positions: 1985c: 164). Chugach tone is not lexically various stress tonic > pretonic posttonic medial > final: a. of !an. ci.vowels qu!a insyllables b. Importantly, ta!a. ta. > !qa specified, but! its !(s(Ss))s distribution is determined exclusively by metrical structure (Leer 1985c, Hewitt ! ! ! HL H H ¡H L falls on adjunct Martinez-Paricio (2014): Chugach-Alutiq pitch-accents; 1991, Rice 1992, Martínez-Paricio 2013). ‘my father’ ‘I’ll go out’ (56) Tone patterns in Chugach Alutiiq words with all light syllables A strictly stress-based account of the distribution of tones in Chugach fails to capture the tonal ! a. ta.!"qu. ma.words lu. "niwith heavy syllables are b. pi.!"su. qu. ta. "qu. !ni the stress-based (56a-d). However, intosyllables, consideration, differences betweenwhen these two forms, since stress falls on taken the same yet their pitch patterns ! ! ! ! ! ! ! account proves inadequate, being unable to predict the presence or absence of Llowvs.tones. is are different. However, inH (57a) (57b) This can be H Lthe tonal H difference between unstressed syllables H L shown in (57), where we provide tonal patterns of two words heavy syllables. These words ‘If hewith is going to hunt’ ‘apparently getting done’ straightforwardly captured withinthe a model that allows reference to(refl.) recursive metrical structure. In have length (both areChugach trisyllabic) andquantity-sensitive stress occurs on exactly the reader same syllables (i.e. first thesimilar recursion-based analysis of Chugach stress, the is referred to the Martínezparticular, — and possibly other c.we propose a. "ku. ta.that "mek d. languages a."ta. ka as well (see §4.3)— exploits a and third).(2013), Still, they differ their melodies: (57a) the syllable a dependent low tone, Paricio which builds heavily on Leer (1985), Rice (1992) and (1993). is important !two !inof ! second !of aKager distinction between types foottonal dependents: (i) in the dependent FtMin andbears (ii)What the H ¡ H H L whereas second syllable in is(57b) does not. a low thethepresent discussion thatin (i)Chugach Chugach feettone are only moraic andonto iambic and (ii) heavy syllables offor a FtNon-min. More specifically, docks an unstressed syllable that ‘kind of food’ (abl sg) ‘my father’ 15 an of their own. These assumptions explain to why forms with the same is constitute directly byfoot a! FtNon-min, whereas no two specific tone is assigned immediate dependents ! Tone ! dominated ! iambic ! !!!! (57) patterns in Chugach Alutiiq words with light and heavy syllables can beof seen from and (56),illustrated stressed syllables are always high,of and somelike of them H number syllables pattern, but in different number morae [ta!a.ta.!qa] ‘my father’ (59a) ofAs FtMin. analysis below (58) and §3 are thatup-stepped forms with(¡H). light a. This !an. ci. qu!ais stress b.(59). Remember ta!a. ta. !qafrom is up-stepped whenfeet it isin preceded by another andand there is nosyllable intervening low the two syllables contain 3n+2 (58a), 3n (3b,H 3d) 3n+1 forms, asbetween long as the latterhighs do ! IL!‘I’ll !go out’ ! leading ! to differences and [!an.ci.qu!a] (59b), display differences in footing, in their tones. H L of H high tones to stressed syllables (i.e. footHheads) ¡His (56c). The an attraction common in mixed not contain even number of syllables (cf. 58c). Note that this analysis correctly predicts thatprosodic in the ‘my father’ ‘I’ll go out’ As illustrated in (59a), the form [ta!a.ta.!qa] contains an initial heavy syllable, which projects its own systemsofwith tonenoand 1987;(58c). Bickmore 1995; de Lacy 2002, 2006). Likewise, absence IL feet, lowstress tones(e.g. will Goldsmith occur in a word up-stepping of afoot. Haccount when by another (e.g. H¡H) common in the literature of minimal bimoraic Sincepreceded thethe second and thirdH light, isthey are into another A the strictly stress-based of distribution ofsyllables tonesHH" inare Chugach fails to grouped capture the tonal (58) Forms with light syllables tone and intonation (Goldsmith 1976; Pierrehumbert 1980; 2002; 2004,unparsed etc.) and bimoraic foot. Thethese construction of asince ternary footfalls would have instead leftGussenhoven the yet finaltheir syllable or differences between two forms, stress on the Yip same syllables, pitch patterns a. ((ta. !qu)FtMin. ma)FtNon-min (lu. !ni)FtMin be easilyHowever, captured by atonal simple rule or via constraint interaction. Whatin is(57a) puzzling in Chugach arecan the difference between unstressed syllables vs. (57b) can be is a different. degenerate foot, ! but none ! of these options ! are allowed in Chugach (Leer 1985c). Next, [!an.ci.qu!a] the distribution of while some H unstressed aretoassigned a Lmetrical (e.g. thestructure. third syllable straightforwardly captured a model that allowssyllables reference recursive In H low tones: Lwithin (59b) contains two heavy syllables (the first and third), each projecting a bimoraic foot. To avoid in 56a),b.other unstressed syllables do receive a other particular tone, their pitch an interpolation particular, we propose that. qu) Chugach — not and!qu) possibly languages as well (seebeing §4.3)— exploits a . ni) FtNon-min. ((ta. FtMin FtNon-min degenerate ((pi."!su) feet andFtMin non-exhaustivity, the third mora is adjoined to the preceding foot, resulting in an between neighboring the dependents: fourth!syllable in 56a,b). If one considers thethe data in (56), a distinction between !twotones types!(e.g. of foot (i)!the dependent of only a FtMin and (ii) dependent IL ternary foot. HOnce their metrical structure is considered, we can understand why these forms L H L non-structural stress-based explanation for the distribution of tones could be proposed. Namely, of a FtNon-min. More specifically, in Chugach a low tone only docks onto an unstressed syllable that it displayc. different tonal. patterns: [(ta!aH)(ta!qa¡H)] (63a) does not present any instance of recursion and, (a. !ku) (ta. tone !mek)docks FtMin FtMin onto every post-stress syllable that is not immediately followed be dominated argued that a low is could directly by a FtNon-min, whereas no specific tone is assigned to immediate dependents ! ! hence, no low tone approach occurs; inwould contrast, inin[((!an )ciL)(qu!a )]distributions (63b), anfrom ILinfoot is aligned with the Hand HRemember a high tone. This derive the words with light syllables ofby FtMin. This analysis is illustrated below (58)correct (59). §3 that forms with lightleft H ¡H !tonal ! edge of the((a. prosodic and,(58a), consequently, the and dependent of the non-minimal foot syllables IL 3n+2 3n (3b, 3d) 3n+1 syllable forms, as long as surfaces the latterwith do a d.contain !ta)feetword .inka) FtMin FtNon-min tone.an even notlow contain ! number!of syllables (cf. 58c). Note 27 that this analysis correctly predicts that in the H L ! !!!!!!!!!!!!!!!! absence of IL feet, no low tones will occur in a word (58c). (59) Forms with heavy syllables Heavy syllables " light in Chugach, those containing a diphthong or a long vowel, and a CVC syllable in (58) Forms with a. (ta !a) (ta. syllables !qa) b. ((!a n) ci) (qu !a) word-initial position" (µ !qu) µ) (µalways µ) attract stress and hence, slightly ((µ alter µ) µ)the ( µbasic µ) footing. For details on a. ((ta. FtMin. ma)FtNon-min (lu. !ni)FtMin ! ! ! ! ! ! ! ! 28 H ¡H H L H H L H of ternary feet could propose an alternative analysis based on WLP, in which the second Detractors b. ((pi."!su) FtMin. qu)FtNon-min. ((ta. !qu)FtMin. ni)FtNon-min ! ! would! then only dock onto unfooted syllables (e.g. Hayes Low tones syllable in (59b) !is left unparsed. H L H L 1995:345). However, as Hayes (1995:343) acknowledges, this proposal fails to explain why a form 7 c. (a. !ku)FtMin. (ta. !mek)FtMin like (59b) favors a parsing [(!an) ci (qu!a)] over [(!an)(ci.qu!a)], given that the uneven iamb in the latter ! ! H ! form is less marked from a¡Htypological perspective. !The recursion-based account is preferable to a Davis, Stuart & Mi-Hui Cho. (2003). The distribution of aspirated stops and/h/in American English and Korean: an alignment approach with typological implications. Linguistics 41. 607–652. Kager, René (2012). Stress in windows: language typology and factorial typology. Lingua 122. 1454–1493. Martinez-Paricio, Violetta and Rene Kager. 2013. Non-intervention constraints and the binary-toternary rhythmic continuum. Utrech U ms. Stanton, Juliet. 2014. Learnability shapes typology: the case of the midpoint pathology. MIT ms. 8 MIT OpenCourseWare http://ocw.mit.edu 24.961 Introduction to Phonology Fall 2014 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.