prince- relating to the grid 1983

8/13/2019 Prince- Relating to the Grid 1983

1/83

Relating to the GridAuthor(s): Alan S. PrinceSource: Linguistic Inquiry, Vol. 14, No. 1 (Winter, 1983), pp. 19-100Published by: The MIT PressStable URL: http://www.jstor.org/stable/4178311

Accessed: 27/11/2010 06:07

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at

http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you

may use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at

http://www.jstor.org/action/showPublisher?publisherCode=mitpress.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed

page of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

The MIT Pressis collaborating with JSTOR to digitize, preserve and extend access toLinguistic Inquiry.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=mitpresshttp://www.jstor.org/stable/4178311?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/action/showPublisher?publisherCode=mitpresshttp://www.jstor.org/action/showPublisher?publisherCode=mitpresshttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/4178311?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=mitpress


2/83

Alan S. Prince Relatingto the Grid

1. Introduction1.1. The ArgumentMetrical theory, as originallyformulated,employs two distinct hierarchical tructures:the slw relational tree and the metricalgrid. Relative prominenceis representedab-stractlyas a relation between constituentsin the slw trees. (I call it "4abstract" ecausethe slw relationship s not interpreted.)Mappingsuch trees terminalby terminal to ametricalgrid provides the basis for a temporal-rhythmic nterpretation.We can thinkof metricaltheory as giving a two-stage mappingbetween surface structures and thegrid: first, a translation nto (binary-branching)lw trees; second, an interpretationofthe slw relationsthus derivedin terms of alignmentwith the grid.

Tb Ps/w(1) Surface Structure I slw Trees - i GridAs the theory has developed, almost all of the researchhas concentratedon Tbandthe gridhas receded into oblivion. For example, Selkirkhas enrichedTb to includetheassignmentof prosodiccategories (foot, word, phrase, etc.) to the nodes in phonologicaltrees (Selkirk (1980)).Many theoristshave sought in constraintson tree form and treelabeling an explanationfor the character of lexical stress patternsin the world's lan-guages. (See, for example, Halle andVergnaud 1978),McCarthy 1979a), Hayes (1980;1981), and the referencestherein.)One mightreasonablysurmisethat the grid,if it evenexists, lies outside linguistic theory; that it is a matterof phonetic realizationand nota properly linguisticlevel at all.In this article, I will pursue the opposite tack. I will show that surface structure(words and phrases) should be relateddirectly to the grid, without the intervention ofa level where calculationswith s andwtakeplaceon trees.Theessentialsof thealignmentare to be accomplishedby a single, one-parameter ule: strengthen he leftmost (right-

This is a revisedversion of a paperexpanded roma talk given in April, 1981, o the TrilateralConferenceon FormalPhonology,held at the University of Texas at Austin and fundedby Sloan Foundationgrantstothe MassachusettsInstitute of Technology, the Universityof Massachusetts,andthe Universityof Texas. Iwould like to thank the participants n that conference (most especially YasuakiAbe, Edit Doron, MorrisHalle,RobertHarms,PaulKiparsky,JohnMcCarthy,Bill Poser, and Lisa Selkirk),as well as MarkLiberman,GennaroChierchia, Jane Grimshaw, and Mats Rooth, for valuable comments and discussion. Thanks toGrimshaw, Halle, McCarthy,and Liberman,and to Ray Jackendoffand an anonymousLI reviewer forcomments that helped shapethe revision.Specialthanksto Jay Keyser and Jerry Allen, who make thingsalot easier. The work reportedhere was supported n part by NSF GrantBNS 77-05682.Linguistic Inquiry, Volume 14, Number 1, Winter 19830024-3892/83/010019-82 $02.50/0?1983 by The Massachusetts Institute of Technology 19


3/83

20 ALAN S. PRINCEmost) element in a domain(= word, phrase).This will be supplementedby a "rhythmrule" that operates locally on the grid to rearrangecertain awkward or disfavoredconfigurations.Where no independentlydefinabledomainsarerelevant,as inside a wordor stem, alignmentwith a rhythmicallyoptimalgridwill be arguedto be the principaldeterminantof stress pattern. On the negative side, then, the argumentwill show thatmuch of the apparatus of metrical theory is inessential to its fundamentalgoals-forexample, binary branchingtrees, slw labeling rules, branchingnessconditions. Morepositively, a full theory of stress patterns will emerge, significantlysimplerthan itscurrentrivals, yet still well within the thematicpremises of the hierarchicalprograminitiatedby Liberman.1.2. The Grid: A Heuristic IntroductionThe metricalgrid comes out of the descriptionof musicalrhythm(cf. Liberman 1975),Jackendoff and Lerdahl (1981; 1982)). Imagine a sequence of even pulses:x x x x x x x x x x.... A time signature,such as 2/4, imposes a kind of implicitmetricon the pulse train,distinguishing ertainpulses or positionsas intrinsically tronger hanothers.

(2) 2x x x xx x x x x x x x ...

The new strengthdistinctionadds a level to the grid. The stronger gridpositions arethose that have entries at the higher level. Furtherdifferentiation ccurs when the beatitself is split into subunits.It is a fact of musicallife thatwhen a beat (or subbeat-anygrid position) is divided in two, the first half is felt to be naturallystrongerthan thesecond half.

(3)a. x xx x x xx x x x x x x xb- IJJ J;l=l Fxx xx x x xx x x x x x x x

The typical 2/4 pattern-a strongerfirst and a weaker second beat-is represented nthe cited gridsas a relationbetween the highestandnext-highest evels. Examples(3a,b)show finer detail in the medial strata. Notice that the absolute heightof a gridcolumnhas no meaning;the layeringof the gridexpresses a network of relations,The grid can also be thoughtof as a "hierarchyof intersecting periodicities" (to


4/83

RELATING TO THE GRID 21use Liberman'splangent phrase). Each level then representsa certainperiod, or rateof repetition, the frequency diminishingas altitudeincreases. In example (3b), level 1elements occur 8 times per measure, level 2 elements 4 times, level 3 elements twice,and top-level elements just once per measure, marking he strongfirst downbeat. Thestrengthof a grid position is determinedby the number of periodicitiesthat coincidethere. In the musical examples, the frequency goes down by half for each transitiontoa higher level; this reflects a binary subdivisionof measure and beat. Nothing in theideaof thegriddemandsstrictbinarity,of course, and other ratios of musicalsubdivisionmay well exist: an empiricalquestion.Inits linguistic ncarnation, hegrid s responsiveto the relativestrengthof syllables,words, phrases, etc., as they are disposed by the rules and freedoms of the language.Consequently, it will not typically assume the immaculatelyalternating,evenly sub-dividedform that is felt behind, for example, 2/4 time.

(4) xx xx x xx x x x x xJimsaw her in the park.

The linguistic grid, however, does aspire to the state of music, and this rhythmicityprovides a fundamentalmotivation for the construct. When infelicities in grid formappear n the normalcourse of linguistic concatenation, t is often the case that varioussteps are taken to remedythem. A clearexampleis the RhythmRule of English,whichreadjustscertain otherwiseexpected patternsof prominencewhen they would result ina nonalternating r "clashing" grid.(5) a. x b. xx x x x

fourteen womenc. xx xx x x xfourteen + women #A ourteenwomend. xx xx x x x

= fourteen womenThe grid of (5c), obtained by merely uxtaposingthe words and supplying he final wordwith unmarkedphrase stress, contains a clash, a too-greatproximityof elements at thesame level. In this case Englishallows a readjustment, epresented n (5d).The explicit hierarchization f prominence n the grid allows a directaccount of the


5/83

22 ALAN S. PRINCEnotion "stress clash" in terms of level structureand proximityof gridelements. Moregenerally, the notion of eurhythmicity or preferredgridconfiguration)will be found toplay a central role in determiningpatterns of prominence n both phrases and words.

1.3. Projecting Grids from Metrical TreesIn Libermanand Prince (1977) two methods of interpretingprominencefromslw treesare discussed, but only one is recommended.Since the trees contain (in one form oranother)all the information hat is generated by the Stress SubordinationConventionof Chomsky and Halle (1968; hereafter, SPE), it is possible to extract it and derive aprominence pattern that exactly recapitulatesthe SPE n-stress numbering.To do thisrequires a tree-measuring alculationof the followingsort:(6) SPE Numbering

For any terminal node a, determine the first w that dominatesa. Count thenumber of nodes that dominate this w. Add 1. This is the SPE stress numberof a.Suppose terminal node a is the main-stress of the phrase. Then no ws dominate it.Adding 1 to this 0 gives 1: a is the 1-stress. To see why the techniqueworks for theother stresses, observe that each node that dominatesthe-first-w-above-a orrespondsto an SPE cycle on which a is not the primary stress: that is, a cycle on which a isdemotedaccordingto the Stress SubordinationConvention.Addingup these demotionscorrectly will give the SPE ranking.

Rule (6) is more elegantlyformalized n Carlson(1978)and in Halle and Vergnaud(1978). These authors assign a stress numberto every node in the tree, not just theterminals.Elegance aside, rule (6) makes clear the rather amazing power of a cyclingStress SubordinationConventionto calculate subtlearithmeticdetails of tree structure.Is there another linguistic rule that distinguishes degree 4 depth of embedding fromdegree 5?There is nothing inherent n the relationalslw tree thatwould lead to the particularrankorderingof terminalsentailed by rule (6). To impose SPE Numberingon metricaltheory involves an auxiliary hypothesis of considerablecomplexity and indeed-fromthe metricalpoint of view-arbitrariness. The relationalrepresentation ays simply thatat a given level one subconstituent s stronger han the other.How then arewe to interpret he dictum"s is stronger hanw"? Given any metrical(sub-)tree,we can find its strongest terminalelement-its head-by the following ar-gument. We start at the root and examine its two daughters:surely the s-sister mustdominatea terminal hat is stronger in terms of the grid)than anything n w (what woulds mean if this were not true?). Therefore,we must directour attentionto the s-daughterof the root. If it dominates a terminal,we are done: it is the head. If not, we can simplyrepeat the argument: or surely this s's own s-daughtermust contain somethingstrongerthan anythingin its w-daughter. f that s-daughter s terminal, we are done. If not, wecontinue, repeatingthe argumentuntil there are no moredaughters o decide between.


6/83

RELATING TO THE GRID 23Inthis fashion,we canpursuean unbrokenchainof ss down from the root of any subtreeto arriveunambiguouslyat its head.This argument s canonizedas the Relative Prominence Projection Rule (Liberman(1975),Libermanand Prince (1977, 316)).

(7) Relative Prominence Projection RuleFor any pair of sisters {s,w}, s must contain a node that holds a grid positionstrongerthanany held by terminalsof w.Equivalently (andmore directly),we can say:For any pair of sisters{s,w}, H(s) > H(w),whereH(N) = the strongestelementin N, the head of N.

To see how the RPPR works out for some typicalexamples, considerthe tree-gridassociations of (8) and (9).(8) R (9) R

I s w sl \

w w w s a b c~~I~I xa b c d x xx x x x xx x x x

In (8), the element d is the head of R. Appropriately, t holds the strongestposition.Going up the ladder of ss, we see that the RPPRis met at every level; therefore, (8)representsa satisfactorymatch.In (9), c is H(R), headof the whole tree, so by theRPPRwe have c > a,b,d. Becauseab is a constituent, a furtherrelation is induced: a > b. The grid of (9) conforms tothese restrictions, so it is licensed by the RPPR.Considernow the grids of (10) as candidatesfor matchingup to the tree of (8).(10) a. b. x c. d. xx x x x xxx x xx x x x xxxxxxx xxxx xxxx xxxxabcd abcd abcd abcd

All of these grids respect the constraint d > a,b,c, which is the only information hatthe RPPRobtainsfrom tree (8). This pluralityof interpretationsmakes it clear that theRPPRestablishesonly a partialorderingamongterminals.Inparticular, he RPPRneverrelates terminalsthat are immediatelydominatedby w (and,conversely, always relatesterminals mmediatelydominatedby s).


7/83

24 ALAN S. PRINCEOf course, not every possibility admittedby the RPPR is commonlyrealized-oreven realized at all-in the actualpronunciationof forms like (8). But this need not bea disastrous consequence. In Liberman and Prince (1977, 323) it is suggested that a"flattened out" structurelike that of grid (8) corresponds more closely to speakers'

actual perceptionsthan the highlyarticulatedresult of SPE Numbering.Grid(8) is distinguishedby being minimal n the obvious way: it has less structurethan any other interpretationof the tree [w w w s]. The RPPRcan be supplementedwith a naturalprinciple of minimality o pick out (8) as fundamental.Divergences fromthe "flattest" interpretationwill arise fromsubtle variationsof emphasisconsistent withoverall slw structure (Pierrehumbert 1980, 37)), as well as from the pressures ofeurhythmicityand phrasaldemarcation. For example, in a [w w w s] tree like (8), thefirst w is often felt to be more strongly stressed than the others. This fact might berecorded as a supplementaryprinciple of prosodic realization, based on constituentstructureand linearorder,distinct from the primary nterpretation f the stress pattern.It is not necessary to retreat to SPE Numbering, which arguably exceeds intuitivejudgments of relative stress in its overspecification.A different,and perhaps irmer, ineof evidence in favor of the RPPR s foundin Pierrehumbert1980).For accurateacousticpredictions,her theory of intonationpatternsrequires the kind of stress values allowedby the RPPR, and it goes distinctly astrayif SPE Numbering s adheredto.Finally, it may be worth noting that the RPPRis the weakest theory of tree inter-pretationconsistent with the intuitive sense of "s" and "w". Were it any weaker, someslw relationswould go unenforced.The theory could be enrichedin a numberof ways(for example, as in SPE Numbering)by takingvarious aspects of tree geometry (andarithmetic) nto account. Any enrichmentwould necessarily preserve the orderings-of-prominencerequiredby the RPPR; t could only add moreprominencerelations to thisbasic set, neither contradictingnordiminishingRPPRconstraints.For these conceptualreasons alone, the RPPR has a strong claim on our attention.2. Direct Relatability2.1. The End RuleLet us assume, then, that the RPPRgives the basis for an accurate account of syllabicstress patterns. With this in mind, let us reconsider the descriptive problemposed byphenomenathat fall under the Nuclear Stress Rule of SPE. Consider the treatmentofa right-branchingree:

(11) R

a b c dxx x x x


8/83

RELATING TO THE GRID 25The goal is to achieve the association presented in (11). In standardmetrical theory,this would be attainedby labeling the tree according o the rule "All sisters stand in therelation [w s]" andthen interpretinghe resultantwls tree in the light of the RPPR. Grid(11) is the minimalgrid consistent with a [w s] labelingof tree (11).

Because the grid carriesover so littleof the information n the tree, there is another,more direct route to the match-up. Instead of assigning a metricalpotency to everynode, we can deal just with terminalsaccording to a rule like this: "In any constituentC, the rightmost terminal is strongest." In tree (11), the constituents are [cd], [bcd],[abcd]. Clearly, strengtheningd alone, as in grid (11), will satisfy the rule.A moment'sthoughtwill bringthe conviction thatthe stated rulewill in fact capturethe effect of [w s] labeling on any tree whatever, no matter how complicatedor erraticits branchingpatternmay be. Inspectionof (12) may be useful.(12) xx xx x xx x x x xx x x x xx x xa b c d e f g h

RFormalproof of the equivalence between uniform[w s] labelingunder the RPPR and"Rightmost terminal is strongest in every constituent" can be accomplished by aninduction on the numberof nodes in a tree, using the RPPRdefinitionof "s is strongerthan w", namely, H(s) > H(w). Notice that under this definition, for any constituent Clabeled [w s] throughout,H(C) must be the rightmost erminalof C.

It should be equally clear that uniform [s w] labeling is equivalent to the gridalignmentcondition"Leftmost terminal s strongest n every constituent".Now becauseuniform abelingplays such a centralrole in prosodic description, a tantalizingspecu-lationpresents itself: perhapsthe theory of stresspatternsought to involve only a directrelationbetween surface structuresand grids, withoutthe interventionof tree-labelingandtree-interpreting perations.Perhaps, ndeed,theessential burdenof assigningstressto a constituent structurecan be borne entirely by the End Rule (13).(13) EndRule

In a constituent C, the leftmost/rightmost erminalin C is associated to astrongergrid position thanany other terminal n C.


9/83

26 ALAN S. PRINCE2.2. ObjectionsCounteredWe have seen thatlabelingof nonterminalss not necessaryto achievea straightforwardwell-formednessconditionrelating urfacestructure o grid, at leastin thecase of uniformlabeling-[w s] or [s w] throughout.Are slw trees then superannuated?To answer, wemust inquire into the uses that the richness of tree structure has been put to. Theresearchers of the last few years have dealt with numerous and diverse phenomena,obtainingresults that appearto depend strongly on the characterof tree form. Specif-ically, three majorcategories of formal operationscan be identifiedthatwould seem toraise serious problems for a grid-onlytheory.(I) Last Foot, Last Word ype of rule. The rule[w s] appliedat a certain evel willpromote the final metrical unit at the next lower level: at word level, it makes the lastfoot strongest;applied phrasally, it makes the last word strongest;etc. In general, ofcourse, this will not make the last syllable strongest:considerexampleslike [Ala][bama]or I saw Mary. Yet syllables are the ultimateterminals.Here tree theorymakescrucialuse of the hierarchyof prosodicunits. How is the End Rule to apply?(II) The Lexical CategoryProminence Rule (LCPR). "Right node (left node) isstrongiff it branches" appeals crucially to aspects of tree form that are not obviouslyrepresentedeither in the terminalstring of syllables or in the metrical grid. No simplestatement like the End Rule is availableto translatethe possibly very complex effectsof the LCPR into a rule of gridmatching.Yet the LCPR,in left-handedandright-handedform, has been invoked in a very large numberof respectableanalyses.(III) Operations on s and w. The RhythmRule, which switches slw sisters, isfound, with some variationof detail, in manylanguages.Both its context of applicationand the change it performshave been plausiblyargued to dependon characteristicsoftree form. Furthermore, he RhythmRule appliesat all levels of the metricalhierarchy,thus giving evidence for those levels and for the proprietyof treatingthem as formallysimilar.Let us examine the problems in turn.(I) Last Foot, Last Word. Phenomenaof this sort clearlyestablish the need forhierarchy in stress representations. The grid itself is a hierarchyof levels, and this issufficient.Consider the last foot case.

(14) 2. x x x1. x x xx x xxxpolyphiloprogenitive

The grid of (14) represents the patternof stressed and unstressed syllables. To projectthe location of main word-stress,we apply the End Rule, right-hand ersion;however,we apply it not to the final syllable, but instead to the endmostentry at level 2.(15) 3. (2. x x x1. x x xx x xxx

polyphiloprogenitive


10/83

RELATING TO THE GRID 27The entry over -gen- at level 2 is (level-)adjacent o the end of the word constituent,because no other level 2 entry intervenesbetween it and word-end. Since it stands atthe end, it is accessible to promotionby rule.From a gridperspective, then, the EndRule must be formulated o express a relationbetween the strongestposition and the entries at a certain level n, within a given con-stituent. The following states the End Rule as a well-formednesscondition:

(16) End RuleLet p be the strongest grid position in a constituent C. There is a level(n + 1) such that (i) p is the only position in C with representationat level(n + 1), and (ii) otherpositions in C have representationat level n. The EndRule says: The entry for p at level n is the rightmost/leftmost ntry at leveln for C.

If we think in processualtermsof buildinga gridfromthe bottomup, thenthe EndRulewill apply to the highestlevel thus farconstructed.If the leftmost/rightmost ntryat thehighest level withinC is not alreadystrongest,the End Rule licenses the builderto addanovertoppingentryabove it, creatinga new level andpromoting he rightmost/leftmostentryto greatest strength.Conceived this way, the EndRule (right-hand ersion)wouldapply to (14) to produce (15). Conceived as a well-formednesscondition,the End Rulelegitimatesthe relation in (15) between entries at level 2 (= "n" of (16)) and level 3(= "n + 1').The End Rule, operatingon the hierarchyof levels explicitly recognized n the grid,is clearly equal to the task of findingthe last or first "foot", which was previouslyassigned to the labelingof constituentsin the metricaltree.What becomes of the "prosodic categories"-syllable, foot, word, phrase? It isplausible to suggest that these (or something ike them) shouldbe used to name levelsin the grid. Fully labeled, example (15) would look like this:

(17) Wd: x1: x x xaT: x x xx x xx x

polyphiloprogenitiveIf, as seems likely, thereis a furtherdifferentiation t level X,due to rhythmicprinciples,then prosodic categories should label contiguousbands, notjust single levels.

(18) Wd: xE fx xx x xa: x x xx x xxxpolyphiloprogenitive

The EndRulenow must function to relateprosodic evels. Wemightconsiderrestrictingit to this function as in (19):


11/83

28 ALAN S. PRINCE(19) End Rule

In a constituentC, the leftmost/rightmost ntry at level x correspondsto anentry at level 1, where a is the next level upfromot n the prosodichierarchyand a is the prosodiccategorythat syntacticcategoryC is related to.If C is a word, then 3 will be Wd;if C is a phrase, C will be Phr;etc. However, it maybe that the EndRule can applywithina prosodic evel to differentiateamongthe stressesthere, as in example (18). Something like the formulation(16) ought perhaps to beretained.Finally, it shouldbe noted that most of these level labels are not really primitivesof grid theory, but are projectedfrom syntactic (or phonosyntactic)structure. We aregiven independentdefinitionsof syllable (or mora),word, phrase;these determinethegrid strata. Only E belongs entirely to prosody, thoughit mightbe thoughtof as gridstructurebetween syllable and Wd.(II) LCPR. The recent evolution of metricaltheoryhas rendered he LCPRvir-tually superfluous.Considera structure ike (20).

(20) R IWd/ s Wd

w w s .........\ A AS w S W S wLabeling of the entire tree can be accomplishedby the LCPR. Withthe advent of the"foot-level"/"word-level" distinction, however, it became clear that labeling rulesshould hold inside a level, not across levels governingthe whole tree. Thus, tree (20)would be described as havingfeet [s w], but word-level [w s]. One motivationfor thischange of perspective is the observation that the LCPR never applies within a footcrucially-that is, in a way distinct from [w s] or [s w]. For example, if the feet of (20)were of the form [a [b c]], the LCPRwould predict [w [s w]]. But no feet of this formhave ever been discovered. With the elegant LCPR account of whole trees like (20)abandoned,we must search inside levels above "foot" for evidence of its operation.

There is, however, another device ready to challenge the LCPR and take over itsresponsibilities: extrametricality. Bruce Hayes has ably championed the cause ofextrametricalityand convincinglydemonstrated ts descriptiveand indeed explanatoryvalue. Hayes's idea is (roughly) hat a phonologicalconstituent-most clearly, segment,syllable,or morpheme-can be declaredextrametricalf it occurs at the edge (beginning,end) of a domain;an extrametrical lement will be ignored n the accountingproceduresthat stress rulesdependupon. If in a language t happensthatword-finalconsonants areextrametrical,a final syllable CVC, ordinarilyheavy, will count as equivalentto CV,and therefore light. If final syllables are extrametrical,and words are to be organizedinto binary[s w] feet, movingfrom the end in, then in a long enoughword the last footwill be ternary,essentially [s w w], because the finalsyllable is not countedin reckoning


12/83

RELATING TO THE GRID 29the extent of the word-finalfoot. (Extrametricalsyllables end up adjoined in weakposition.)Let us advance one step beyond Hayes's view of the role of extrametricalitywiththe observation that the significanteffect of the LCPR is also to be found at the edgeof a domain. Considera structure ike (21a), typical of those posited by tree theoriststo govern the placement of word-stress. Labeled [w s], it appearsas (21b);labeled bythe LCPR, as (21c).

(21) a. b.5

w w w 5u v y z u v y zC. d.

S~~~

w w sw w w 5u v y z u v y (z)

The difference between (21b) and (21c) lies in the treatment of the final element z: in(21b)it is strong; n (21c)weak, makingy strong.Clearly he same effect canbe achievedby rulingz extrametrical,as in (d). Moreover, the notion of extrametricalityn no waydepends on tree structure or its utility:applicationof the End Rule to the constituentsin u v y z will produce the same effects as [w s]-labelingunder the same conditions ofextrametricality.(22) a. b. x c. x

x x xx x x x x x x x (x)[u [v [y z]]] u v y z uvy zThere remains an importantconceptual difference between the LCPR and theextrametricalitydescriptions: where extrametricality s relevant only to the edges ofa domain, the LCPRapplies to the entiretree and should in principlemake a numberofpredictions about the domain-internalpattern of secondary stress. Unfortunately, itappearsthat this difference is doomed to remain in the realmof the conceptual. Firstof all, the use of trivial,uniformly eft-orright-branchingreesin wordstressdescriptions

essentially guarantees that no subtle predictions will be forthcoming. Uniformity ofbranching ranslates nto uniformityof labeling,except at the edge, wherethe otherwise


13/83

30 ALAN S. PRINCEalways-branching ight(left) node touches down and ceases to branch,throwingprom-inence back (forward)onto its sister. Furthermore, econdarystresses inside words arestronglysusceptibleto rhythmicreshufflings,andthe force of eurhythmicitys likely tooverwhelmany contribution hat the LCPRplus branchingstructurecan make, even iftherewere sufficient structure o beginwith. Syntacticbranching, akenas the basis forphrasal stress patterns, could conceivably provide the complexities required for aninterestingLCPRpatternto emergeamongsecondarystresses, but the fact seems to bethat the LCPR never applies at phrase level. Strandedbetween foot and phrase, theLCPR is starved out by the poverties of the word level.If extrametricality s to subsume the LCPR, it must be relativizedto grid stratum.In English, for example, a word like execute wouldlook like (23a) up to the I-level; thefinal syllable is evidently not extrametrical n any absolutesense. Yet it must be extra-metricalat the I-level. so that the End Rule (right-hand ersion)does not count it.

(23) a. b. Wd: xE: x x E: x (x)U: xxx: x x xexecute executeThe more familiarcases are examples, then, of a-extrametricality,as in (24).

(24) a. b. xx x x x x x x(x)Armorica ArmoricaIn (24b), r-extrametricality f the final syllableallows the Hayesianpenultimatestressrule to apply successfully.Generalizingmildly from Hayes's practice, I suggest that the appropriatenotationfor relativized extrametricality s parenthesizationat the level where extrametricalityhas its effect, as in (23b)and (24b).If Englishcompoundstressingtrulyfalls under the LCPRgeneralization,we mustsay that the last word of each simplebinarycompoundis extrametrical: abor (union),strike (committee), [[labor(union)][strike(committee)]],[labor(union)](strike)].Com-poundsgo by the End Rule(right-hand ersion),like everythingelse in English,althoughthe effect of extrametricalitys often so great thatthe resultingstresspattern s the sameas that of the End Rule (left-handversion).

(25) a. b. c. xx x x xx (x) x (x) (x) x (x) x (x)x x x x x x x x x x xx x xlaborunion labor unionstrike laborunionstrike forceNotice that the compound rule holds true of every level of constituency within thecompound.


14/83

RELATING TO THE GRID 31A tree theory with both the LCPR and extrametricalitydiffers in one descriptiverespect from any theory-tree or grid-with extrametricalityalone. Either the LCPRor extrametricalitycan be used to derive penultimate stress. Using both, tree theorycan compute antepenultimatestress directly from a word tree: let the final syllable be

extrametrical, and let the (right-branching)word tree be labeled by the LCPR. Sche-matically, [a [b [c [d (e)]]]] is equivalentto [a [b [c d]]] via extrametricality; pplying heLCPR produces [w [w [s w]]], which emerges as [w w s w w] when the final syllableadjoins. It is not clear that this is a desirable result. First, in a theory like Hayes's, ifd and e are simply unstressed, the same effect can be achieved with extrametricalityalone by anchoringan isolated foot [s w] on c d at the "end" of the word (end minusone extrametricalsyllable);in this case, the additionaldescriptiveresource is superflu-ous. Second, if d and e are in themselves (monosyllabic) eet in a language hat has footstructure hroughout he word, the result is a completelyunheard-of orm of main-stressassignment. The LCPRand extrametricality annot coexist withoutredundancyand, itappears, empirical shortfall.Even within tree theory, then, there is scantjustification or "branchingness"con-ditions such as are encoded in the LCPR, so long as the descriptivenotions "prosodiclevel" and "extrametricality" are also part of the theory. Furthermore,since thesenotions do not dependin any crucialway upon tree structure, hey can be easily trans-plantedinto grid theory.(III) The Rhythm Rule. It is a rule of thumb of practical ontology that a thingexists to the extent that other things interactwith it, make use of it. The ubiquityof theRhythmRule could provide excellent evidence for metrical rees, because its formulationappeals to both aspects of the construct:constituencyand labeling.The version of theEnglish rule in Kiparsky (1979, 424) shows this admirably:

(26)w s w s

w s s wThe rule given in Libermanand Prince (1977)has another dimensionto it: while thestructuralchange is described in tree terms (basically, [w s] -> [s w]), the structuraldescription depends on grid configuration.The idea is that a theory of the grid, basedon principlesof rhythm,can provide explanationfor the contextualfactors that affectthe rule's likelihood of applying.

First, we need an account of linguistic rhythmin terms of which the appropriatestressconfigurationsaremarkedas "clashing",thusproducingapressurefor change.Second, weneed a specification of the circumstances n which a given languagegrantspermissionforsuch a changeto occur. (Libermanand Prince(1977, 311))The first requirementwas to be met in the grid, the second in tree structure.I would


15/83

32 ALAN S. PRINCElike to propose that both can be met equally well in the grid alone; more precisely, thatboth context and change should essentially be framed in grid terms, structuraleffectsbeing referreddirectly to syntactic constituency.Clashis a departure rom smooth alternation n the directionof a too-nearadjacencyof prominences. Grids (27a) and (27b) show perfect alternation,such as is found in theunmarkedsubdivision of musical time (recall examples (2) and (3)). Grid (27c) clashesat level 2; grid (27d), at level 3.

(27) a. b. x xx x x x x x xx x x x xx x xx x xx x xc. x 3 d. x ----x 3*x---x 2* x x x 2x x x I x x x x x I

In a perfect binary alternation,entries that are adjacent n level (n) will be separatedbyan intervening entry at level (n - 1). If two entries are adjacent,with no interveningentry one level down, they will be said to "clash". Thus, in (27c), the level 2 entriesbelong to positions that are adjacentat all levels. In (27d), the level 2 entries are ap-propriatelyseparated;at level 3, however, the entries clash, even though they are notstringwise (level 1) adjacent,because the correspondingentries at level 2 are adjacent.The claim is, then, that the RhythmRule operates to remove clashes that arise inthe course of linguistic concatenation. Example (28) displays two words with theircitation stress patterns. Example (29) shows the result of simply concatenatingthemwithnouns, assumingno readjustment note the clashes). The actual surfaceforms,withclashes removedby the Rhythm Rule, are given in (30).

(28) a. x b. xx x x xx x xx x xachromatic Dundee

(29) a. x b. xx----x x----xx x x x x x xx x xx x x x x xx

achromatic ens Dundee marmalade(30) a. x b. xx>_ ,x xI ,x xx -xI, x x \xI' x xx x xx x x x x xx

achromatic ens Dundee marmaladeMoregenerally, the propositionthatclashes are disfavored should be thought of as one


16/83

RELATING TO THE GRID 33of the well-formednessconditions (or perhaps,better-formedness onditions) that givecontent to the notionof "eurhythmicity"and have influence on variousaspects of wordand sentence phonology.A glance at the clashes of (29) and the resolutions of (30) suggests a simple gridoperationto relate them: we mightdub it Move x. An entryat a certain level-3 in thepresentcase, corresponding o the prosodicstratumWd-is movedwithin ts level awayfrom a position of clash. Where does it move to? Evidently, to the first position it canlegitimatelyoccupy. Move x is a kind of minimal readjustmentof grid configuration,and as such is a naturalcandidate o considerfor the formalmechanismbehindobservedrhythmicreadjustments.Move x is by no means a merenotationalvariantof the familiar ree operationthatinverts the strength relation between sister nodes. The Rhythm Rule is universallyconstrained rommovingthe absolute stresspeakof the phraseto whichit applies,evenwhen moving the peak is the only way to improve the rhythm.The clash of stresses ina compoundlike antfquedealer cannot be mitigated.(Contrastacntiquechair.)

(31) a. Wd: x xx--.* --x x xx x x x x xa: x x x x x x x x

antique dealer -# *antique dealerb. P: x xWd: x --*-x x xE: x x x x x xc: x x x x x x

antique chair > antique chairThis constraintfollows from the intrinsic characterof Move x. There is no way to gofromone side of the arrow in (31a) to the other by means of Move x; that is, by slidingone grid entry around within its own level, preservingwell-formednessat all times (inparticular,preservingthe requirement hat a column must have entries at every levelup to its peak). Thus, if we shouldattemptto resolve the clash in (31a) by movingthelevel-3 entry rightward, rom -tique to an-, we would leave a hole in the column over-tiquebetween levels 2 and 4.

(32) x xx--x x xx x x x x xx x x x - x x x x (ill-formed grid)Clearly,this resultgeneralizesto phrasalpeaks of allkinds. Treetheory does not providean explanation or the immovabilityof main-stress.Example(31a)has the representation[[w s][s w]]; there is no obvious reason why the initial unit [w s] should not invert toeliminatecontiguity of ss. Previous analysts of Rhythm Rule phenomenahave had to


17/83

34 ALAN S. PRINCEstipulate this constraint anguage-by-language, espite its apparentuniversality; ndeed,the ease with which it has been possible to bury it in a natural-looking nvironmentalconditionhas often effectively disguisedthe stipulatory haracterof the usual treatment.Formalizing the Rhythm Rule in terms of the level structure of the grid leads to afundamentalexplanatory advance.

Move x must also be constrainable n various ways that appearto be somewhatextrinsic to the operation the rule performs. For example, the directionof movementfalls underlanguage-particularontrol. English, as is well known, permitsonly leftwardshifting; German and Swedish are bi-directional. Sports + contest does not producesports contest, but Feld + Madrschalloes indeed come out as Fedmarschall. Finnishhas a rightward rule operating in compound nouns, reported in Hayes (1981, 122).Thus,posti + saasto#pankki gives rise to postisaistopankki 'postalsavings bank'. Ob-viously, the directionalityof the rule will respond to stress conditionsin the languageas a whole. Finnish, with overwhelmingly nitial stress both phrasallyand lexically, maynot even provide the circumstances or leftwardshift to show itself. And, as Irene Heimhas observed to me, German forms that would benefit from rightwardshift are quitecommon because of the strict initial stress rule in compounds, whereas the relevantcases in Englishare quiterare. The fact that the ruledoes not affect the occasional formlike sports contest indicates that directionalitymust be part of the rule; the backgroundsituation in the language provides at best a functional motive for various details offormulation.The action of the rule is often much more local than it is in English: see, forexample, the accounts of French in Dell (1980), Hebrew in McCarthy(1979a),Italianin Nespor and Vogel (1979), and Spanishin Solan (1981).This can be interpretedas arestrictionof the rule to the lower reaches of the prosodic hierarchy.A constraintvisiblein Englishis that stressless syllablescan nevergain (or regain)prominenceby rhythmicreadjustment:maroon + sweater cannot lead to mairoon weater.As interesting and as potentially informativeas such constraintsmay be, our at-tention must be focused on the operationMove x itself, for the chief goal of the presentexcursion is to establishthe plausibilityof a grid-basedaccountof the RhythmRule. Tothat end, let us examine certainmore complicatedcontexts of application.Four distinct types of prenominalstructuringwill be considered here, coveringthebasic rangeof possibilities.

(33) a. b. c. d.w SW

Type (a) is the ordinaryright-branchingNP, with right-handNuclearStress Rule (NSR)stress. Type (b)has a complex phrasemodifying hehead, yielding eft-branching verall,but with right-handNSR stress throughout.These types will show Move x applyingrepeatedly o a structure,sometimesfeedingitself. Type (c) hasaright-branchinghrasalmodifier,with right-handstress. Type (d) has a compoundas modifier.Types (c) and


18/83

RELATING TO THE GRID 35(d)have nonuniformityn branching, n stressing,or in both;they inhibitthe applicationof Move x in characteristicways.Type(a), ordinaryright-branchingNP. Some cases are listed in (34).

(34) a. bamboo tablesb. thirteenbambootablesc. thirteenJapanesebambootablesd. John's thirteenJapanese bambootables

Move x applies readilyto each end-stressedword, resulting n a derivation ike (35):(35) x xx x x x x x x xx x x x x x x x x x x x x xthirteenJapanesebamboo tables a thirteenJapanesebamboo tables

It mightbe thoughtthatsuch examplesdemonstrate he necessity of cyclic or directionalapplication,which would move the motivatingstress clash alonglike a density wave:(36) x x x x xx xx x x x xxxxxxx...-*xxxxxx... -->xxxxxx...-*xxxxxx...

Regrettably,no such strong conclusion can be drawn.A closer look at the relevantdatasuggests ratherthat our notion of stress clash is not strongenoughto actuallymotivateall instances of Move x. For example, in the phraseJapanese bamboo, rhythmicstressshift (Jdpanese) is obligatory, yet-as in example (35)-formal clash is not present.(37) x

x x N,x." xx x x x xJapanesebamboo

Notice the interveningentry that stands between the two main word-stresses. Underthe theory given, it should alleviate gridpressure; but it does not. Move x applies in awider rangeof environments hanwe predict.Perhaps"clash" ought to be characterizedsomewhatmorebroadly;or perhaps other conditions on eurhythmicityare having theireffect-for example, a distaste for upbeats.Cleavingto the intentionof exploringMovex itself, let us shirkthese problems.Type(b), left-branching n the modifier.Here the role of repeatedapplication,withself-feeding, is clear. Considerthe following examples. (Phrase(38a) is due to RobertJohnson; (38b)to J. Pierrehumbert.)

(38) a. thirty-twotwenty bluesb. Alewife Brook Parkwaysubway stationc. WoodrowWilson Avenue generalstored. thirteenforty MainStreet


19/83

36 ALAN S. PRINCEEach of these has three stresses (before the main-stress)under rhythmiccontrol; theorderingof prominence n thephraseappears o be:2nd/4th/3rd/lst.Consider he analysisof (38a):

(39) a. xP: x x

x x xWd: x x x x[[[thirty-two] wenty] blues] (applicationof End Rule to each phrase)

b. x x xxx *-?x x x

xxxx -* xxxxIf Move x is restricted to treating one x at a time, then derivationmust proceed as in(39b); otherwise, the process could get stuck as in (40).

(40) x xOXx xxxx xxxx x x x -> x x x x *thirty-two twenty blules

In (40) the first (and therefore only) applicationof Move x is to the topmost movableentry. Diagram (39b), in contrast, shows a course of derivation that can be variouslydescribedas left to right, bottom to top, or cyclic. Left to right we can rule out as non-universalizable.In Germancompounds,for example,withright-branching nd left-handstress, the rule will appear to move right to left; this follows without furtherstipulationfrom either cyclic or bottom-upapplication.Type (c), right-branching modifier. A characteristic inhibition of rhythmic re-adjustment s found in this structure.(41) a. one thirteenJay Streetb. Red Chinese diplomacy

c. U.S.-Chinese relationsd. Sino-Japaneseconflicte. truly antiquemacassarsf. well-maintainedgardensg. Maine-New York Railroadh. Fort Tom Paine GardenCommitteei. Hundredand ThirteenthStreet BluesThese examples are essentially of the form [a [bc]]-d'.Secondarystress appearsnaturallyon constituent a, by virtue of the expected rhythmicshift; but within [b c] the pattern


20/83

RELATING TO THE GRID 37of end-stressing s maintained,even in the face of clash. Move x operates like this:

(42) p x x xx x x x x xWd: x x x x xx x3) x1: x x x x x x x x - x x x xone thirteenJay (Street)

There may be some question whether the facts are exactly as claimed. I assumeuniversal agreement about the shift of "2-stress" to the initialunit; but perhapstherewill be doubt about the stabilityof the "3-stress" in its clashing position. After all, thedistinction between tertiary and quaternarystress is subtle. Nevertheless, it can bebroughtout clearly by attention to certain contrasts. Considerthe second wordin suchcollocations as these:(43) a. sports contest review committeeb. social insect study groupc. vanilla extract bottling company

In each case, the word occupying the second or [b c] position-that of thirteen inexamples (41a)and (42)-has a lexical stress pattern o o. Stress is already,as it were,shifted. A clear difference shouldbe felt between this patternand that of (41). A nearminimal contrast holds between "No Propane Blues" and "No Cocaine Blues"; but thismay be marredfor many speakers by the increasing currency of the pronunciationcocaine.A second instructive comparison can be made with phrases like Jay's thirteenwontons. This type (a) example ends up with a stress pattern exactly like the onepresented in the far right-handside of (42). The stress contrast with one thirteen Jay(Street) lies entirely in the word thirteen.It seems clear that stress homophonycannotbe achieved without significant oss of naturalness.What, then, inhibitsa second applicationof Move x in (42)?A firstguess mightbethat strict bottom-to-top grid processing is required.Since Move x moves only one xper application, he topmost(P-level)x on -teen mustbe removedfirst in orderto provideaccess to the Wd-level x on it, this being the only one that can move back to the syllablethir-. But, the argumentgoes, bottom-to-topapplication orbids us to descend from P-level to Wd-level; therefore, the end-stress of thirteen is protected in (42). By thisreasoning, it is actual P-level application that forestalls Wd-level application. We cantest it by constructinga case which presents no P-level clash, but which is identical to(42) at Wd-level. In such a case, the Wd-level clash should be accessible to Move x onits way up. To this end, consider such compoundsas name cartouche and dandruffshampoo. Since they have main-stress on theirfirst elements-contrast one thirteen,Red Chinese-there will be no clash between secondary and primarywhen they areattached to a following more strongly stressed item, as in (44).


21/83

38 ALAN S. PRINCE(44) a. name cartouche deciphermentcommitteeb. dandruffshampooresearchgroup

c. x xx x x xx X] x x xx x x x xxxx

dandruff hampooresearch(group)Yet, as indicatedin (44c), Move x is clearly inhibited, ust as it is in the examples of(41). We must concludethat a bottom-to-topconstraintgives no insight ntotheproblem.It is more illuminating o examine the relationbetween syntactic structureand theease of movingx. Stress clash is disclosed only at a certain evel in the tree: for example,in [[one thirteen]Jay Street], the constituent [one thirteen]has no clash; it is only at theNP level that the clash between thirteenandJay becomes visible. Each clash thus hasa natural domain associated with it, the minimal domain that includes the clashingelements. If we think of Move x as occurringon that naturaldomain,we observe a kindof syntactic boundingcondition on the rule. In a structure [A B] C], shift motivatedbyC is ordinarybetween B and A, but unnatural f it takes place entirelywithin B (or A,as we shall see below).The Bounding Condition could be formalizedas a strict cycle constrainton deri-vations that build up or manipulate he grid. Alternatively, t could be formulatedmorein the spirit of Subjacency.In (45), notice that the circled x, representing he secondarystress of the collocation, is just one level down from the peak of the motivatingmain-stress; this x moves. The boxed x, however, is two levels downfromthe peak;it is fixed(as it is in example (44)).

(45) xxx FX xx x x xone thirteenJay (Street)

A Subjacency-style account would allow Move x to operate only one level down fromthe peak of the motivatingstress. The relevant notion of "height" of the peak is definedby constituency.In (45), for example,the syllables -teen andJay peak on adjacent evels;but if the phrase is furtherembedded,Jay could acquire a few more levels (as in, forexample, I lived at one thirteen Jay Street). Such further structure, which relates toexternalelements, is clearly irrelevantto the phrase-internal djacency measure. If wethinkof the grid as being constructedcyclically in its entirety, then at any stage of thecycle thenotion "one level down fromthe motivatingpeak" would be directlyapplicable.The fundamental nsight behind these formal alternatives is that Move x dependsnot only on grid structure, but also on syntactic organization.Of course, exactly thispoint is encoded in a standard ree-theoretic ormulation uch as (46).


22/83

RELATING TO THE GRID 39(46) w w

w s s s w sDoes this indicatea superiority n the tree theory?I thinknot. Rule (46)consists of twoindependentparts:(i) the wslsw switchand(ii)the superordinate tructural ontext. Thesuperordinatews environmentspells out the BoundingCondition;the important hingto note is its status as a stipulation.The environmentof (46) could be generalizedandsimplified n various ways; the rule could be written to applyto any [, w s], or to any[w s]-s sequenceregardlessof the constituencyrelationbetweens and[w s]. Treetheoryprovides convenient means for expressing the Bounding Condition,but no particularinsight into its nature.Type (d), compound modifier.Furtherevidence concerning he natureof boundingis provided by examples like the following, patternedroughly [[a b] c]-[d (e)]:

(47) a. antiqueshop zoning boardb. Thirteen Club festivitiesc. ThirteenthStreet Bar and Grilld. Tom Paine Street Bluese. free verse club art festivalf. Hundredand ThirteenthStreet Bluesg. kangaroorider's saddleThe observation to explain is that readjustment akes place in these structureseithernot at all, or with palpable reluctanceand a sense of erroror omission.A first try at explanation might insist that the RhythmRule is not even expectedin cases of this form, because clash is absent. An alternatingpatternis surely present(Tom PacineStreet Blues), and a minimalgriddingshows the patternclearly.

(48)

a. Tom Paine Street Bluesx

P*L x xWd: x x x xb. Tom Paine Street Blues

Unfortunately,the definition of "stress clash" is not so secure that we can afford torest our case with the observationthat formal clash is absent. Consider the followingexamples, whichdisplay the sameunderlyingcontourof alternation,yet readilyundergoshift:


23/83

40 ALAN S. PRINCE(49) a. U. Mass. free verse clubb. U. Mass. Departmentof Linguisticsc. very special old portd. very fat old mene. thirteenpontoons

Example (49b) is diagramed n (50):(50)

a. U. Mass. Departmentof Linguisticsx xP:- x x x x

Wd: x x x x x x xb. U. Mass. Departmentof LinguisticsThe examples of (47)-(48) and those of (49)-(50) are not obviously distinguished nterms of stress structurealone. However, a strict-cycle interpretation f the BoundingCondition would cause them to be treatedquite differently.In (50), the first word, U.,has shared only one cycle with Mass. when the motivating quasi-clash, triggered by

Linguistics, becomes visible. In (48), by contrast, when the quasi-clash appears, theonly possible landingsite for the secondarystress (namely, the word Tom) s buriedanextracycle down; any readjustmentwouldhave to takeplace entirelywithina bypassedcycle and is thereforeproscribed.Type (d) cases appearto provide difficulties for the "Subjacency" interpretationof bounding.Notice in (48b) that the quasi-clashingstress on Paine lies but one leveldown from the highest projectionof the phrasalpeak. Beingthuslevel-subjacent,shouldit not be movable?A look at otherexamples suggestsanotherapproach o the problem,with potentially interestingconsequences. Consider the griddingof (47a):(51) p.f xl ? xWd: x x x x1: x x x x x

antique shop zoning boardHere the chief stress of the compound antiqueshop must tower above the I-level bytwo strata. The circled entry is rendered immovable, since it has no place to go. If,similarly, the correct picture of such collocations as TomPaine Street Blues is not theminimalgrid in (48b), but rather the more articulatedstructureof (52), then the sameaccount will hold for it.


24/83

RELATING TO THE GRID 41(52) P: xB: xA: x xWd: x x x xTom Paine StreetBlues

xGrid(52) is nonminimal n the sense that the configurationx x x is an adequate repre-sentation, according to the Relative ProminenceProjectionRule (7), of the pattern[[s w s] w] that would be assigned to Tom Paine Street by various rules of English. (Iuse metrical tree notation as a convenient lingua franca.) The significant propertyof(52)is that it projects more constituencyinformationnto the layeringof the grid.Is thisjustifiable?The issue turns on the status of compoundsin the prosodichierarchy.It has beenassumed without argumentthat compound stress registers in level P; yet compoundsare words syntactically. Suppose, then, that compoundsmust, like other words, cul-minatein an entry at Wd-level. The compoundsunder discussion-Tom Paine Street,free verse club-are peculiar n that they contain a phrase-Tom Paine, free verse-astheir first constituent.If we take these categoriesseriously, then we must identify levelA of (52) as P, level B as Wd (again), therebymotivating he extra structure.Any decision about the level structure of the grid will of course be laden withconsequence. For example, the celebrated ambiguityof Americanhistory teacher willnot be distinguishedby grid shape.

(53) a. P: xWd: { xtx x xAmerican [historyteacher]b. Wd: xP: xWd: x x x

[Americanhistory]teacherThe predictionis that these should behave identicallyunder embedding, that Move xshould be equally impeded in both. Some examples of the [A [B C]] type of modifierfollow:

(54) a. plastic towel rackresearchgroupb. faculty laborunion duesc. Frenchmath teacher search committeed. young film starmanagementproblemse. HarvardGlee ClubT-shirtf. sliced rumpsteak souffleg. Haflerpower amptest resultsJudgmentsare delicate, but seem to go in the rightdirection.


25/83

42 ALAN S. PRINCEThe interest of this line of reasoningis that it challengesthe effort to comprehendthe restrictions on types (c) and (d) underthe same structuralprinciple,be it strictnessof cycle or level-subjacency. The failure-or uncertainty-of Move x in the type (d)environment(compound modifier)follows already from the too-greataltitude achieved

by the potentially mobile secondary stress. The intrinsiclocality of Move x-one x orstratum at a time-suffices to inhibitreshuffling.Returning o type (c)-one thirteenJay Street, dandruffshampoo researchgroup-we notice that the still-clashing ertiarystress (thirteen,shampoo)faces an obstacle to its retreat;namely, the secondarystresslodged on the first element.(55) a. x x xx x x x x xx x x x x ?x x--? xx x x x x x x x x + x x x xone thirteenJay (Street)

b. x xx x x xx ? x x x--@ xx x x x x x xxxdandruff hampoo research (group)(Certaindetails of hierarchyhave been suppressedin the interest of clarity.)It appears, then, that in such cases Move x cannotapplywithoutcreatinganotherclash, or at least without bringingtwo entries into closer proximity. Given that thefunctionof Move x is to ease tension in the grid, we do not expect it to create tensionas well; thus, we can derive the relativestabilityof type (c) from the definitionof clashand from a proper understandingof the role of Move x in alleviatingclash. What wehave called the BoundingCondition then follows from a set of independentlyrequiredprinciples: (i) the level-locality of Move x (that it affects only one x at a time); (ii) thedefinition of clash; (iii) the clash-sensitivityof Move x (that it removes but does notintroduceclash);(iv) the substantive evel-structuring f the gridthatleads to the propergriddingof type (d) (compound modifier).For this argument o go through,the notion of clash mustbe relativizedto domain.As noted above, there is a naturaldefinition of the domain of a clash: the smallestconstituent thatcontainsthe clash. It is only in this domain hat Move x can be inhibitedby the possibilityof addinga clash. Consider (56), where a clash is added, but outsidethe domain of the originalclash:

(56) x xx x x xx x x xx xx x x x ->xxxxJay's bamboo table


26/83

RELATING TO THE GRID 43The crucial difference between (56) and (55) lies not in the grids, wnlch are identical,but in the syntactic structuresthat are associated with them. If grids are built up in acyclic fashion from syntactic materials, then clash will be necessarily "relativized todomain" in the appropriateway. Bounding,or strictness of the cycle, which does notfollow from the cycle per se, remainsa logical consequence of fundamentalprinciples.Our Cook's tour of the prenominalregionshas establishedmore than the technicalfeasibilityof a grid-basedRhythmRule. The level hierarchyof the grid,a formalfeaturenot intrinsic to tree notation, leads to a new and principledaccount of some basicproperties of the phenomenon. Move x is a minimalreadjustment,operatingon oneentry and within a single level. The immovabilityof clashing main-stress follows im-mediately from this formulation.The subtle inhibitoryeffects comprehendedunderthe"BoundingCondition" can also be derived fromthe characterof Move x and the natureof the grid's level structure. Since these effects are probably typical of sufficientlyarticulated stress systems-see, for example, the excellent work of Bing (1980) onAfghan Persian-it is appropriate o explain them in terms of general principles. Thegrid-theoreticaccount, then, is not a notational variant or translationof familiarpro-posals, nor is it merely a less cluttered alternative o tree theory, superiorby virtue ofan abstract increment of restrictiveness.Gridtheory offers a new range of solutionstopreviously unsolved or unrecognizedproblemsof a palpablyempiricalcharacter.2.3. Additional Remarks on the RhythmRule2.3.1. Remark 1. There is a similaritybetween type (d) structures(compound modi-fier)-e.g. Tom Paine Street Blues-and the recalcitrantMontana cowboy type. Thecontour of TomPaine Street mimics that of Montana at a higher level in the prosodichierarchy. Whatever prevents stress from shifting in the Montana class of cases mayalso be responsible for the behavior of the higher-level analogue. If so, this providesanother account of type (d) that does not depend on strict cyclicity.Once again, type (c) (right-branchingmodifier) s freed up for the clash-based ex-planation suggestedin the text, and the Bounding Conditionfollows from independentfactors.2.3.2. Remark2. As noted earlier,there is a pronounced endencyto supply sequences

xx x xof even upbeats x x x x with an initial downbeatx x x x. Presumably his is a conse-quence of a eurhythmicavoidanceof upbeats.The process of initialdownbeatcreationis well integrated nto phonology, feedingthe rhythmruleMove x. To see this, consideran example like Apalachicola Falls.(57) a. Wd: x (simplestformdemandedby1: x x x lexical stress rules)a: x xx x xxApalachicola


27/83

44 ALAN S. PRINCEb. Wd: x (simplest form consistent with

X: fx x bothinitialdownbeatrule andx x x lexical stress rules)r: x xx xxxApalachicolac. x xO x 0 xx x x x x x x xX XX X XX X Move x XXX X XX XApalachicola Falls - > **Apalachicola Falls

d. x xO x xx x x x x xx x x x x x x xx xx x xx x Move x x xx x xx xApalachicola Falls > Apalachicola Falls

As indicated, the only output of the RhythmRule is Apalachicola F6lls; the version in(57c), Apalachicola Falls, is quite impossible.2.3.3. Remark 3. In certain complex configurations,such as those examined above,there may be a perceived evenness of stressing. Internally, heremaybe a flatteningoutof the tertiary, quaternary,etc., distinctions. Initially, Tom Paine Street Blues may

xxx xbecome x x x x in fluent speech; contrast TomPaine AvenueBlues, where the RhythmRule operates easily. Notice that in the latter the tertiary/quaternaryistinction-Painevs. Avenue-is clear. Is Delete x at play? Or Add x (the End Rule) applying o the firstelement to steady the upbeat?2.3.4. Remark4. Peters Sells observes that the Rhythm Rule, applyingto trees, willoften result in a reductionof the grid requiredby the Relative ProminenceProjectionRule, where Move x is always conservative of the initial level structure.Tree (58a) hasgrid (58b). Tree (58c), the image under the RhythmRule of (58a), has (minimally)grid(58d). However, grid (58b) turns into grid (58e) under Move x, all levels preserved.

(58) a. b. xw ~~xxA \ ~~~~~xxw x x x x

w S S S


28/83

RELATING TO THE GRID 45c. d. x

w \ x xx x x x

s w w se. xx xx x xx x x x

First, what are the facts? I do not believe that they seriouslycontradict(58e). Second,appeal can be made to the flatteningof Remark3, if need be.2.3.5. Remark5. E. 0. Selkirk observes (personalcommunication) hat both Delete xand Add x are required ndependently n stress theory (cf. Remarks2 and 3). Perhaps,then, she suggests, Move x shouldbe analyzed nto these two components.The evennessphenomenoncould then be understoodas Delete x withoutAdd x. In the context of thepresent proposals, it is plausible to identify Add x with the End Rule. This gives anempiricallydifferentpicture of what rhythmicreshufflingaccomplishes.An entryx nolonger moves to the nearest landing site; rather, when Delete x and the End Rulecombine, it "moves" to a peripheralposition, which may or may not be nearest. If thisis correct, it is no longer necessary to accept the argumentof Remark 2, that initialdownbeat creationfeeds the Rhythm Rule. Instead, Delete x removes the circled entryon the left-hand side of (57c); initial downbeat creation-the End Rule-then comes inand treats the leveled-out Apalachicola just as it does any other too-flat stretch ofmaterial. There are various problemswith extending this approach o the full range ofcomplex structures,but it is sufficientlypromising o merit serious consideration.Noticethat analyzingthe Rhythm Rule into independentapplicationsof Delete x and the EndRule goes well beyond the capacities of tree theory, making key use of grid-onlypos-sibilities.2.3.6. Remark6. There is a sense of disjuncture n the type (d) examples: Tom PaineStreet/Blues, antique shoplzoning board, Thirteen Clublfestivities. Does this play anindependentrole in inhibiting he RhythmRule, providingyet anotherpossible reasonfor distinguishing ype (d) from type (c)?2.3.7. Remark 7. Looking briefly at the effect of coordination,notice hundred andthirteenth avenue, as if structured hundred and [thirteenth avenue]. Perhaps, as F. R.Higgins suggests, a kind of across-the-boardapplicationdefies normal phrasal expec-tations.


29/83

46 ALAN S. PRINCE(59) a. x | p

x xJx x x :Wdx x x x :1[phundredandthirteenth]avenueb. P:Wd: xE: x x :Phundred and) x :Wd

P: xWd: x avenueE: x xthirteenthIn (59a), ultimate end-stress on thirteenth s protected by the bounding phenomenon;in (59b), arrangedacross-the-board tyle, each modifierhas independentstatus, so thathundred and thirteenth no longer resembles a type (c) modifier such as one thirteen,discussed above. Notice thatinmahoganyandbamboo tables, applicationof theRhythmRulegoes alongwith the interpretation mahogany ables and bambootables',as opposedto 'tables each of which is constructedout of some amalgamof mahoganyand bamboo'.

3. UniversalStress Theory3.1. IntroductionMajor impetus behind the formal development of metrical theory has come from thestudy of lexical stress patterns. Halle and Vergnaud (1978) and Hayes (1980; 1981)represent comprehensive and influentialattempts to formulatea suitably parametrizeduniversaltheory of word-stress; he work of McCarthy 1979a,b;1982,chapter3) shouldalso be included here. Hayes supportshis theory with a survey of stress systems that isunrivaled n its combinationof breadthand accuracy; manyof the factualassumptionsmade below derive fromhis work, and his hypothesisthat alternationof stress is alwaysessentially binarywill be presupposed.The proposals of these authors are couched in strongly tree-theoreticterms-thebasic constructs are uniformityof branching, directionalityof branching, labeling ofnodes (sensitive to branchingness).Given the high degree of success attainedby thesetheories, it might seem that a grid-centeredprogrammust founderon the facts of lexicalstress distribution, ackingthe crucial descriptive resources of tree theory. We will see,however, that thefundamental epertoryof patternscan be generatedon the griddirectly,with the notion of clash playing an indispensableexplanatoryrole. In addition, a prin-cipled grid-theoreticaccount of heavy syllable behavior will be suggested, free of ref-erence to syllabic geometry.


30/83

RELATING TO THE GRID 473.2. TheEnd RuleIn manylanguages, placementof stress does not respondto phoneticinfluence,butonlyto morphology:stress is fixed with respect to the end of a domain,typicallythe word.Often such languageshave strictlyinitialstress or strictlyfinal stress. Hayes (1981, 56)notes that "Hyman (1977) lists 144 languageswith 'predominant' nitial stress and 97languageswith 'predominant' inal stress. To be sure, many of these languageshavesecondary stress . . . but a fair number do seem to have just plain initial or final stress."Of these languageswe can simply say that lexical stress is determinedentirely by theEnd Rule, applyingin either its right-handor its left-handversion.A commonvariant s penultimateor (whatmightbe called) peninitialstress: secondsyllable from the edge. These patternsresult fromapplicationof the End Rule when theperipheralsyllable is extrametrical.Standardmetrical heory(post-Hayes)providestwo descriptions orpeneperipheralstress: one usingextrametricality nd [w s] (or [s w]) labelingof the wordtree;the otherusing LCPR-type abelingalone.

(60) a. b.

A~~~~~~WWWS W5

w w w s w w w s wo o o o (o) 0 0 0 0 0

Because the LCPRand extrametricalityare independentdescriptors,they can be com-posed to generateanotherpattern:thirdfrom the edge. This patterncannotbe deriveddirectlyin the presenttheory, in which the LCPR is not feasible. Hayes (1981,68) citesthree languageswith main-stressthree syllables in (wheneverpossible): Macedonian,Parnkalla,and Winnebago.The Winnebagosystem has an essentiallybinaryalternationof stress (Hale and WhiteEagle (1980)),and, as we shall see forthwith,gridtheorycanonly derive antepenultimateor postpeninitialstress as the extrametricality ariantof abinary alternatingpattern. How, or whether, Parnkallaand Macedonian bear on thispredictionremainsto be determined.3.3. SimpleAlternatingPatterns: ThePerfect GridThe first duty of a stress system is to distinguish he stressedfromthe stressless. Thisrequires the two levels of grid structurethat we have labeled crand E. Suppose thatclashes are prohibited, and suppose further that the grid is endowed with maximalorganization-maximal up to clash. We arrive at the perfect two-level grid:


31/83

48 ALAN S. PRINCE(61) x x x x x x

...xx xx xx xx x xx xx...The mainburden of lexical stress theory is to mapwords onto the perfect grid.Given the by now standardassumption hat such mappings ake place eitherleft torightor rightto left, only one furtherparameter anbe fixed: whetherthe mapping tartsxat a peak (x) or a trough(x). Four cases exhaust the logical possibilities.

(62) a. L-R; trough: x x xx x xxx x...

#000000 ....b. L-R; peak: x x x

x x xxx x...#0 0 000 ....

c. R-L; trough: x x x.... xxxxxx.... oooooo#

d. R-L; peak: x x x.... xxxxxx.... oooo0o#

The languageWeri is said to exemplify (62d); Warao, (62c); Marunungku, 62b); andSouthernPaiute, (62a), mappingVs rather than syllables to gridpositions. (Data fromHayes (1981, 50-53).)By what formal means is the association of syllable stringand grid to be accom-plished?A naturalcandidate s an autosegmental-stylemapping o (or from)a precom-piled grid, the gridbeing treatedas a kind of rhythmicmelody. Anotherview, more inline with standardphonologicalpractice, wouldconsider the gridto be builtup positionby position duringa leftwardor rightward weep of the word. Although the "autoseg-mental"mode of associationis certainlymoreinteresting rom the broaderperspectiveof the general theory of phonological mappingprocesses, to use it would require adistractingamount of technical development, and I shall speak with a constructionistformalvocabulary,largelybecause it is familiarand adequate.The construction,then, of a perfectgrid can interactwith the End Rule to producenonbinaryalternationof stress. Considerthe case of Garawa,describedby Hayes (1981,54) as follows: "Main stress falls on the initialsyllable, secondarystress on the penul-timate, and tertiarystress on alternating yllables precedingthe penult." Puttingasidefor a moment the primary/secondary/tertiaryistinction,we describe the basic stress/unstresspattern n two steps: (i) the EndRule(ER)appliesword-initially I); (ii) PerfectGrid Construction(PG) applies right to left (RL), startingwith a trough(tr) and pro-ceeding throughthe word.


32/83

RELATING TO THE GRID 49(63) a. x x x xxxxxxx xxxxxx xxxxxxER(I) PG(RL;tr)#000000#-> #O O0000# =#OO0 OO00#

b. x x xxxxxx xxxxx xxxxx#00000# ER(I)) 00000 PG(RL;tr) #0 0#Observe that in an odd-syllabledword like (63b), the no-clash clause should inhibitPerfect Grid Construction(PG) from erecting a stress next to the initial stress. Thispredictionis borne out by the facts of Garawa:"Nonprimarystress may never occuron syllables directly following the main stress" (Hayes (1981, 54)). It remainsmerelyto note that the End Rule (Initial)applies to relate the I-level to the Wd-level;and theEnd Rule (Final)applieswithin the v.-levelto differentiate he final stress from theothernonprimary tresses. (Note the resemblance o the mirror-image rocess of Englishthatstrengthensthe first of the secondarystresses in a domain;cf. section 2.3.2.)This kind of interaction is by no means limited to cases where the initial stressemerges as primary.In Hawaiian,accordingto Elbert (1970),main-stress falls on thefinal syllable if it contains a long vowel, otherwise on the penult; secondary stressesalternateback from the main-stresstoward the beginningof the word, except that infive-syllabled (and presumably longer) words, there is a strong tendency to have aninitialdactyl in the mannerof (63b). Similarfacts are reportedfor Modern Hebrew inBolozky (1980), and indeed for English in Libermanand Prince (1977), where it isobserved thatalternationof secondarystressespreceding he main-stressmaybe binary(Pq'p6caWpe't1)r ternary(Thitdmcdgouchi),ependingon whichpatternwillput a stresson the initialsyllable.This divergencefrom pure binarityregularizes he stress situation at the beginningof the word. In Hawaiianall even-syllabledwords will begin with a secondary stress;odd-syllabledwords, if there were no ternaryinterference,would begin with an un-stressed syllable. In the actual language,all long words (greaterthan three syllables)begin with a stress. The stress pattern s therefore ocally determinableat both ends ofthe word. Given main-stress(which lies in a two-syllablewindow at word-end), it ispossible to ascertain whether the first syllable is stressed by examininga two-syllablewindow at the beginningof the word: if that window is empty (does not containmain-stress), then the first syllableis stressed. Thereis, plausibly,a realcognitiveadvantagein such local determinacy, compensatingfor a certain amount of formal inelegance.Since processing runs ineluctablyrightward n the modalityof the audible, it is con-venient to be able to beginwithouthavingto sort through he entire(perhapsvery long)word that is immediate to one's intentions. This argument eads one to expect a leftrightasymmetry n thephenomenon:a finalanapestwould conferno comparableproces-sing advantage.As far as I know, only the initialdactyl has been reported.Some care must be exercised in formalizingthis type of pattern. Let us take asimplifiedHawaiianas our descriptivegoal, ignoringthe contributionof long vowels.


33/83

50 ALAN S. PRINCEThe End Rule (Final), applying at Wd-level, determines the location of main-stressstraightforwardly nough, but there is a certain amountof jostling for position withinthe I-level. Final syllables are extrametrical.The End Rule (Final) applies at I-level,followed by the End Rule (Initial), followed by Perfect Grid Construction(Right-to-Left). Derivations ike those in (64)result. Observe that the End Rule (Initial) s blockedfromapplying n three-syllablewords by the presence of prior penultimatestress; wereit to apnly, it would introducea clash.

(64) a. xx xxx x x x x xER(F) ER(F)#o0o (o)# - #o o(o)# -> #oo o#

b. xxxxxx xxxxxER(F) ER(1)#0 o o o o (o)# > #0 0 0 o 0 (o)# -x x x x xxxxxx xxxxxPG(RL) ER(F)#0 o o 0 0 (o)# -- > #0 o o o o (o)# -

xx x xxxxxxx

#0 0 0 0 0 0#

c. xxxxxxx xxxxxxER(F) ER(1)#0 0 0 0 0 0 (o)# - #0 o 0 0 o o (o)# -x x x x xxxxxxx xxxxxxPG(RL) ER(F)#0 0 0 0 0 0 (o)# - #0 o 0 0 o o (o)# -

xx x xxxxxxxx

#0 0 0 0 0 0 0#

It is not possible in this case to simply lay down a trough-firstperfect grid and thenderive main-stressby applyingER(F)to the last entryat I-level. The perfect gridwouldrenderinitial stressing either redundantor impossible: even-syllabledwords would al-


34/83

RELATING TO THE GRID 51ready be initially stressed; in odd-syllabledwords, any ER-derived nitialstress wouldclash with the second-syllablestress already ntroduced.Nor could initialstressingtakeprecedence over everything else: for in three-syllablewords-cf. (64a)-word-stressmust remainpenultimate.1

A potentiallysignificanteconomy would allow the End Rule to directlyapply Wd-level stress, skippingthe E-level stage in determiningmainword-stress.As somethingof a side issue in the present context, it will be left for anotherday's exploration.A final note on the role of the perfect grid.There is a certain amount of (doubtlessundesirable) competition between descriptorsat the edge of a domain. The effect oftrough-firstPG can usually be obtainedfrompeak-firstPG plus extrametricality.Fur-thermore, peripheralstresses laid down by PG couldjust as well come from the EndRule. These conflicts can be resolved by attributingall peripheralstresses to the EndRule and eliminatingthe parameterpeak-firstvs. trough-first.PG would then simplyreact to the presence of an End Rule stress andpropagate tself automaticallyacross theword, driven only by clash avoidance and the directionalityof phonological mapping.Even the parameterof direction (leftwardvs. rightward)mightbe dispensable,for PGcan orient itself with respect to the EndRule stress andsimplymove awayfromit. Thismapping process strongly resembles that of autosegmentalphonology, particularlyasinterpretedby Clements and Ford (1979), in which an initial association is made andsubsequent associations spreadout from there. On this view, PG is subservientto theEnd Rule and rather characterless: t fills out those portionsof the grid that the EndRule cannot reach, in an entirely predictableway. Such a strippingdown of PG wouldhave a very healthy effect on the theory; removingtwo binary parameterseliminates75%of the availabledescriptiveoptions.Unfortunately, hisinterestingly ompacttheoryencounters certain difficultieswhich preventus fromacceptingit immediately.First, incases where the End Rule applies to both ends of the word, what is to decide whichstress shouldserve as anchor for PG? Second, what of systems where stress fallson thethird-syllable-in?These show that trough-firstmapping can be composed with extra-metricality,and therefore cannot be reducedto it. Clear examples are English, Latin,and most obviously Winnebago,discussed by Hale and White Eagle (1980).Winnebagohas an essentially binaryalternatingpattern hatspreadsrightward rom the main-stress.But main-stress tself is located three syllablesfrom the beginningof the word wheneverwords are long enough. The analysis must be as in (65):

' There is another approachto the Hawaiianconfiguration 64) that uses neitherextrametricality orER(I). Lay down a perfect grid, trough irst, from right to left. Determinemain-stressby ER(F)-this givespenultimate tress. Then apply Move x. If Move x cannot create a clash and if it cannot affectmain-stress,it can apply only to the second syllable of odd-lengthwords, and it can only move the I-level entry back tothe first syllable. Why should Move x apply if the grid s already"perfect"?One can point to the eliminationof the upbeat as desirable, simplifying:paradigmatic niformity f initial stress, mentionedearlier,may alsoprovidea sufficientteleology.


35/83

52 ALAN S. PRINCE(65) x x x(x) x xx x xxx (x) xx xx xx xPG(LR; tr)

#0 o o o o ooo# #0 Ooooooo#xx x x

xxxxxxxxER(I)> #o o o o o o o o#

A thirdtype of problem,perhaps technical, concerns the interactionof PG with heavysyllables.Before we give in to despair, however, it is well to observe that there are somepurely descriptive tasks for which the parameterlessPG is better equippedthan thedirectionally specified version. Suppose that stress is fixed somewhere in the root. IfPG uses this stress as an anchor, alternation will spread out automaticallyin bothdirections, moving away from the originalfixed stress. This result cannot be obtainedby simple directional sweep from one end of the word to the other. Exactly such apattern s reported or Cahuilla Desert and Mountaindialects) in Levin (1982), referringto the work of Seiler (1965; 1967). (I am grateful to Bill Poser for bringing Levin'sunpublishedwork to my attention.) In Cahuilla, according to Levin, "Primary stressfalls regularly on the first syllable of the root, with few exceptions. Secondary stressfalls regularlyon alternatingmorasprecedingand followingthe primaryword stress."The End Rule, initial version, establishes main-stress, but it applies only in the root-domain. Prefix andsuffixsequencesare stressedby PG, neutralwith respect to direction.If this type of patternproves to be at all ordinary,parameterlessPG may be at least theunmarkedoption, if not the only one.3.4. Heavy Syllables in TreesThe smooth alternationof prominence n the maximalclashless grid is often disturbedby a special statusgrantedto heavy syllables; they may attractstress regardlessof theirparityin the syllable string.In previous metricaltheory, the effort has been to expressheavy/lightbehavioraldifferencesin terms of constraintson tree formand tree labeling.Prince(1976b)offers anearly tree-theoreticaccount of stressing, nwhichterminalnodesof tree templatescan be restricted to dominatingeither a syllableor a mora.

Following essentially the line of Trubetzkoy, et us portray he [light/heavy] ontrastas beingbetween syllables which containone, and syllableswhich containtwo moras. What then isa mora? We offer the following account:(39) Assumingthat long vowels are sequences,a. The first vowel of a syllableis a mora;b. The segment mmediately ollowingthe firstvowel, if it is in the same syllable

as that vowel, may be a mora, subjectto language-specific onstraints.


36/83

RELATING TO THE GRID 53The language-specific onstraintsare few in number.In the first case discussed the constraintwas that allmoras mustbe [+ syllabic],i.e. vowels. . . . In certain anguages,e.g. Lithuanian(Kiparsky 1973))andKwakiutl Bach (1975)),the restriction s loosened so thatany [+ son-orant] segmentcan qualify. ... Finally, there [may be] no restriction,and the second moramay be vowel or consonant:here the contrast s between heavy andlight syllables. (Prince(1976b,17))Halle and Vergnaud 1978)develop their accountin geometrical erms. Stress rulesare based on the rime constituent of the syllable rather than on the syllable per se.Syllable quantityenters the calculationas sensitivity to whether the rime branchesornot. Feet are assumed to be uniformly(left- or right-)branching.An immediate conse-quence is that, in quantity-sensitive anguages, heavy syllables can occur only at themarginsof feet, left margin or left-branching, ightmargin or right-branching.(66) a. b.

R R R R R *R R RR R

C. d.

R R R R *RR R R R

The account is not yet complete, however, for the foot-trees must be labeled as well.And here is a problem. If the account is to be explanatory, the properties of heavysyllablesandof feet must emergefrom the interactionof principles ree fromstipulationsthat specificallyconcernfeet andheavy syllables. Branching heorysucceeds in placingheavy syllables peripherally n feet. Why always at the stressed end of the foot? Whycan this not mean on occasion exile to the antipodesof prominence?Use of the simplelabeling strategy [w s] or [s w] poses this conundrum.Applyingleft-strong-[s w]-toleft-branching66a)gives the satisfactory oot [s w w w w], just as applyingright-strong-[w s]-to right-branching66c) gives [w w w w s]. If combination s free, and it shouldbe, we must also expect right-strong o go with left-branching giving [w s s s s]) andvice versa (giving[s s s s w]): impossiblefoot shapes in general,and de-stressersof theheavy syllable in particular.


37/83

54 ALAN S. PRINCEHalle and Vergnaud(1978)have a clever answer. Let the only labelingrule be theLCPR-right node strong ff it branches-and its mirrormage,LCPR'-left node strongiff it branches. Then, given uniformbranching,only the following four kinds of treescan participate n stress theory:(67) a. right-branching;LCPR:

5

5

w w w s wb. right-branching;LCPR':

5

w w w w Sc. left-branching;

LCPR:

s w w w wd. left-branching;LCPR':

w s w w wOfcourse, all these trees areattested at various evels. Sinceheavy syllablesarebranch-ing nodes, as portrayed n (66), they must always attractstress by the LCPRor LCPR'and attract it at the peripheryof the foot, by uniformbranching.Thus, a considerabledegree of explanatorysuccess is achieved.


38/83

RELATING TO THE GRID 55Various problems lurk, however, not far beneath the surface. First, there are nofeet (67a) or (67d): feet always have the pattern [w* s] or [s w*]. Worse, the commonsuprafootpatterns [w* s] and [s w*] cannot be guaranteedby the LCPR (LCPR')alone.Considera languagewith final main-stress and feet. There is no way to describe this

directly. Relevant are words structured F R R] [F R RI [F RI; the combinatoricsaregiven in (68):(68) a. LCPR: b. LCPR':

c. LCPR: d. LCPR':w s w s w w

Similarly,the uniformend-stressingof the Nuclear Stress Rule is inexpressible, giventhe nonuniformityof syntactic branching.Nor can the uniform nitial stressingof com-pounds in languages like Finnish and German be expressed, given the range of inputstructures(often right-branching).I conclude reluctantly hat apotheosisof the LCPRdoes not, in itself, explicate thebranching/labeling ond in a way that does full andequal ustice to heavy syllables, footshapes, andsuprafootstresspatterns.Recoursemaybe had to plausibleHilfshypothesenof various kinds; but such explorationsmust be left to those who share the intuitivevision behindthe originalproposal. Finally,andbeyond technicalia, the theory is weak-ened to the extent that the LCPR is not independentlymotivated. As shown above,post-Halle and Vergnaudextrametricality heory seriously underminesword-level sup-port for the LCPR. If the LCPR applies only to feet-and that only in the restrictedbranching/labeling ombinations (67b) and (67c)-then it really exists only to expressthe generalization "heavy-syllables-attract-stress".Heavy syllable behavior no longerfollows from the free interactionof independentand motivatedprinciplesgoverningthetwo componentsof metricaldescription, branchingand labeling;explanation s lost.Hayes (1980; 1981) pursues a different line, taking as central the evident predom-inance of metrical units [w* s] and [s w*]. Instead of appealingdirectly to labels s andw, he builds his theory on the more abstract notion of dominant(d) and recessive (r)nodes. Metrical structure s binaryand metricalsister-pairscome as either [d r] or [r d].The first law of such structures is that recessive nodes may not branch. It followsimmediately that metrical trees must be uniformly right-branching r uniformly left-branching. N.B.: Halle and Vergnaud ake this as an axiom.)


39/83

56 ALAN S. PRINCE(69) a. d ... b ... d c. d.

d drA Ad r r ... ... r r d *d r *d r d

The second law is that trees may be specified by one of only two rules: right nodedominantor left node dominant.By these laws, there can be only two tree types:(70) a. left-dominant:

dd

d r r r...b. right-dominant:

d

...r r r dIt remainsto cash in dlr for slw. In the unmarkedcase, d = s tout court; the markedoptionis "d = s iff it branches",the LCPR.Havingassumed these laws anddefinitions,one can call concisely for a left-dominant oot (or a right-dominant ne) and be servedimmediatelywith [s w*] (or [w* s]).The content of Hayes's system emergesperhapsmore clearly under a slightrefor-malization hat does without the intermediariesd and r. Identifyd withs; r with w. Thebasic laws translate as follows:

(71) a. Hayes # 1: W-nodesdo not branch.b. Hayes #2: Metricaltrees (at any level) fall under one of these patterns:i. left node strongii. rightnode strongThe LCPRcomes out as a relabelingrule, invoked at cost, which turnsanynonbranchings into w:

(72) "LCPR": s- wI

Hayes, then, has interestingly nverted the dependencybetween branchingandlabelingposited in earlier work. For Halle and Vergnaud,branching s defined independently,


40/83

RELATING TO THE GRID 57without reference to labels; but labelingrefers to branchingness.For Hayes, labelingis fundamentallyalways [s w] or [w s], and this imposes uniformityof branchingvia(71a).But hasn't Hayes given up on the key explanatory ssue by baldly declaring"w-nodes may not branch"?Afterall, we were hopingthat the desired universalset of treescould be generated by free combinationof independent aws of branchingand labeling;here the first thingwe do is to abrogatethat independence.Of course, the LCPRdoessomething similar,with its reference to branchingness.Empirically, t turns out to beimpossibleto have bothbranching-freeabeling aw andlabel-freebranchingaw. Movingon to the next best of allpossible tree-worlds,we look for a stipulation elatingbranchingto labeling that is redeemed by its generality. The LCPR, in the hands of Halle andVergnaud,was one such attempt; principle (71a) is another.Hayes has not given up,but his move deserves careful scrutiny.

The explanatoryvalue of (71a) rests on the strengthof the uniformbranchinghy-pothesis that it entails. (The hypothesis itself is inheritedfrom Halle and Vergnaud.)Above the word level, there is no hope of finding support: phrasal and compoundbranching s grammar-determined nd in general nonuniform;w may be observed tobranchfreely. Word-internally, wo sources of evidence emerge:word-treesand feet.T

prince- relating to the grid 1983

Documents