Calculating Metrical Structure

William J. Idsardi
University of Delaware
idsardi@udel.edu

CUNY Symposium on Phonological Theory
February 20, 2004

I am inclined to be sceptical about this approach since the manipulation of brackets seems to imply a conception of phonology that is preoccupied with the notational system and not so much with its "semantics", i.e. the content of the theory.
van der Hulst 1995/2000: 319

This talk will update the state-of-the-art with regard to the calculation of metrical structures. This talk will be biased toward the theory of simplified bracketed grids (SBGs) which developed out of Halle & Vergnaud 1987.

Since Harry is giving one of the responses to this paper, I felt I might remind him of his previous assessment in his state-of-the-article in GLOT. I don't know whether my attempt to resynthesize the theory will make matters better or worse in his eyes. In fact, I agree with the denotation of the quote, if not with its connotations (I would say "explicit about" instead of "preoccupied with" and "representational" rather than "notational"). SBG theory certainly aims to be explicit, and when it succeeds in that goal, it can appear mechanistic because it simply works. As to the "semantics" of a theory, I think there are none beyond the operational semantics. This theory defines a calculus over marks and brackets, and the marks and brackets have no meaning beyond what it is that they actually do in the theory. If analogies help, I have called the brackets "metrical monopoles", and I think they share some of the characteristics of the monopole theory of magnetism. One bracket (pole) serves to define a group (field), and it is difficult (or impossible) to observe the effect of a bracket (pole) separate from the manifestations of the group (field). But tree structures (or quarks) are no more directly observable than brackets are.

The last (and first) general introduction to SBGs, Halle & Idsardi 1995 is now nearly ten years old, and I feel it is reasonable to go back over that ground again now, and to update the theory. I am, of course, aware of Optimality Theory proposals for stress and metrical structure, of which Generalized Alignment (McCarthy and Prince 1995) is the best known. However, I do not intend in this presentation to re-present the arguments against such approaches, such as those in Halle & Idsardi 2000. By and large, I think the more serious problem with the OT approaches is the failure to explicitly articulate the representations which are employed, for stress as well as for other phonological information. In the case of OT, in my opinion, the vagueness leads to very unclear results (such as the difference between "crisp" and "sloppy" alignment, again see Halle & Idsardi 2000). Against these general comments, Hyde 2002 does attempt a restrictive and explicit formulation of a small portion of metrical theory (namely binary quantity insensitive systems). My own assessment, however, is that once mechanisms are added to deal with unbounded, quantity sensitive and lexical stress systems, that its initial apparent restrictiveness will give way to a theory at least as rich in devices as the present one is.

Instead, in this presentation I will try to achieve these goals:

For me, the most pertinent point is the nature of the revisions to the theory. Briefly put, I will propose to eliminate avoidance constraints and circumcription (conflation), by making greater use of projection and the difference between open and closed feet. That is, there will be more analyses which will project brackets onto higher grid lines. At the moment there still seem to be certain cases (Old English, e.g.) which will still require bracket deletion rules. If these cases could be successfully reanalyzed, then we might be able to achieve a monotonic system in which information is only added during the derivation. I will have some speculations on this at certain points below.

In addition, we will make much greater use of the identification of metrical calculations with finite state automata (FSA), (Howard, Johnson, Kaplan, Kartunnen, Kay, van Leeuwen, ...). This was briefly discussed in Idsardi 1992:72, but has stayed in the background since then. Recently, Nigel Fabb, as part of his collaboration with Morris Halle on metrical verse structure (Fabb 2003, Fabb & Halle forthcoming) has suggested that we highlight this way of understanding the rules. I will shamelessly steal this idea in this presentation, and will formulate the whole system in these terms. However, I will not illustrate metrical verse calculations in this talk (for reasons of time), but I do wish to emphasize that scansion of poetic lines uses exactly the same set of metrical parameters described below. In addition, there are many more poetic traditions which employ ternary constituents, which should lessen the unwillingness of phonologists to fully accept them, as they are rare in natural language stress systems (but not absent).

Formulating the rules as FSAs has certain advantages, as many modern programming languages (Sed, Awk, Perl, Ruby, JavaScript, etc.) offer regular expression facilities that can be used to implement FSAs. In fact, I have written the new basic parameterized grouping function and the projection function in JavaScript, and this file is used in some of the examples in this document. Beesley & Karttunen 2003 have now made available the Xerox finite state automata tools as well, and the theory here is also easily implemented with those tools.

I unfortunately do not have time in this talk to provide a comprehensive introduction to the use of FSAs in understanding the application of phonological rules. There is a good introduction to the topic in Kenstowicz & Kisseberth 1977:188ff and in Kenstowicz & Kisseberth 1979:326-327. Textbooks on mathematical linguistics, such as Gross 1972 and Partee, ter Meulen and Wall 1990 or introductions to automata theory, such as Hopcroft and Ullmann 1979 offer further information.

The SBG theory follows Halle & Vergnaud 1987 in viewing the calculation of prosodic structure as being governed by a system of parameterized rules. By this we mean that there this is a set of ordered rules, constituting a derivation. However, now all rules are allowed, rather, they fall into a fairly narrow classification. In Idsardi 1992 I also required a strict ordering of the parameterized rule classes there -- for example, Edge Marking universally preceded Iterative Constituent Construction. In Idsardi and Purnell 1999 we proposed to derive the ordering from more general principles (rule complexity and the Elsewhere Condition). We will touch on these issues at various points below.

I will offer first a new set of formal parameters, and then spend the rest of the time illustrating and defending them, and discussing various possible alternatives. Although the SBG theory remains a work-in-progress, there have been several advances in our understanding since Halle & Idsardi 1995 and this paper will offer a synthesis of those findings.

I will explicitly state here an idea that has long been in the background in understanding the nature of metrical grids. The basic line for all metrical structures (i.e. the lowest line of all grids) is the x-tier (i.e. the timing tier). I will offer some more speculations at the end as to how to unify a theory of syllabification with the precise proposals about projection made here. For the present time, we will assume that the syllabification module can define a subset of the x-tier elements relevant to the calculation in terms of standard syllable positions (onset, nucleus, rime or mora, etc.). These will be "projected" onto the initial line of the grid, and will be represented here by "x".

In addition, syllable configurations can project grouping junctures — ( or ) — onto the initial line of the grid, for example, to mark heavy syllables. The grid will be built entirely bottom-up and locally. Under this conception, no information other than that embedded in the x-tier can be used to project the initial grid line, and the x-tier information cannot be used to directly affect any higher grid line. This requirement may ultimately have to relaxed somewhat (see Shuswap, below) but we will try to maintain it as much as possible.

Thus, we will reduce the options to projecting the left- or right-most element of each group, and also to projecting left or right brackets onto the next line of the grid: Projection: Each group projects

Languages can also lexically specify (store) various aspects of line 0, including non-projecting grid marks.

The two junctures, "(" and ")" serve to define groups on the gridlines. All elements to the right of "(" or to the left of ")" fall within a group (or foot). The junctures thus serve to partition the gridline. Following Selkirk 1984 and much other word, the junctures often also reflect aspects of syntactic structure, which is then "crushed" out of recursive system into a non-recursive one, leading to non-isomorphic mappings between syntax and phonology. We take this to be a fundamental difference in the data structures available in syntax and phonology (here we part company with Jean-Roger Vergnaud).

Languages can also lexically specify line 0 boundaries, but not boundaries or elements on higher lines of the grid.

We will thus reduce all grouping to the operation of parameterized rules having the following choices: Grouping: Scan the gridline, inserting brackets,

This implies 32 different basic parsings for gridlines, shown for odd and even strings with binary groupings in the following table:
BracketSizeDirectionIterateStart
 x x x x x x
 x x x x x x x
Example languages
a.L (2L ⇒IterativeInsert
(x x(x x(x x
(x x(x x(x x(x
Maranungku, Auca stems
b.L (2L ⇒ISkip
 x(x x(x x(x
 x(x x(x x(x x
Winnebago
c.L (2L ⇒Non-iterativeI
(x x x x x x
(x x x x x x x
North Kyungsung Korean
d.L (2L ⇒NS
 x(x x x x x
 x(x x x x x x
Tokyo Japanese
e.L (2R ⇐II
 x(x x(x x(x
(x x(x x(x x(x
Suruwaha?
f.L (2R ⇐IS
(x x(x x(x x
 x(x x(x x(x x
Nengone, Auca suffixes, Garawa
g.L (2R ⇐NI
 x x x x x(x
 x x x x x x(x
Turkish?
h.L (2R ⇐NS
 x x x x(x x
 x x x x x(x x
Polish, Indonesian, Turkish?
i.R )2L ⇒II
 x)x x)x x)x
 x)x x)x x)x x)
Maranungku?
j.R )2L ⇒IS
 x x)x x)x x)
 x x)x x)x x)x
Araucanian
k.R )2L ⇒NI
 x)x x x x x
 x)x x x x x x
Tauya
l.R )2L ⇒NS
 x x)x x x x
 x x)x x x x x
Garawa
m.R )2R ⇐II
 x x)x x)x x)
 x)x x)x x)x x)
Suruwaha, Tauya
n.R )2R ⇐IS
 x)x x)x x)x
 x x)x x)x x)x
Latin, Greek
o.R )2R ⇐NI
 x x x x x x)
 x x x x x x x)
Russian, Japanese palatal
p.R )2R ⇐NS
 x x x x x)x
 x x x x x x)x
Shingazidja, Latin, Greek clitics

Here is a finite-state automaton (FSA) for (j):

This one is R2LIS, it inserts ")" every 2 marks, from left to right, iteratively, skipping (not inserting) on the first mark. The basic machine is shown on the left. We read the arcs in the following way: simple arcs (without :) match and consume the symbols shown on the arc (the labels are to the right of the arcs). Transductions (arcs with :) match the symbol to the left of the : in the input, and replace it with the symbols to the right of the :. So, in state 0, the machine accepts "x", outputs "x" and moves to state 1. In state 1, the machine accepts "x", outputs "x)" and moves back to state 0. In the terminology suggested by Nigel Fabb, from state 0 we "skip" a mark, and from state 1 we "insert" a bracket.

The full machine, which additionally respects pre-existing metrical structure (using the phrase from Halle 1990), is shown on the right. Notice that the arcs for when the machine encounters "(x" always go to state 1, and the arcs for "x)" and "(x)" always go to state 0. That is pre-existing brackets are always treated in the same way, regardless of the current state of the machine.

The FSA for R2LII, the one that inserts on the first mark, is:

These machines are identical to those for R2LIS except for the starting state (by FSA convention numbered 0). That is, we have exchanged the state labels in the diagram. A better method for us would be to simply annotate the diagram to say which is the starting state, similar to conventions on final states. We will continue to follow the established FSA conventions, however.

The FSA for L2LII is:

Again, the FSA for L2LIS is the same, with the state labels reversed. That is, the machine starts in the other state. This exhausts the binary machines, as the right to left machines simply scan the string from the opposite side.

As an example of an FSA for ternary parsing, here is L3LI:

Notice that the only difference is that the basic ternary parser has two "skip" states but the same two additional rules describe how to elaborate the basic machine to get the full machine:

Thus, for iterative machines there is a basic machine, which is elaborated in the same way each time to produce the full machine. In addition, the start state can be specified for a parsing, and the size of the machine (number of skip states) can be specified. Thus, there is a direct relation between the parameters used here and the construction of the FSA.

No look-ahead with any of these machines. Compare this to a variant of L2LII which would require two marks at the end, resulting in a ternary constituent at the far side. A mirror example of this would be Garawa, xx)xx)xx) and xxx)xx)xx). The machine for this looks like the following: In this machine state 0 has two arcs for "x". One inserts (outputs "(x") and moves to state 1, the other skips (outputs "x") and stays in state 0. This is a non-deterministic FSA because of the choice of what to do in state 0. Furthermore, state 1 is not an acceptable finishing state. In that way the output "(xx(xx(xx(x" is not allowed. However, we need to also establish the priority of inserting over skipping in this case, which is usually done in FSAs by assigning a value (probability) to the arc. The problem with NDFSAs is that they need additional information to work properly. In order to ensure that we don't use the skip when we don't need it we need to make a more complicated machine. Additionally, "(x" is OK at the end of the grid as long as it is pre-existing (in other words, the machine has to respect the bracket). This leads to the following machine: which is clearly more complicated than L2LII. Instead of making progressively more complicated elemental machines, we will combine elemental machines to create more complicated machines.

We do need to address at this point what the non-iterative machines look like. As a simple case in point, we will take L2LNI, which is:

The behavior of non-iterative machines that begin with a skip is not quite as clear. I give my proposal for R2LNS here:

The question at issue is whether we should wait for a successful insertion before consuming the rest of the string, or whether the application should be vacuous under various circumstances. Given the paucity of relevant evidence at the moment, I will simply leave this question open.

We will start our discussion of various languages by looking at those that have unboundedly large groups. It is a puzzling fact that these systems generally receive very little attention in the literature. The most obvious example of this is Hayes 1995 who devotes only five pages (32-33, 296-299) of a 455 page book to such cases. Hayes identifies two types of systems: default to same side (e.g. Russian: leftmost accented otherwise leftmost) and default to opposite side (e.g. Kwakw'ala: leftmost heavy, otherwise rightmost).

Idsardi 1992 treats the default to same side cases as examples of the unbounded extent of single brackets. In each of these languages, the marked (heavy) syllables project brackets (or have them lexically stored in the case of lexical accent systems), and the languages inserts a bracket non-iteratively. Given the unbounded extent of the brackets, inserting a bracket at the right edge can create a constituent across the entire word. The idea here is to modularize the system; that is to define a simple interface between the syllabic information and the metrical information. The idea is that the only effect syllables can have on the grid is to provide elements or brackets, nothing else.

Let us assume, at least as a heuristic (Elan!), that in unbounded systems words without marked syllables will indicate which side of the foot is the head. Under this idea, Russian must have left-headed feet (i.e. must project the left-most element in each line 0 group onto line 1), and Kwakw'ala must have right-headed line 0 feet. Then, given this, Kwakwa'ala heavy syllables must project "x)" and Russian accented syllables must be stored with "(x". If we apply R2RNI to such cases we get the following structures:
Russian Marked:(, R2RNI, Project:L Kwakw'ala Marked:), R2RNI, Project:R
Xxxxxx)x(Xxx(Xx)xxxxxX)xX)xxX)X)

and in each case the main stress is on the first foot, accomplished by another layer of metrical calculation. We will eschew the HV device of conflation, however, and say that whatever phonetic manifestations of stress are in the language, they are defined in terms of features added on the basis of the metrical grid. This will become clearer in the case of pitch-accent systems. That is, there is no phonetic universal saying that all differences in grid heights will be manifested in every language. Russian manifests only a two-way difference: the element with the most grid marks versus everything else. Other languages (English, Polish) assign secondary stress characteristics based on lower grid lines. This is similar to the use of formal features in syntax: languages have syntactic agreement and case even if they do not manifest it morphologically.

In OT with Generalized Alignment, this is handled somewhat differently. There are constraints mandating stress on marked items (Weight-to-Stress, Max(Stress), Dep(Stress)), and Alignment constraints such as Align(Word,Left,Stress,Left) and constraints mandating one stress per word. So the overall division of labor and complexity is similar in the two theories: Project brackets is similar to Weight-to-Stress and Faith(stress) and Footing is similar to Alignment.

Some ambiguities remain about alignment of feet or feet-heads (stress) with edge of word. Assuming undominated constraints mandating one stress per word, we then have for Russian the following crucial ranking of violable constraints: Dep(stress) >> AlignLeft(Stress,Word) whereas for Kwakw'ala we have: Weight-to-Stress >> Dep(stress) >> AlignRight(Stress,Foot) >> AlignLeft(Stress,Word)

We are ignoring here many alternative proposals within OT; we will return to this issue in the final section.

Kashmiri (and some varieties of Hindi) show a minimally more complex system, with three degrees of weight. Stress in Kashmiri is never final (R2RNS), and falls within the remainder on the leftmost long vowel, otherwise the leftmost closed syllables, otherwise on the leftmost vowel. This system is the mirror image of Moses-Columbian, which has three degrees of lexical weight, strong, alternating and weak. In Idsardi 1992 M-C was analyzed as strong = closed foot (x), alternating = open foot x) and weak as no foot x. The correct stress placement was accomplished using a rule of unmatched bracket deletion. Since Kashmiri is the mirror image, we will use the following representations: long vowel syllable = (x), closed syllable = (x, short syllable = x.
 x  x  x) x
ku.ni.vi.zi
'sometime'
 x) (x) 
ki.taab
'book'
(x) (x)  x 
baa.laa.dər
'balcony'
 x  x (x) (x 
mɔ.kɨ.laa.vun
'to finish'
(x  (x) (x 
vah.raa.vun
'to spread'

R2RNS skips over final x or (x or (x), and inserts on the next position, yielding x)x, x)(x and x)(x) respectively. Kashmiri is left-headed, and also projects right brackets onto the next line:
 x      )  
 x  x  x) x
ku.ni.vi.zi
'sometime'
 x) x) 
 x)(x) 
ki.taab
'book'
 x)  x)    
(x) (x)  x 
baa.laa.dər
'balcony'
       x) x 
 x  x (x)(x 
mɔ.kɨ.laa.vun
'to finish'
 x   x)  x 
(x  (x) (x 
vah.raa.vun
'to spread'

Now it is a simple matter to finish the calculation. We project the rightmost elements of each line 1 foot, make a new foot on the next line and project the leftmost element:
 x         
 x)        
 x      )  
 x  x  x) x
ku.ni.vi.zi
'sometime'
 x     
 x  x)
 x) x) 
 x)(x) 
ki.taab
'book'
 x         
 x   x)    
 x)  x)    
(x) (x)  x 
baa.laa.dər
'balcony'
       x    
       x)   
       x) x 
 x  x (x)(x 
mɔ.kɨ.laa.vun
'to finish'
     x     
     x)    
 x   x)  x 
(x  (x) (x 
vah.raa.vun
'to spread'
To summarize, the rules required to generate Kashmiri stress are:

  1. Project long = (x), closed = x) (line 0)
  2. Foot R2RNS
  3. Project L,) (project leftmost and right brackets onto line 1)
  4. Project R (project rightmost onto line 2)
  5. Foot L2LNI
  6. Project L (project leftmost onto line 3)
As we can see, this generate four degrees of grid strength as well. Both closed and long syllables project to line 1 (as well as the occasional short syllable). All long vowels project onto line 2, with occasional closed or short syllables, and the first of these gets main stress.

One point about the nature of the rules in is that they always apply to the top line of the grid. Elevating this observation to a principal of rule-application to the grid has interesting consequences. It gives a principled underpinning to HV's Stress Equalization Convention HV:265 and their Convention (43) HV:71 which applies line 1 parameters to line 0 when line 1 fails to have any marks. In the terms developed here, the rules simply apply in an order, always to the highest available grid line. If projection should fail to generate a new line, then any subsequent rules will apply to the old line. The Stress Equalization Convention amounts to concatenating grids at their tops. While applying all rules to the current top line has effects similar to these, there are subtle differences, and unfortunately I don't yet have cases to examine whether these differences are beneficial or not.

Recapitulating the previous sections, Russian distinguishes between underlying accented and unaccented vowels. It makes additional distinctions which we will deal with momentarily. Giving concrete examples for these cases, we can consider two feminine stems, accented /koróv/ 'cow' and unaccented /golov/ 'head', followed by either the accented nom. sg. /-á/ or the unaccented acc. sg. /-u/:
Suffix
accentedunaccented
Stem accented
 x(x (x)
koróv-a
 x(x  x)
koróv-u
unaccented
 x x (x)
golov-á
 x x  x)
gólov-u

The grammar adds to line 0 only the final ")". The rest of the information is stored lexically in Russian. And so there is almost no computation involved in these cases. The representations for stem and suffix are simply concatenated and the stress can be read relatively directly off this. This fact is directly related to the conception of feet employed here. For feet can be open at one end, and will then automatically accomodate any grid marks to that side, something which tree-based theories need a special trick (stray adjunction) to accomplish. This theory makes stray adjunction a representational rather than a procedural question, and in this way reduces the amount of information that must be calculated on-line. The rest of the calculation is like that of Kashmiri, placing main stress on the first foot.

Interestingly, Russian has an additional class of stems, which are post-accenting. These are stored in the lexicon with a final dangling "(", as shown in . The bracket insertion rules will not create such configurations, but the fact that they can be stored lexically provides a crucial piece of evidence for the reality of the boundaries.
Suffix
accentedunaccented
Stem post-accenting
 x   x((x)
gospož-a
 x   x( x)
gospož-u

Notice that the concatenation of the stem and suffix representations yields two brackets in a row: "((". This plays no role in the Russian grammar, but does have consequences in Slovenian stress retraction (Marvin 2002).

The possibility of post-accenting stems follows directly from our choice of representation. In Faith-based theories within OT no such direct prediction exists. Instead, some fundamentally different statement must be made in these cases. Thus, for example, Alderete treats the post-accenting stems as unaccented (contra the history of Balto-Slavic enshrined in Dybo's Law Collinge 1985:31-33) and sees the choice as a competition between stem and suffix stress, leaving no place for the mobile stress observed in the actual unaccented cases. The present theory correctly allows for direct representation of post-accenting stems. Vachon 1996, in contrast, handles the cases handled here in OT, but requires both Alignment and anti-Alignment constraints defined on arbitrary classes of morphemes. This fails to distinguish simple cases (here done by direct concatenation) and more complicated cases (retraction, see below). In addition, it does not handle derivational suffixes, to which we now turn.

When we turn to the derivational suffixes in Russian, we find some extra kinds of suffixes, which Melvold 1990 classifies into two major types: recessive, which respect the accent of the stem, and dominant which over-rule the accent of the stem. Chew 2003 shows that this question is not entirely simple, as combinations of particular stems and suffixes can have idiosyncratic properties. Such morphologically-oriented stress can be handled by applying morphologically-governed rules of bracket insertion. I will not handle these cases here. I will only give here a representational analysis of some of the possibilities, capitalizing on having two different brackets, and making use of the difference between open and closed feet.
TypeExampleRepresentation
Recessive unaccented[look up cases]x(as golov, -u above)
Recessive accented-jag(x(as korov, -a above)
Recessive post-accenting-ovx((as gospož above)
Dominant accented-jag)(x
Dominant post-accenting-ač )x(
The dominant versions of accented and post-accenting have an additional preceding right bracket. Projecting right brackets onto line 1 (as in Kashmiri) partitions the grid into "dominance" domains, and the main stress goes on the leftmost accented element within the rightmost dominance domain. That is, we have the rules:

  1. line 0: Foot R2RNI, Project L, )
  2. line 1: Project L
  3. line 2: Foot R2RNI, Project R
XXX add examples

Jers and retraction

o-facts

OT interpretation of retraction, deletion of vowels crucial, stays near deletion site, movement toward beginning of word emergence of Align-L

exceptions to retraction úzel, vosem'jú

open on the left, prepositions

retraction with epenthesis, pitŕbhis not predicted by OT at all

The accentual system of Vedic Sanskrit (Kiparsky (1973, 1982)) is also characterized by the Basic Accentuation Principle. But see Wilson (1991, 1993) for a differing interpretation. There are some interesting stress shifts in Sanskrit, one of which is discussed by HV, arguing for the persistence of metical constituent structure. The Vedic word for ‘goddess’, devíi has lexical stress on its final vowel.
devíidevíi-bhisdevíi-ṣudevy-áasgoddess
In the case of vowel hiatus, a high vowel is converted to a glide (an internal sandhi rule) and in that case stress shifts to the right. HV took this as diagnostic of the headedness of the language, with right-ward shift indicating left-headed constituents, under the assumption that the grid marks were deleted in these cases:
 x(x  (x
devíi-aa
 x( (x
devy-áa
If stress shifts can occur when elements are eliminated from the grid, then can such shifts occur when new elements are added to the grid? Interestingly, Sanskrit seems to offer a case for this, too. The unaccented stem pitar ‘father’ undergoes ablaut before lexically stressed endings:
páad-ampad-áapad-bhís'foot'
pitár-ampitr-áapitṛ́-bhís'father'
Notice that the places where pitar loses a vowel are those places where the suffix is accented in the paradigm for pad ‘foot’. [The first column corresponds to the pre-accenting suffixes, which we will not treat in this talk, but is included to show the underlying existence of the vowel, also the stem vowel of pad is lenthened by a second quantitative ablaut]. Of interest here, however, is the last column, where the accent is retracted back onto the stem. Notice that this retraction does not happen with the vowel-initial suffix in the middle column. Kiparsky pointed out that these two cases are differentiated in another way as well, as r becomes syllabic in the last column but not in the middle one, because in the middle column the syncope leaves (maximally) an unsyllabified /tr/ sequence, which can be accomodated (appended) to the surrounding syllables, giving:
 x x (x 
pitar-aa
 x  (x 
pitr-aa
No such luck in the last column, there is no way to syllabify this sequence into two syllables. Thus, in this case the /r/ vocalizes, becoming a syllable peak.
 x x  (x 
pitar-bhis
 x   (x 
pitr-bhis
 x   (x 
pitṛ-bhis
Now, having created a new syllable peak, this could project a new mark onto the grid. But where should this new mark go? We know that due to the no crossing-lines constraint of Autosegmental Phonology (which Projection is a special case of), the new mark must go in-between the marks for the two i’s. However, there is a left boundary in-between these two marks as well, and it isn’t connected to anything. Therefore we could introduce the new mark either to the left (outside) or to the right (inside) of the boundary. Evidently, what Sanskit does is project the new mark to the right (inside) of the floating left parenthesis:
 x x  (x 
pitar-bhis
 x   (x 
pitr-bhis
 x(x  x 
pitṛ-bhis
We should now return to look at the zero-grade ablaut in one other case. We saw that it applies in disyllabic unstressed stems. It also applies in disyllabic stressed stems, as shown by the paradigm for ‘brother’:
bhráatar-ambhráatar-aabhráatṛ-bhís'father'
Thus, the final vowel of the stem is subject to ablaut before inherently stressed suffixes regardless whether or not the suffix carries the word stress (ictus). (For a dissenting view see Wilson (1991)). We can handle this within the present theory very simply. The metrical component of the zero-grade ablaut rule is: x → Ø / x _ ( x
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a The ablaut rule also has further morphological and phonological conditions. For example, ccording to Kiparsky, the vowel must be adjacent (on either side) to a continuant. Further, lexically stressed vowels do not ablaut (as might be expected). I have encoded this condition as the left context of a grid mark. The presence of an immediately adjacent grid mark necessitates that there is no intervening boundary, ensuring that the target vowel does not begin a constituent. It is the direct interpretation of BGs that allows the negative condition of “unstressed” vowel to be recast as the positive condition of an immediately left adjacent grid mark. In tree theory this negative condition is particularly tricky to state, as the preceding grid mark may belong to the same foot (as in brother) or may be unmetrified (as in father). However, this formulation of the ablaut rule will restrict its operation to bisyllabic stems. I have no idea whether there is anything to be gained or lost by this, as I do not know the facts with mono-syllabic stems. Thus, Sanskrit zero-grade ablaut provides evidence for the “abstract” constituents in the analysis of Indo-European-like systems.

Russian plus tone rule (Purnell 1997)

Not a separate system of tone (contra Inkelas and Zec)

Jakobson p.c. to Morris

Tom Purnell, Sun-Hoi Kim, Vance, Pierrehumber and Beckman

Russian in reverse

difference between final accented and final unaccented phonetically

= open (unacc.) vs. closed (acc.)

Cognition versus phonetics

Sun-Hoi: Narada = Tokyo with tone-flip

Sun-Hoi Kim: analysis like Japanese

Woohyeok Chang: phonetic evidence for open vs. closed

Unbounded system

Last coronal else first

Project onsets, coronals also project "(", Feet: R2RNI , Project:L

van der Hulst and van de Weijer

plain: x, stressed: x), pre-stressing: )x

or (x with Foot: L2LNI -- no, then final pre-stressing will foot

Foot: L2RNS gets lack of secondary stress in clash

gel-)me-DI-)mI --> gélmedìmi for Barker, apparently w/o final secondary stress

Like Turkish (!) + Russian

Stem + suffixes + enclitics

Foot: )x#, plus non-iterative foot: xx) -> (xx)

Enclitics: +...)x+

Follow Russian dominant story, but all line 2 get tone

Greek could probably have iterative feet on stem, no way to tell.

Iterative versus non-iterative (extra conditions on rule?, EC)

Simple iambic system, but tone not stress

Threes (Foot: R3LIS) and! twos (Foot: L2RIS)

Evidence for both ( and ) with fortition, stress

no more avoidance constraints

Failure to project degenerate feet?

Other way: (xxx -> (xxx), (xx -> (xx), Project R,) etc

resolution: #LH gets initial stress

still need deletion (clash) rules?

Foot: R2LNS

MacDonald 1990:84 Primary stress falls on the final syllable in a word, with secondary stress on preceding alternate syllables. The initial syllable in a word is never without stress; if a word is polysyllabic, the initial syllable always receives secondary stress, even if this resulsts in adjacent stressed syllables.

Foot: R2LNI, R2RII; Project: R

Stress trains clash at end of stem

Stems: L2LII, Suffixes L2RIS, Project L

Another BAP-type stress system

Glottalization prosody like Japanese palatal prosody

Near the stress

Project rimal sonorants, stress vowel projects (

Foot: R2LIS, Project: R(, Project: L

Applied to syllable structure?

Very simple CR → (CR), R → R), ) → Ø / _ x ) (hiatus)

mna → mnmna in reduplication (man, men)

pwi → pupwi

Rules ordered by sonority

Ca → (Ca), etc.

Codas = unsyllabified elements

Line 0 projection by Head:R

"breaks" in syllabification project as ) onto grid?

Can all heavy-syllable languages be done with )????

End of document.


References


Notes