Harmonic Grammar and Harmonic Serialism consists of thirteen chapters addressing matters of empirical, theoretical and typological concern to Harmonic Grammar (HG) and Harmonic Serialism (HS).Footnote * As the editors note in their preface, HG and HS are ‘in some ways relatives of OT [Optimality Theory] in that they incorporate much of its structure (e.g., candidate comparison by markedness and faithfulness constraints)’, except that ‘HS questions the choice of parallel over serial evaluation, while HG questions the assumption that constraints are ranked rather than weighted’. Anyone interested in an introduction to and further developments within either HG or HS, or wondering why one would want to pursue one or the other of these theories rather than their better-established relative, will be more than profitably occupied by perusal of the chapters in this book.
In Part I, ‘Introductions to Harmonic Grammar and Harmonic Serialism’, the editors each contribute a chapter: ‘Universal grammar with weighted constraints’ (by Pater) and ‘The theory and practice of Harmonic Serialism’ (by McCarthy). The rest of the chapters are divided into ‘Analysis and typology’ (Part II: Chs 3–11) and ‘Learning’ (Part III: Chs 12 and 13). Part II is the focus of this review, with some discussion of Part I along the way and (with regret) little more than honourable mention of Part III.
1 More HS than HG
Ten of the thirteen chapters are concerned almost exclusively with HS, as opposed to HG. Two of these chapters (Emily Elfner's ‘Stress-epenthesis interactions in Harmonic Serialism’, and Robert Staubs & Joe Pater's ‘Learning serial constraint-based grammars’) contain some discussion of a hybrid theory, Serial HG, which assumes both weighted constraints and serial evaluation. Pater's introduction also contains discussion of Serial HG, as well as of Maximum Entropy Grammar (MaxEnt; on which also see Staubs & Pater's chapter) and Noisy HG (see also Paul Boersma & Joe Pater's ‘Convergence properties of a Gradual Learning Algorithm for Harmonic Grammar’).
The bias toward HS is either welcome or unfortunate, depending on one's point of view. On the one hand, work in HS tends to address more ‘traditional’ phonological problems (locality vs. globality of process interaction; opaque process interaction), and it has the appealing veneer of a just-right compromise between constraint ranking and process ordering. On the other, HG is the more direct gateway from OT to theories such as MaxEnt and Noisy HG that are featured in more of the bleeding-edge work in our subfield on variation and learning – including Staubs & Pater's chapter, where MaxEnt is also used in the context of learning (variation in) HS grammars. Being something of a traditionalist myself, I was generally unperturbed by the skew while reading the book; taking a step back afterwards, and considering what I could have learned from a book with this title, however, I felt a little more disquieted. But, as the preface notes, HG and HS are ‘the two theories that give this book its title’, which hardly commits the editors to a balanced review of both.
2 Defining theories
The discussion to follow will benefit from a (very) brief overview of HG and HS, and how each differs from OT. OT defines the mapping from underlying forms (more generally, ‘inputs’) to surface forms (‘grammatical outputs’) as follows. A given input is related to a set of output candidates by a generation function called Gen; each candidate in the set represents a set of modifications, possibly empty, of the input.Footnote 1 Output candidates are compared against a set of constraints referred to as Con: markedness constraints, which penalise particular output structures, and faithfulness constraints, which penalise particular disparities between input and output. These constraints are ranked in a strict dominance hierarchy, such that the grammatical output is the output candidate that, in every pairwise comparison with another output candidate, better satisfies the highest-ranked constraint on which the two output candidates differ. This is the evaluation function in OT, generally referred to as Eval.
HG differs from OT primarily in terms of how the evaluation function works. In HG, constraints are weighted, rather than ranked as they are in OT. Violations of a given constraint by an output candidate (represented as a negative integer) are multiplied by that constraint's specified (and positive) weight; the sum of the weighted constraint violations incurred by a given output candidate is that output candidate's Harmony, and the grammatical output is the output candidate with the highest Harmony value.Footnote 2
HS differs from OT primarily in terms of how the candidate-generation function works. In HS, Gen is limited to making up to one modification to the input, rather than the potentially larger set of modifications allowed by Gen in OT. All such minimal modifications are compared against the set of ranked constraints, exactly as in OT's Eval, but the winner of this comparison is then resubmitted as a new input to Gen, which generates another round of minimal modifications that are again compared – and so on until the winner is the output candidate with no modification at all. This final ‘step’ is the point of convergence, and the winning output candidate at this step is the grammatical output.
A final, terminological note. Both HG and HS have the word ‘Harmonic’ in their name, perhaps giving the impression that these are more related to each other than either is to OT. Such an impression would be a false one, however. The term ‘Harmony’ refers specifically to the sum of weighted violations of all constraints by a given output candidate; that is, to the evaluation function as it is defined in HG. Harmony per se is thus nowhere to be found in either OT or HS, where no number of violations of a lower-ranked constraint is sufficient to outweigh a single violation of a higher-ranked constraint, due to the strictness of strict domination property of OT/HS constraint ranking. So while the term is found in the name ‘Harmonic Serialism’ and in phrases like ‘harmonic bounding’ and ‘harmonic completeness’ in OT/HS work, in these contexts it stands at some distance from its original meaning.
3 Constraints
Alongside the usual questions of interest to phonologists (what are the phonological representations of inputs and outputs?; what are the right analyses of particular phonological patterns?; etc.), a key question to be addressed in OT, HG and HS is: what are the constraints? Answers to this question are typically informed by evidence from various sources: analytical concerns, formal commitments, functional convictions and typological considerations.
In this context, a typology is a set of grammars predicted by a given hypothesis about the content of Con.Footnote 3 As Pater discusses in Chapter 1, the difference between the evaluation functions in OT and HG means that the typology predicted in OT will in general be a subset of the typology predicted in HG, given the same set of constraints.Footnote 4 Assuming that other sources of evidence (analytical, formal and functional) are not relevant, then if the ‘right’ (i.e. sufficiently expressive and appropriately restrictive) typology is the smaller one predicted in OT, then a different set of constraints will be necessary to generate that same typology in HG; conversely, if the ‘right’ typology is the larger one predicted in HG, then a different set of constraints will be necessary to generate that same typology in OT.
Karen Jesney's ‘Positional constraints in Optimality Theory and Harmonic Grammar’ offers a particularly convincing demonstration of this point. As Jesney shows, accounting for complex positional licensing patterns requires two types of constraints in OT: positional markedness for conjunctive licensing (given two licensing contexts A and B, a feature F is licensed only if it appears in both A and B) and positional faithfulness for disjunctive licensing (F is allowed only if it appears in either A or B). In HG, both conjunctive and disjunctive licensing patterns can be accounted for with just one or the other type of positional constraints, given the right weighting conditions. Adopting HG thus accounts for both types of positional licensing pattern while reducing the set of constraint types, and thus (more significantly) avoids pathological predictions particular to positional faithfulness.
The difference between parallel and serial evaluation in OT and HS respectively also means that the typology predicted in OT will differ from the typology predicted in HS. McCarthy discusses this point in Chapter 2, focusing mainly on Jesney's (Reference Jesney2011) HS solution to the problems with positional faithfulness alluded to just above. This solution relies on the hypothesis that faithfulness constraints in HS assign violations locally, to the single disparities between inputs and outputs incurred at each step of an HS derivation, rather than globally, to the (potentially) larger sets of disparities between underlying and surface forms (as they do in OT, where there is only one relevant ‘step’).Footnote 5
Wendell Kimper's ‘Positive constraints and finite goodness in Harmonic Serialism’ also illustrates this point. As Kimper shows, HS can include constraints that reward output candidates – in addition to, not instead of, constraints that penalise them – without necessarily running afoul of the ‘infinite goodness’ problem that inevitably arises when such positive constraints are allowed to roam free in OT (Prince Reference Prince and de Lacy2007b). Briefly, the infinite goodness problem is this: given a markedness constraint M that rewards the presence of some structure X, then under certain ranking conditions X will be inserted ad infinitum in order to better satisfy M. This problem is avoided in HS to the extent that insertion of the relevant X requires more than one modification: if any modification on the way to X-insertion does not satisfy M, then it will not win the local comparative evaluation, and the path to ultimate X-insertion will be blocked. In this way, Kimper argues that a positive feature-spreading constraint avoids the infinite goodness problem to the extent that (a) only spreading of a feature satisfies the constraint, and (b) insertion of a segment and spreading of a feature to it are distinct modifications.
4 Modifications
As McCarthy notes in Chapter 2, a specific question arises in HS about the nature of Gen: what counts as one modification? McCarthy helpfully illustrates a method for answering this question within the context of a particular analysis, and links the result of that illustration to a theoretically grounded hypothesis. The illustration involves syncope and resyllabification in Cairene Arabic, and the particular version of the question is whether these occur separately (because each counts as a modification) or in tandem (because only one counts as a modification). McCarthy provides evidence internal to Cairene Arabic that syncope and resyllabification must count as one modification in tandem, and points to the consistency of this result with McCarthy's (Reference McCarthy2007) proposal that unfaithful modifications (such as syncope, which violates Max(V)) count as modifications, while faithful modifications (such as resyllabification, which violates no faithfulness constraint) do not.
Several other chapters confront the issue of whether – and if so, in what way or to what extent – (re)syllabification counts as a modification. These chapters generally acknowledge and cite each other's sometimes competing claims (and those made in other HS work), but the only explicit acknowledgement that some common ground must be reached – and a proposal for how to get there – is found in a footnote by Pater in Chapter 1 (note 7 on page 35): ‘serial initial syllabification, and parallel resyllabification’.Footnote 6
The more general what-counts-as-one-modification theme emerges with respect to processes other than (re)syllabification in other chapters. Claire Moore-Cantwell's ‘Contexts for epenthesis in Harmonic Serialism’ outlines a specific theoretical hypothesis, that ‘epenthesis respects Exhaustivity’ – more transparently, that an inserted constituent must be dominated by a constituent at the next level up the prosodic hierarchy. Exhaustivity was proposed as a violable constraint in Selkirk (Reference Selkirk, Beckman, Dickey and Urbanczyk1995) to allow for weak layering, for example (see Ito & Mester Reference Ito, Mester and Honma2003); Moore-Cantwell recruits it as part of a hard restriction on Gen, and demonstrates how it constrains HS derivations in such a way as to allow epenthesis to resolve segmental and syllabic markedness, but not metrical markedness.Footnote 7
This key question aside, the assumed gradualness of HS derivations vs. the relative gestalt of OT mappings means that the typology predicted in HS is both more restrictive (because it curtails excessively global interactions) and more expressive (because it allows certain opaque interactions) than the typology predicted in OT. Arguments for the benefits of both of these differences are highlighted in several chapters in the book.
Right out of the introductory gate, McCarthy, Pater & Kathryn Pruitt's ‘Cross-level interactions in Harmonic Serialism’ defends HS's curtailment of excessively global interactions by demonstrating that both top-down and bottom-up interactions between syllabification and foot structure, which formed the basis of early arguments for OT's parallel architecture and ‘against serialism’, are still accounted for with HS's serial architecture, because those early arguments were ‘arguments against specific serial theories that have very little to do with [HS]’ (p. 134). In other words, these authors argue that interactions in HS are ‘global enough’ to account for a range of observed effects that were heretofore thought to require OT's parallelism. Minta Elsman's ‘Parallelism vs. serialism, or constraints vs. rules? Tongan stress and syllabification revisited’ makes a similar point, focusing on a single case. And while these two chapters focus on the sufficiency of HS's globality, the focus of Robert Staubs’ ‘Serial restrictions on feature/stress interactions’ is on its limits. More specifically, Staubs shows that a set of pathological interactions between features and stress predicted by OT's more expressive globality, identified by de Lacy (Reference de Lacy2002), are avoided in HS.Footnote 8
Near the other end of Part II lie two cases for HS's allowance of certain opaque interactions. Elfner's chapter makes the case for stress assignment and epenthesis being separate, serially ordered operations in HS to account for the behaviour of well-known examples in which epenthetic vowels are ‘invisible’ to stress. This is helpfully contrasted with Alderete's (Reference Alderete, Hermans and van Oostendorp1999) Head-Dep account, which Elfner argues to be both too expressive and too restrictive. Torres-Tamarit's paper makes the case for vowel lengthening and consonant deletion/devoicing being separate, serially ordered operations in HS, to account for compensatory and other opaque vowel-lengthening patterns.
Rounding out Part II is Matthew Wolf’s ‘Cyclicity and non-cyclicity in Maltese: local ordering of phonology and morphology in OT-CC’. This chapter is technically concerned with McCarthy's (Reference McCarthy2007) OT-CC (‘OT with candidate chains’), a distinct theory with HS under the hood, and further elaborated to accommodate opaque process interactions that are beyond the reach of OT, HG and HS. In OT-CC, an HS-like system constructs from a given input a finite set of candidate chains: ordered sets of representations that consist of the input, an output and harmonically improving, one-modification-at-a-time representations in between. These candidate chains are compared with a constraint hierarchy that includes ‘Prec’ constraints, which essentially require particular precedence relations between modifications within the candidate chains. In McCarthy (Reference McCarthy2007), these Prec constraints are largely limited to typical phonological operations (e.g. insertion, deletion and feature changes); Wolf extends these to include morphological spell-out operations to address an apparent paradox in the cyclic interaction of stress and syncope in Maltese.
5 Software check
One of the extraordinary benefits of working in formal linguistics nowadays, and in OT, HG and HS in particular, is the availability of software tools to aid in the analysis of individual language patterns, in the analysis of typology, and in the verification of both. Several authors mention their use of OT-Help (Staubs et al. Reference Staubs, Becker, Potts, Pratt, McCarthy and Pater2010), a tool developed at the University of Massachusetts Amherst (where nearly all of the authors in this collection have been affiliated) specifically to do (comparative) analytical work in parallel OT, HG, HS and Serial HG.Footnote 9
At many points in my reading of the book, I wished for easy access to the files created by these authors so that I could verify specific analytical claims myself, or so that I could quickly follow up on an idea generated by consideration of those claims. Of course, one could correspond with the individual authors to see if they would be willing to share their files, but a centralised, accessible repository of online supplementary materials to accompany the work would be ideal. I'm pleased to add that the editors agree with this suggestion, and now plan to create such a repository.Footnote 10
6 Concluding remarks
The editors point out in their preface that both HG and HS technically antedate OT: ‘[HG] is the name of the weighted constraint predecessor of OT first characterized in [Legendre et al. (Reference Legendre, Miyata and Smolensky1990)], while [HS] was used in Prince and Smolensky's early analysis of Berber syllabification that became the first substantive chapter of [Prince & Smolensky (Reference Prince and Smolensky1993)]’. The use of OT as a yardstick is thus not due to its prior chronological claim to our attention, but rather to how established it has become (or how entrenched, depending on one's point of view). For better or for worse, the benchmark status of OT means that much of the content in Harmonic Grammar and Harmonic Serialism is taken up by (sometimes defensive-seeming) comparison: OT predicts some good thing (e.g. limited global interactions) and HG/HS can too; OT predicts some bad thing (e.g. excessive global interactions) and HG/HS can't; OT doesn't predict some good thing (e.g. some opaque interactions), but HG/HS does. While it's hard to see how this could have been avoided, it leaves less room for the reader to assess HG and HS simply on their own terms.
An example that particularly struck me can be found in McCarthy, Pater & Pruitt's chapter. The authors compare OT and HS analyses of the same set of facts (epenthesis, shortening and apocope in Yawelmani), requiring two overlapping constraints in the HS analysis (*Complex-Coda and *Superheavy), but only the latter in the OT analysis. The distinction is argued to be independently necessary in both OT and HS by appeal to another set of facts in a different language (syncope in Sudanese Arabic). This argument left me wondering when the postulation of a constraint in an HS analysis will be defensible solely on HS's own terms, without asking whether it is also necessary in OT.
And yet the overall impression I am left with is distinctly positive. The chapters are required reading for anyone interested in HG, HS, OT and related theories, from the minds of many who have been working most intently on them.
