To explain the effect of rounding, they note that rounding lengthens the vocal tract, but the vowel constriction remains in the same horizontal location; this advances the area of perceptual stability, so that a front rounded vowel can be retracted less than a front unrounded one before changing perceptual categories. Similarly, for height, they note that the constriction required for lower vowels has less flexibility along the horizontal dimension, so that the potential for perceptually stable retraction of a lower front vowel is less than that of a higher vowel.
Overall, they suggest that the effect of height and rounding on neutrality has a phonetic basis in the relationship between articulation, acoustics, and perception for vowels of different height and rounding. Moreover, Beddor et al. These authors and others e. As such, if coarticulation has a smaller effect on higher vowels, then these vowels are less likely to harmonize in a phonological system i. Thus, the height effect could be attributed to phonetic properties of coarticulation, independent of phonological harmony.
A proper account of the behaviour of Hungarian front unrounded vowels must consider their quality as potential targets in order to capture this critical broader generalization. Specifically, the theory should predict the Hungarian pattern, but not a case where lower vowels are neutral and higher vowels are not, which is unattested. Although it is typically ignored in analyses, the non-neutrality of Hungarian [e:] in suffixes i. This section describes the problems that this alternation poses to standard categorical analyses of Hungarian and the new view of neutrality that it suggests.
In standard analyses of Hungarian vowel harmony e. Ranked above the harmony-enforcing constraint, this general markedness constraint prevents [e:] from undergoing harmony and allows it to be neutral. To my knowledge, there is no discussion in the theoretical literature about why [a:] does undergo harmony, despite also being unpaired. The fact that [e:] can act as the harmonic counterpart for [a:] raises critical questions about this view of neutrality.
The tableaux in Tables 4 and 5 demonstrate this problem, adapting the analysis of Maasai re-pairing from Pulleyblank et al. Thus, the disparate behaviour of the two unpaired vowels [a:] and [e:] in Hungarian means that we cannot assume that general markedness, alone or in combination with faithfulness to other features, determines whether a vowel is a harmony target. Instead, neutrality must be derived in some other, more vowel-specific way. Before considering the target-based view adopted here, I outline two potential solutions that are formulated within more traditional views of harmony, as well as the reasons for rejecting them.
Thus, the height generalization cannot be captured in an analysis where the asymmetry falls to the separation of faithfulness constraints.
In this type of analysis, it is also impossible to connect this alternation to the idea that [e:] is intermediately neutral. A second possibility framed within more traditional work is that only [—back] vowels trigger harmony, and non-low front unrounded vowels are unspecified for [back]. In that case, only back vowels can undergo harmony. Such an approach fails to account for why front rounded vowels are not neutral in suffixes. Given Richness of the Base and the wide inventory of suffixes in Hungarian, we expect the possibility of underlying front rounded vowels in Hungarian suffixes.
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In other words, we would predict a divide in which all front vowels can occur in native non-alternating suffixes, while back vowels cannot. This is unexplained if only [—back] can trigger harmony. Thus, this solution is undesirable as a way to explain the asymmetry between [a:] and [e:]. Moreover, if only [—back] can trigger harmony and front unrounded vowels are unspecified, there is no way to derive the variability described in Section 2. This argument also extends to the behaviour of disharmonic roots i. If only [—back] can trigger harmony, then back vowels cannot trigger backness in the suffix, and so it is incorrectly predicted that front-back disharmonic stems should take front suffixes.
We might try to claim that stem-internal disharmony begins a new harmony domain, and that back suffixes are a default value; however, doing so would leave the last-resort triggering in 3 unexplained. Indeed, if front unrounded vowels are unspecified for [back], suffixes for neutral-only stems should also contain a default value, yet the value in this case is front.
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Thus, it is inconsistent with the Hungarian data to claim that only [—back] can trigger harmony. Due to the aforementioned problems with solutions in which neutrality is determined by lack of a harmonic counterpart, I argue that the Hungarian patterns require a fundamental change in how we view targets of vowel harmony: it suggests the need to consider the nature of each vowel as a possible harmony target. I propose that the drive to undergo vowel harmony differs by vowel, in a way motivated by cross-linguistic and phonetic properties, and that cases of neutrality do not occur simply because harmony is impossible, but because the vowel-specific drive to undergo harmony is too weak to force unfaithfulness.
This notion is gradient, and so will be able to avoid the issues of the categorical views. As such, the drive for lower vowels, such as [a:], to undergo harmony should be stronger than the drive for the non-low, unrounded vowel [e:]. The result, in Hungarian, is that [a:] is consistently a harmonic vowel, while [e:] can be neutral. The additional fact that [a:] is unpaired in the inventory, yet required to be a target, is what forces it to re-pair to [e:].
Moreover, the basic height effect in Hungarian is in direct accordance with the phonetic facts: the higher the vowel, the worse it is as a target of harmony, and therefore the more likely it will be to be neutral. To formally implement the new view of neutrality described in Section 4. This section provides the theoretical background, assumptions and motivations of my analysis; the application to Hungarian is left for Section 6. Harmonic Grammar HG; Legendre et al. In the specific implementation that I adopt here, I follow Potts et al. There are often many options that will work for the weight of each constraint; the specific choice is arbitrary e.
Bowman Within HG, it has been proposed that violations of a constraint can be multiplied by a scaling factor , which allows properties of a specific violation to influence the degree to which the violation is weighted e.
Kimper ; see also Coetzee and Kawahara for scaling factors of a different type. As an example, in this paper, a scaling factor based on target quality will be applied to the harmony constraint. However, if the vowels [y] and [i] have target scaling factors of 4 and 2 respectively, then [u…y] will incur twice the penalty for this disharmony than will [u…i]. Further details are reserved for Sections 5.
The total of all penalties for all constraints is called the harmony score, and the candidate with the highest harmony score wins. Since the expression is always negative, the winning candidate will be the one with a harmony score closest to zero Potts et al. An important theoretical implication of the Hungarian pattern is that the target-sensitive harmony constraint must be negatively formulated, in the sense that disharmony is penalized.
However, in Hungarian, the good target [a:] becomes a poor target, [e:], while the reverse does not always occur. Instead, the direction of the Hungarian asymmetry necessitates a penalty for good targets that have not undergone harmony. Non-harmonized [a:] will be heavily penalized, and so [a:] is required to harmonize, whereas non-harmonized [e:] will be penalized less and therefore permitted.
As long as there is a mechanism to distinguish trigger and target, the specific constraint used to enforce harmony is independent of both the principle of target scaling and the perspective that neutrality is caused by the drive to undergo harmony being too weak. For example, a sequence such as [u…y 1 …y 2 ] violates 7 twice, once for [y 1 ] and once for [y 2 ], both of which are preceded at some distance by a back vowel [u]. The fact that [y 1 ] intervenes between [u] and [y 2 ] is irrelevant to the fact that a violation is assigned. On the other hand, the sequence [y 1 …y 2 …u] violates 7 only once, for the [u] that is preceded by a front vowel.
Since Hungarian harmony is progressive, this constraint counts violations based on the number of vowels that could be targets of harmony but are not. Thus, for each pair of vowels violating the constraint, the target scaling factor is based on the vowel for which the violation is counted the focus , while the trigger is the closest preceding vowel of the opposite [back] value the context. For example, in [y 1 …y 2 …u], the one violation has trigger [y 2 ] and target [u]. The two violations in [u…y 1 …y 2 ] both have trigger [u], and the targets are [y 1 ] and [y 2 ] respectively.
This approach therefore differs from that of Pulleyblank in that the constraint is consistently oriented not to a specific value of the feature [back], but rather to the second vowel in a disharmonic sequence. This choice offers a conceptual advantage for a case of harmony like Hungarian, which is arguably progressive and triggered by either feature value, because it offers an easy way of identifying the trigger and target for each violation.
In addition to providing an inherent definition of trigger and target, this type of constraint has a more natural way of dealing with transparency than other options. Spreading-type constraints like A LIGN [back] or S PREAD [back] generally require significant representational complexity, such as line crossing, gapped configurations, or output underspecification, to deal with transparency e. In contrast, a target-oriented constraint captures the generalization that all vowels should be targets of harmony when a potential trigger is present; no additional representational complexity is required, and transparency is derived because whether other potential targets intervene is irrelevant to whether the constraint is violated.
It is worth noting that the main cases of harmony that Pulleyblank discusses are dominant-recessive systems, and the constraints are oriented towards the recessive target feature value, such as ATR in Yoruba. Thus, although Pulleyblank does not discuss targets, the constraint here is consistent with the insight of his constraints, despite the distinct implementation. The next two subsections deal with how this constraint will be scaled in the current framework to allow for transparency.
In order to explain asymmetries in triggering behaviour in vowel harmony, Kimper introduces a trigger strength scaling factor for his harmony constraint. As described in Section 5. Thus, it has the effect of increasing the likelihood of harmony when the potential trigger is perceptually impoverished for the harmony feature, which is a characteristic of good harmony triggers Kimper Trigger strength is therefore vowel-specific, but cross-linguistic and phonetically motivated, exactly parallel to the concept of target-specific harmony advocated for here.
Kimper employs a more complex formal model than the one necessary here, but the scaling factor that he develops for trigger strength forms the basis for the current approach to vowel-specific targeting.
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This constraint refers to rewards, since Kimper and Bowman use a harmony constraint that is formulated positively, meaning that harmonic configurations are rewarded. As discussed in Section 5. However, the trigger strength scaling factor can easily be reformulated for a negative constraint, as in 9. The result is that not harmonizing is worse with a good trigger than with a bad trigger. This scaling factor is then applied to the weight of the harmony constraint in the way described in Section 5.
As such, a disharmonic sequence in which [y] is the potential trigger will receive a greater penalty than one in which [i] is the potential trigger. In order to capture the fact that Hungarian neutral vowels are transparent instead of opaque, I adopt the trigger scaling factor in 9 in addition to the target one introduced in Section 5. See Kimper and Bowman on the application of trigger strength to Hungarian. Kimper also proposes a distance scaling factor, which is particularly relevant for the count effect in Hungarian; he suggests that the reward of harmony decreases as the distance between the trigger and target increases.
Since I formulate the harmony constraint negatively here, in this case, the penalty will decrease. A definition of the distance scaling factor, based on the simplified version in Bowman , is given in In Hungarian, this factor will have the effect of penalizing disharmony less at a greater distance, which will create the count effect; with multiple neutral vowels, the back vowel in the root is further from the suffix target, and so a front suffix will be penalized less than it would with only a single neutral vowel.
As argued in Sections 2 through 4, whether a vowel undergoes harmony or not is sensitive to its quality as a potential target. The statement of this scaling factor is given in Parallel to the one for trigger strength, this scaling factor has the effect of increasing the penalty for disharmonic pairs when the potential target is a good harmony target.
In this definition, I remain agnostic on the precise factors that determine target quality; an in-depth analysis of the underlying mechanisms behind target quality is left for future research. This scaling is implemented within the model as described in Section 5. Both trigger and target scaling factors are hypothesized to be universal, but only in the sense that they are motivated by cross-linguistic phonetic facts and are options across languages. The option for equality allows for symmetry, but if there is asymmetry, it must be in the direction of less participation of non-low, unrounded vowels.
Formally, this universal hierarchy is implemented here through the phonetic motivations behind the target scaling factor in the definition, and the possibility of conflation comes from the option for multiple categories to have the same scaling factor. Recall that the target scaling factor itself is defined in terms of phonetic correlates of target quality, so that this hierarchy is not simply stipulated.
It remains for future research to determine whether the scaling factors described here and the stringency hierarchy of constraints discussed by de Lacy are notational variants or whether they in fact make distinct predictions. As discussed in Section 2.