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Factorial Typology

To have a basic understanding of what kinds of languages the model predicts, let us consider the possible fates of an underlying contour tone that are predicted by the factorial typology of the proposed constraint families.

Suppose that in language L, there exists an underlying contour tone T with a pitch excursion of f under the standard speaking rate and style. Let us see what the possible predictions of the grammar are when the contour encounters a rime R whose CCONTOUR value is c and whose minimum sonorous rime duration is d. The predicted input-output mapping may be the characterization of either alternation or static phonotactic requirement. The latter construal requires the assumption of the Richness of the Base (Prince and Smolensky 1993, Smolensky 1996).

During the discussion of the factorial typology, since the only attested way to increase a syllable’s CCONTOUR value from the input to the output is to lengthen its sonorous rime duration, as discussed in §7.2.2, for candidates that differ from the input in CCONTOUR value, I only consider those that manipulate the sonorous rime duration, and I use the sonorous rime duration d instead of directly referring to the CCONTOUR value c in the candidates. Again, I refer the interested reader to Steriade (2001) and Wilson (2000) for possible ways of eliminating other fixes.



      1. No Change Necessary

The first possibility is that the Pres(Tone) and *Dur constraint families outrank *Contour(T)-CCONTOUR(R) en masse. Under this ranking, the contour faithfully surfaces on the given rime without lengthening. This is because any flattening of the contour or lengthening of the sonorous rime duration in order to satisfy *Contour(T)-CCONTOUR(R) will incur violations in the higher ranking Pres(Tone) or *Dur constraint families, as illustrated by the tableau in (0).


(0) Tf, Rd —> f, d


Tf, Rd

Pres(Tone)

*Dur

*Contour(T)-CCONTOUR(R)

faithful:

f, d







*

contour reduction:

f-f0, d



*!







rime lengthening:

f, d+d0






*!



This ranking also predicts that on a rime R’ with a greater CCONTOUR value than c, f will also be faithfully realized, since the constraint *Contour(T)-CCONTOUR(R’) will be even lower ranked than *Contour(T)-CCONTOUR(R). This is consistent with the implicational hierarchies established in the typological survey of contour tone distribution, since the implicational hierarchies all show that if a contour can occur on a syllable with a shorter canonical duration, then it can also occur on a syllable with a longer canonical duration. And indeed, languages of this sort are attested in the survey. As I have discussed in §4.6.3, a number of languages in the survey do not exhibit any restrictions for the occurrence of contour tones. For example, !Xu) (Doke 1925, Heikkinen 1986, Snyman 1970), ¯Khomani (Doke 1937), and a number of Chinantec languages allow all tones on all syllable types, be they open or checked, long-vowelled or short-vowelled. Although most of the sources I consulted on these languages do not give phonetic details of tone and duration, thus it is possible that the contour tones on shorter syllable types are somewhat flattened, or these syllables are somewhat lengthened, there is some phonetic documentation on Lalana Chinantec (Mugele 1982) which shows that the same contour tone exhibits relative stability of onset and endpoint on different syllable types, and the same syllable type exhibits relatively stable duration when carrying different tones.



      1. Partial Contour Reduction

The second possibility is that *Contour(T)-CCONTOUR(R) outranks some, but not all Pres(Tone) constraints, but the *Dur constraint family en masse is still undominated. Under this ranking, the contour is flattened to satisfy the *Contour(T)-CCONTOUR(R) constraint, but no extra duration can be added to the sonorous portion of the rime. This is illustrated in the tableau in (0).


(0) Tf, Rd —> f-f0, d


Tf, Rd

*Dur

*Contour(T)-CCONTOUR(R)

Pres(Tone)

faithful:

f, d




*!




contour reduction:

f-f0, d







*

rime lengthening:

f, d+d0



*!






This ranking also predicts that on a rime R’ with a greater CCONTOUR value than c, f will be more faithfully realized, i.e. realized with less or no reduction of the pitch excursion. This is because the relevant *Contour(x)-CCONTOUR(y) constraint *Contour(T)-CCONTOUR(R’) will be lower ranked than *Contour(T)-CCONTOUR(R), and this will allow more Pres(Tone) constraints to exert influence on the output form. This, again, is consistent with the implicational hierarchy established in the typological survey in Chapter 4. It reflects the pattern in which certain contour tones can have a full realization on syllables with longer sonorous rime duration, but are partially flattened on syllables with shorter sonorous rime duration. Pingyao Chinese’s flattening of 53 and 13 on CVO syllables to 54 and 23 is an example of this sort.



      1. Complete Contour Reduction

The third possibility is to have all *Contour(x)-CCONTOUR(R) and *Dur constraints outrank all the relevant Pres(Tone) constraints. That is, *Contour()-CCONTOUR(R), where represents the smallest pitch excursion, outranks the Pres(Tone, i) constraint that penalizes changing the tone T to a level tone. This ranking predicts that the tone T will be flattened all the way to a level tone. This is illustrated in the tableau in (0).


(0) Tf, Rd —> f-f0, d


Tf, Rd

*Dur

*Contour()-CCONTOUR(R)

Pres(Tone, i)

faithful:

f, d




*!




partial contour reduction:

f-f0, d




*!




complete contour reduction:

0, d







*

rime lengthening:

f, d+d0



*!






For the same reason as the ranking for partial contour reduction, this ranking still predicts that on a rime R’ with a greater CCONTOUR value than c, f will be more faithfully realized, i.e. realized with less or no reduction of the pitch excursion: *Contour()-CCONTOUR(R’) will be lower ranked than *Contour()-CCONTOUR(R), and this will allow more Pres(T) constraints to exert influence on the output form. This is yet again consistent with the implicational hierarchy established in the typological survey in Chapter 4. In fact, this is the most commonly attested pattern of contour tone restrictions in languages, i.e., certain contour tones cannot occur on syllables with low CCONTOUR values. We have seen many examples of this sort, e.g., Xhosa’s restriction of contour tones to stressed syllables, Navajo’s restriction of contour tones to long vowels, Cantonese’s restriction of contour tones to non-checked syllables, etc.





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