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Contour Reduction + Rime Lengthening
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Contour Reduction + Rime LengtheningThe last possibility is that *Contour(T)-CCONTOUR(R) outranks some *Dur constraints and some Pres(Tone) constraints. Under this ranking, the avoidance of the *Contour(T)-CCONTOUR(R) constraint violation is achieved by contour reduction and rime lengthening simultaneously. To illustrate this, let us assume the following: f0>f1, d0>d1, ST(f-f0)=i (meaning that the pitch excursion f-f0 is i steps away from tone T, which has the pitch excursion f, see §7.4.4), and ST(f-f1)=j (meaning that the pitch excursion f-f1 is j steps away from tone T). Given that f0>f1, we know that i>j, meaning that f-f1 is perceptually closer to tone T than f-f0. Based on the intrinsic rankings among the *Dur (§7.2.2) and Pres(Tone) (§7.2.3) constraint families respectively, these relations render the intrinsic rankings shown in (0).
b. Pres(T, i) » Pres(T, j) If *Contour(T)-CCONTOUR(R) is ranked on a par with *Dur(d0) and Pres(T, i), but outranks *Dur(d1) and Pres(T, j), then the winning candidate will have a flattened contour f-f1 and a lengthened duration d+d1. Just flattening the contour to satisfy the *Contour(T)-CCONTOUR(R) constraint is too costly for the Pres(T) constraint family as it incurs a violation of the highly ranked Pres(T, i); and just lengthening the rime is too costly for the *Dur constraint family as it incurs a violation of the highly ranked *Dur(d0). The tableau in (0) illustrates these arguments. (0) Tf, Rd —> f-f1, d+d1
This ranking also predicts that on a rime R’ with a duration longer than d, there will be a lesser degree of flattening, or a lesser degree of lengthening, or both, depending on the ranking among the lower-ranked *Contour(x)-CCONTOUR(y), Pres(Tone), and *Dur constraints. This is consistent with the implicational hierarchies established in the survey. This pattern is instantiated by Hausa, which shows both partial contour flattening and rime lengthening when a CVO syllable carries a falling contour, as shown by the phonetic data in §4.2.2.3. The factorial typology clearly predicts many variations of this pattern, but this pattern does not seem prevalent in the survey. An explanation is surely needed. I again conjecture that this might be due to the close-to-exclusive attention to the distributional facts about contours and the lack of detailed phonetic documentation of many languages. Upon closer scrutiny of the phonetic realization of tonal contours and duration of rimes that carry them, many such patterns might emerge and the range of variation predicted by the typology can be tested against these phonetic data. SummaryTo visualize the interaction of the three families of constraints, let us consider a 3-D space. The x-y plane represents candidates for the input (Tf, Rd). The origin is the faithful candidate (f, d). The x-axis represents the amount of rime lengthening, and the y-axis represents the amount of contour reduction. The z-axis represents constraint ranking. Again, the higher the z value, the higher the ranking. Let us consider three planes in this space *Contour-CCONTOUR(x, y), *Dur(x, y), and Pres(Tone)(x, y) that represent the highest ranked constraint in the *Contour-CCONTOUR, *Dur, and Pres(Tone) families respectively that the candidates on the x-y plane violate. These planes should have the following characteristics. For the *Contour-CCONTOUR(x, y) plane, it has the highest value at the origin of the space, and it decreases monotonically when x increases or when y increases. This means that the faithful candidate violates the highest ranked *Contour-CCONTOUR constraint, and reducing the tonal contour and lengthening the rime will both help resolving the violation of this highly ranked tonal markedness constraint. This plane is schematically shown in (0). (0) The *Contour-CCONTOUR(x, y) plane: 
For the *Dur(x, y) plane, its value increases when x increases, but is constant with respect to y. This means that the more lengthening the candidate has, the higher *Dur constraint it violates. But *Dur is insensitive to contour reduction. This plane is schematically shown in (0). (0) The *Dur(x, y) plane: 
For the Pres(Tone)(x, y) plane, its value increases when y increases, but is constant with respect to x. This means that the more contour reduction the candidate has, the higher Pres(Tone) constraint it violates. But Pres(Tone) is insensitive to rime lengthening. This plane is schematically shown in (0). Notice that the candidates that do not have any contour reduction do not violate Pres(Tone) constraints. (0) The Pres(Tone)(x, y) plane: 
To find the optimal candidate is to find the minimum value of the function in (0). (0) z = f(x, y) = max(*Contour-CCONTOUR(x, y), *Dur(x, y), Pres(Tone)(x, y)) This function is plotted from two different angles in (0). The optimal candidate (f-f1, d+d1) is indicated in both graphs. (0) 3-D graphs of z = max(*Contour-CCONTOUR(x, y), *Dur(x, y), Pres(Tone)(x, y)): 
We can prove that the point of intersection of the three planes is the point where the highest constraint that the candidate violates is the lowest as compared to all other candidates. Let us suppose that the three planes intersect at point (x0, y0, z0). That is to say, max(*Contour-CCONTOUR(x0, y0), *Dur(x0, y0), Pres(Tone)(x0, y0)) = z0. For a different candidate (x1, y1), if *Contour-CCONTOUR(x1, y1) < z0, then x1>x0 or y1>y0. But when x1>x0, *Dur(x1, y1) > *Dur(x0, y0) = z0; and when y1>y0. Pres(Tone)(x1, y1) > Pres(Tone)(x0, y0) = z0. Therefore, max(*Contour-CCONTOUR(x1, y1), *Dur(x1, y1), Pres(Tone)(x1, y1)) > z0. Thus we have proved that the projection of the point of intersection of the three planes on the x-y plane—(x0, y0)—indeed represents the winning candidate. As we have seen, the interaction of these three families of constraints yields six possible outputs for contour tone T on rime R. This is summarized in (0). (0) Outputs of Tf, Rd generated by the factorial typology:
In the following chapter, I provide detailed analyses for the contour restrictions in Pingyao Chinese, Xhosa, Mitla Zapotec, Gã, and Hausa, each representing a distinct contour restriction pattern. The purpose of the analyses is two-fold. Firstly, they provide a more complete picture of how the proposed theoretical apparatus can be used to capture positional prominence patterns regarding contour tones. Secondly, they provide reassurance that the theoretical apparatus can indeed capture the desired contour tone patterns. Directory: files files -> Answer True False 2 points Question 2 files -> Integer programming and game theory files -> 4 Integer Programming files -> Bpa vehicle Window Repair Scenario #1 task: Procure vehicle window relacement. Objective files -> Pop Warner History files -> North Carolina Inclusion Initiative Mapping Where Children with ieps are Being Served Purpose files -> Fall 2013 Spring 2014 Program Data: Standard 1 Exhibit 4d files -> Hanban – asia society confucius classrooms network 2010 request for proposal files -> Northern England’s set-jetting locations Download 3.01 Mb. Share with your friends:
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