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Chapter 4An OT Analysis
In this chapter, an OT analysis will be displayed and divided into two sections.
First we will discuss about rhymes without a nasal coda, including the following structures: V, GV, VG, GVG. The other section will focus on rhymes containing a nasal coda, including the structures of VN and GVN. For the structural indicating capital letters, the G preceding V indicates the prenuclear glides and the G following V indicates the postnuclear ones. For other symbols, V stands for vowel and N stands for nasal coda.
4.1 Rhymes without a Nasal Coda
4.1.1 Mid/Low Vowel Assimilation
As is mentioned in section 2.2.1, the phenomenon of mid/low vowel assimilation has been widely discussed in previous research (Duanmu, 2007; Lin, 2015). Let’s review their constraints about this phonological phenomenon in (1 – 2).
(1) NC-Harmony (Duanmu, 2007) or RIME-HARMONY (Lin, 2015)
Assign one violation mark for every syllable whose nucleus and coda have different values for [back] and [round] features.
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(2) GN-Harmony (Duanmu, 2007) or GV-HARMONY (Lin, 2015)
Assign one violation mark for every syllable whose nucleus and prenuclear glide have different values for [back] and [round] features.
Both of these analyses mention the [back] and [round] features in a single constraint. However, in order to avoid predicting the wrong outputs *[ɥə], Duanmu assigns two violation marks for each of the two features, as (3) shows.
(3) /ɥə/ → [ɥe] (Duanmu, 2007)
/ɥə/ NC-Harmony Avoid-[ø] {GN-[back], GN-[round]}
a. ɥə * *!
b. → ɥe *
c. ɥø *!
The analysis in (3) rules out *[ɥə] because [ɥ] and [ə] do not agree in not only [round] feature but also [back] feature. Therefore, I think it will be better if we separate the constraint into two, one assigning a violation mark for the [back] feature and the other for the [round] feature.
Moreover, in Duaumu’s analysis, there is a high-ranked constraint “Avoid-[ø]” to prevent the ill-formed *[ɥø] from surfacing out. In Taiwanese Mandarin though, in addition to [ø], we still need to avoid segments like [ɤ] or [ɒ]. Therefore, we can just high-rank a constraint to avoid all the segments that are not listed in the inventory instead of introducing such specific constraints, which is displayed in (5). Constraints (6 – 9) are separated from Duaumu’s and Lin’s based on the different features.
Constraint (10) is developed to ensure it is the vowel instead of the glide that changes
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its feature. Constraint (11) is the violated faithfulness constraints. The descriptive generalization is in (4).
(4) The descriptive generalization for mid/low vowel assimilation
The vowel should agree with the prenuclear glide in [back] and [round] features, but if there is a glide coda following it, it should agree with the following glide.
This requirement is enforced by vowel fronting/backing and rounding.
(5) PHONOTACTICS
Assign one violation mark for every ø, ɶ, ɯ, ɤ, ɒ and ɰ in the output.
(6) AGREE[bk]-VG
Assign one violation mark for every syllable whose vowel and glide coda do not agree in the [back] feature.
(7) AGREE[rd]-VG
Assign one violation mark for every syllable whose vowel and glide coda do not agree in the [round] feature.
(8) AGREE[bk]-GV
Assign one violation mark for every syllable whose vowel and prenuclear glide do not agree in the [back] feature.
(9) AGREE[rd]-GV
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Assign one violation mark for every glide which has a different value for the [F]
feature from its input, where [F] = [back], [round] or [nasal].
(11) IDENT[F]-V
Assign one violation mark for every vowel which has a different value for the [F]
feature from its input, where [F] = [back] or [round].
Since the [back] feature and the [round] feature should be agreed in together, constraints (6) and (7) are ranked the same high, and so are constraints (8) and (9).
Constraint (5) is never violated, so it is ranked the highest. AGREE[F]-VG8 is always prior to AGREE[F]-GV, so (6) and (7) are ranked higher than (8) and (9). In order to satisfy the constraints above, the vowel, instead of the glide, changes its value, so (10) is ranked higher than (11). Tableaux (12 – 14) illustrate how these constraints work.
The parenthesized exclamation marks indicate that either violation is fatal. The Hasse Diagram is illustrated in (15).
(12) /ɥə/ → [ɥe]
8 The F in the bracket stands for Feature, which can be substituted into [back] or [round].
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(15) The Hasse Diagram of mid/low vowel assimilation PHONOTACTICS
AGREE[bk]-VG AGREE[rd]-VG
AGREE[bk]-GV AGREE[rd]-GV IDENT[F]-G
IDENT[F]-V
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Example (12) shows how AGREE[bk]-GV and AGREE[rd]-GV both assign violation marks to rule out the candidate *[ɥə]. Example (13) proves that AGREE[F]-VG is ranked higher than AGREE[F]-GV, for candidate (13c) will be wrongly predicted as the winner if AGREE[F]-GV is ranked higher. Example (14) proves that PHONOTACTICS should be ranked higher than AGREE[F]-VG because it will be a problem to determine whether [ɑw] or *[ɒw] is the optimal candidate if these constraints are ranked the same high.
Note that the constraint IDENT[F]-G is only illustrated in example (14) because satisfying this constraint will lead to [ɰ] in examples (12) and (13), which also violates the high-ranked constraint PHONOTACTICS. For simplicity, IDENT[F]-G is only listed when it is active.
These constraints and their ranking successfully predict the correct output from each
“phonemic group” (see 3.3). However, there are still some gaps that “should be legal”
throughout this constraint ranking. For example, given an input /wəw/, an optimal output *[wow] should be predicted, but it is not attested in Taiwanese Mandarin, as is illustrated in (16). Another problem lies in the rhymes with a high vowel following a prenuclear glide. For example, given an input /ju/, this constraint ranking will predict its output as [ji], which may be interpreted as a lengthened [i]. However, it seems not to be the fact, as shown in (17). These two problems will be later discussed in sections 4.1.2 and 4.1.3.
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(17) /ju/ → ?[ji]
/ju/ PHONOTACTICS
AGREE[F]-VG AGREE[F]-GV
IDENT[F]-V [bk] [rd] [bk] [rd]
a. 💣 ji *
b. ju (*!) (*!)
c. jy *! *
4.1.2 The Phonotactic Restriction of Triphthongs
As what is mentioned in 4.1.1, rhymes such as *[jej], *[jaj] (see 3.2.3), *[wow],
*[wɑw], *[ɥej], *[ɥaj], *[ɥow] and *[ɥɑw] should be surfaced out because all of these patterns are actually the optimal choices throughout the constraint ranking. It seems that there are some more constraints which are active to these triphthongs.
To observe these absent patterns, it is found that glide [j] cannot precede a diphthong with a coda [j], glide [w] cannot precede a diphthong with a coda [w], and glide [ɥ] cannot precede any diphthongs, as is simplified in (18) below.
(18) Triphthongs that are not allowed a. *jVj
b. *wVw c. *ɥVj d. *ɥVw
Regarding to this phenomenon, Duanmu (2007) has also proposed an analysis. In
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and the postnuclear glide. In Taiwanese Mandarin (as well as other dialects), the prenuclear glide and the postnuclear glide should have different values for both of their [back] and [round] features. This is the reason why there are no such rhymes in Taiwanese Mandarin where the prenuclear glide and the postnuclear glide are identical, and [ɥ] cannot precede any diphthongs, for it is [-back] as [j] and [+round] as [w].
To deal with this dissimilation phenomenon, the Obligatory Contour Principle (henceforth OCP) is usually used. OCP was first developed by Leben (1973) for tonal dissimilation in African languages. The definition is shown in (19) below.
(19) The Obligatory Contour Principle (Ito and Mester, 1998) Adjacent identical elements are not allowed at the melodic level.
As (19) shows, OCP can only confine that two adjacent elements should not be identical (at least in the value of a certain feature). However, the problem going to be coped with here does not lie in an adjacent pairs, but two glides with a vowel in between.
To solve this problem, I refer to Ito and Mester’s (1998) interpretation to OCP. In their opinion, OCP is in fact a self-conjunction effect.
Take a look at Hsiao’s (2000) example about tone sandhi in Southern Min. In Southern Min, only the last syllable in a tone sandhi domain remains its base tone; other syllables will undergo tone sandhi. This phenomenon seems to be able to be predicted with an OCP constraint as (20) shows, where T stands for base tone. However, this is awkward because OCP is used to prevent two adjacent segments from having identical
“tone level” or “tone contour”, while the base tones for each syllable are not the same.
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(20) OCP-T
Assign one violation mark for every adjacent pair of segments which remain the base tone.
Nevertheless, if we adopt Ito and Mester’s interpretation to revise this OCP constraint as a self-conjunction, as (21) shows, the original definition of OCP will not be violated, and the constraint still remains its essence.
(21) *T2δ
Assign one violation mark for every tone sandhi domain where there are two syllables of the base tone.
Adopting this theory, the dissimilation phenomenon of the two glides in a same syllable can be enforced by a self-conjunction. This way, we can rule out the ill-formed outputs without violating the original definition of OCP.
Reviewing the unallowed triphthongs listed in (18) and Duanmu’s analysis that the prenuclear and postnuclear glides should not share the same value for either [back]
or [round] feature, we can introduce a self-conjunction to prohibit a syllable from having two glides that have the same value for the [back]/[round] feature, as is in (23), which is self-conjoined by constraint (22) below.
(22) *GαF
Assign one violation mark for every glide of [αF] feature, where F = [back] or [round].
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Assign one violation mark for every syllable which contains two glides of [αF]
feature, where F = [back] or [round].
Constraint (23) successfully rules out all the ill-formed triphthongs. However, when these candidates are ruled out, there should be another candidate to be selected as an optimal output. To solve this problem, here we have to mention the experiment in 3.2.3 again. The result of the experiment shows that Taiwanese Mandarin speakers tend to pronounce the word yai ‘cliff’ [jaj] as [aj] instead of [ja], which indicates that it is the prenuclear glide that is dropped when there are two glides having the same value for [back] or [round] feature in a syllable. The descriptive generalization is shown in (24).
In addition to constraints (22) and (23) introduced above, there are still other constraints active, as below. Constraint (25) indicates the strategy of deleting the prenuclear glide.
Constraint (26) is also listed to show another possible strategy to repair the ill-formed triphthongs. In addition to the strategy of deleting the coda, changing the coda might also be a method to satisfy the higher-ranked constraints. Therefore, IDENT[F]-G is also active here.
(24) The descriptive generalization for the phonotactic restriction of triphthongs The prenuclear glide and the postnuclear glide of a syllable should have different values for both [back] and [round] feature. This requirement is enforced by prenuclear glide deletion.
(25) MAX
Assign one violation mark for every segment in the input which does not have a correspondent output.
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(26) MAX-CODA
Assign one violation mark for every coda in the input which does not have a correspondent output.
Constraints (25) and (26) both assign a violation mark for deletion; however, (26) has a stricter definition, which is only violated when a coda is deleted, while (25) is violated no matter which segment does not surface out. Logically, it is known that when a candidate violates constraint (26), it must violate (25) as well; but not vice versa.
Therefore, it is certain that (26) should be absolutely ranked higher than (25).
To observe the result of the [jaj]-to-[aj] experiment, it is observed that there should not be two [j]’s in the syllable, so *[G2αF]σ is satisfied, and it absolutely dominates *GαF, for it is a self-conjunction (see. 2.1.3). In fact, MAX should dominate *GαF because *GαF
is violated by every candidate containing a glide. Therefore, MAX should be ranked higher than *GαF to avoid glide deletion. The prenuclear glide [j] is deleted, so MAX is violated, but the coda [j] is not deleted, so MAX-CODA is satisfied. Both of the glides do not change any features, so IDENT[F]-G is satisfied. Through these descriptions, we can rank the satisfied constraints higher and the violated ones lower, as tableau (27) shows.
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(27) /jaj/ → [aj]
/jaj/ *[G2αF]σ IDENT[F]-G MAX-CODA MAX *GαF
a. → aj * *
b. jaj *! **
c. ja *! * *
d. waj *! **
e. jɑw *! **
f. a *! **
Note that candidate (e) in tableau (27) changes its vowel from the input. Here we do not have a candidate *[jaw], which violates IDENT[F]-G as well but remain the same vowel as its input because *[jaw] is absolutely a worse choice than [jɑw] no matter how these constraints are ranked, for we have already discussed the low vowel assimilation phenomenon in 4.1.1. The Hasse Diagram of the triphthong phonotactic restriction is illustrated in (28).
(28) The Hasse Diagram of the phonotactic restriction of triphthongs
*[G2αF]σ IDENT[F]-G MAX-CODA
MAX
*GαF
As (28) shows, the example in tableau (27) shows that the optimal output for /jaj/
is [aj], which violates MAX (and of course *GαF). This indicates that the violations of
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*[G2αF],IDENT[F]-G and MAX-CODA are not allowed. Therefore, all of these constraints dominate MAX. Furthermore, since glides should not be deleted in most contexts (for example, /ja/ does not surface as [a]), MAX dominates *GαF.
The constraint ranking developed in this section may also explain the absence of the high vocoid sequences *[ɥi] and *[ɥu], for the two high vocoids which have the same values for [back] or [round] features are in the same syllable no matter whether there is a mid/low vowel between them or not. However, this analysis is controversial because the constraint *[G2αF]σ only prohibits two glides that have the same values for [back] or [round] features from appearing in the same syllable, while [i] and [u] are actually vowels. If we transcribe the sequence as two glides, it is still awkward for there will be no peak in the syllable. Moreover, in addition to *[ɥi] and *[ɥu], *[ju] and *[wi], which are also sequences of two high vocoids, are also not allowed to surface. The absence of these patterns is going to be discussed in the next section.
4.1.3 The Sequence of High Vocoids
As the previous section mentions, here we are going to discuss patterns composed of two high vocoids, none of which is surfaced out. Duanmu (2007) considers *[ju] and
*[wi] to be accidental gaps, but it is apparent that the absence of these patterns are systematic. Regarding to this phenomenon, Lin (2007) has mentioned that “glides cannot be followed by a high vowel which has a different value for the [back] feature.”
This statement here does not rule out the ill-formed pattern *[ɥi]. In fact, it is weird for Lin to specify “what kind of high vowel cannot follow a glide” because there is actually no high vowel following a glide.
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segments that are prohibited to share a certain feature, OCP, which is mentioned in 4.1.2, can be introduced as a constraint here, as in (29).
(29) OCP-HIVOCOID
Assign one violation mark for every pair of adjacent high vocoids.
In fact, it is not necessary to specifically prohibit two adjacent “high vocoids”
based on the analysis in this section. Instead, we can just prohibit two adjacent segments that are both [+high]. However, if we substitute a more general constraint called “OCP -HI” for constraint (29), it will wrongly predict the output of /iŋ/ as *[eŋ], which will be elaborated in 4.2.1.2. Therefore, in order to take the analyses of the following sections into account, here we have to specifically define that it is two high vocoids that cannot be adjacent.
In the previous section, we predict that the ill-formed triphthong *[jaj] is repaired by deleting the prenuclear glide according to how Taiwanese Mandarin speakers pronounce the word yai ‘cliff’. Likewise, now that the sequences of two high vocoids have been ruled out by constraint (29), there should be optimal outputs for these inputs.
Then, how do the sequences of two high vocoids surface out? The answer can be found from the evidence of loanwords and translated names. The examples are shown in (30 – 31) below.
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(30) Loanwords and translated names containing the sequence of [ju] in the input
English Taiwanese Mandarin
a. UFO [ju.foʊ] youfu [jow.fu]
b. Ulysses [ju.lɪ.siz] Youlixisi [jow.li.ɕi.sz̩]
c. New Zealand [nju zi.lænd] Niuxilan [njow.ɕi.lan]
d. Hugh Jackman [hju dʒæk.mən] Xiu Jiekeman [ɕjow tɕje.khə.man]
(31) Loanwords and translated names containing the sequence of [wɪ]9 in the input
English Taiwanese Mandarin
a. whisky [hwɪs.kɪ] weishiji [wej.ʂʐ̩.tɕi]
b. Will Smith [wɪl smɪθ] Weier Shimisi [wej.ɚ ʂʐ̩.mi.sz̩]
c. Quinn [khwɪn] Kuiyin [khwej.in]
d. quinacrine [khwɪ.nə.khɹin] kuinakelin [khwej.na.khə.lin]
Examples in (30) and (31) show that when a loanword or a translated name has a sequence of two high vocoids in its English origin, there will be a mid vowel inserted between the high vocoids in the translated form, and of course, the vowel will undergo a glide formation, for there should not be two vowels in a single syllable. The descriptive generalization is shown in (32).
(32) The descriptive generalization for the sequence of high vocoids
a. Two high vocoids cannot be adjacent. This requirement is enforced by mid vowel insertion.
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b. There is only one vowel in a single syllable. This requirement is enforced by glide formation of a high vowel.
According to (32a), we developed constraint (33) as a violated faithfulness constraint for an output satisfying OCP-HIVOCOID. Constraint (34) is developed to ensure the inserted vowel is a mid one instead of a low one. Constraints (35 – 36) are developed based on (32b). Constraint (35) is based on McCarthy’s (2008) list of common markedness constraint, which includes constraints called “COMP-ONSET” and “COMP -CODA” assigning violation marks for consonant cluster in the onset or coda position.
Here the candidates containing a vowel cluster should be ruled out, so a new constraint
“COMP-NUC” is introduced, where NUC stands for nucleus. Constraint (36) is used for vowel gliding since a vowel changes its value for the [syllabic] feature when it becomes a glide. In addition to the constraints mentioned in this paragraph, MAX is also active here. Tableau (37) provides an example of how a sequence of two high vocoids surfaces out.
(33) DEP-MIDV
Assign one violation mark for every mid vowel in the output which does not have a correspondent input.
(34) DEP-LOWV
Assign one violation mark for every low vowel in the output which does not have a correspondent input.
(35) *COMP-NUC
Assign one violation mark for every vowel cluster in the nucleus position.
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Assign one violation mark for every segment which has a different value for the [syllabic] feature from its input.
(37) /ju/ → [jow]
Different from previous tableaux, this one contains a doubled frame line, which indicates that the constraints left to it and right to it have no domination relations. Let’s first take a look at candidates (37a – d). The optimal candidate is (37a) [jow], which has an inserted mid vowel. Other candidates worse than (37a) include (37b) [jɑw], which has an inserted low vowel, (37c) [u], which deletes the prenuclear glide, and (37d)
*[ju], which has a sequence of two high vocoids. Among these candidates, the one violates DEP-MIDV is the most tolerable. Therefore, we can have a result that OCP -HIVOCOID, DEP-LOWV and MAX all dominate DEP-MIDV.
On the other hand, if we compare candidates (37a) and (37e), the violation differs in the fact that the former violates IDENT[syl] while the latter violates *COMP-NUC. The better output is (37a) [jow], which proves that *C -N dominates I [syl]. Here I
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studies. In this thesis, however, it is necessary to view a diphthong as a vowel plus a glide coda because it has been discussed that the prenuclear glide and the postnuclear glide should not have the same value for their [back] and [round] features (see 4.1.2).
If we transcribe the postnuclear coda as a vowel, it will be considered as a part of the nucleus, and then the constraint prohibiting the prenuclear glide and the postnuclear glide to have the same value for their [back] and [round] features will become weird, for it is therefore regulating a “segment” and a “part of segment” to share the same value for the features. As a result, in order not to be contradicted, here we introduce these constraints to ensure the vowel gliding rule.
Now two constraint rankings have been developed, as the doubled frame line in tableau (37) indicates. The fact is that we have no evidence to prove that there are domination relations between the constraints left to the doubled frame line and the ones right to it. To illustrate the constraint ranking clearer, the Hasse Diagram is available in (38). It does not matter for the candidates to be evaluated by the ranking on the left side or the right side first because [jow], the optimal output is always the last one to be ruled out.
(38) The Hasse Diagram of the sequence of high vocoids
OCP-HIVOCOID DEP-LOWV MAX *COMP-NUC
DEP-MIDV IDENT[syl]
As (38) shows, to repair a rhyme composed of two adjacent high vocoids, the best policy is to insert a mid vowel to violate DEP-MIDV. DEP-MIDV is thus dominated by OCP-HIVOCOID, DEP-LOWV and MAX. On the other hand, in order to make sure that a
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high vowel becomes a glide when there is another vowel, *COMP-NUC should dominate IDENT[syl].
4.1.4 Summary
We have discussed all the rhyme patterns that do not contain a nasal coda in Taiwanese Mandarin through the analyses so far, and have obtained the conclusions as below:
(i) Mid vowels and low vowels agree with the glide coda in [back] and [round]
feature. (see 4.1.1)
(ii) Mid vowels and low vowels agree with the prenuclear glide in [back] and [round] feature when there is no glide coda. (see 4.1.1)
(iii) When two glides that share the same values for [back] or [round] feature are in the same syllable, the prenuclear one fail to surface out. (see 4.1.2) (iv) A mid vowel is inserted between two adjacent high vocoids. (see 4.1.3) These results can almost explain the presence and the absence of the rhymes without a nasal coda listed in 3.1. As for the constraint ranking, we have developed the Hasse Diagrams at the end of each subsection. However, the constraint rankings should not be independent. After all, they are all evaluating the patterns of the same language, and even the same dialect. In addition, the constraints MAX and IDENT[F]-G are active
(iii) When two glides that share the same values for [back] or [round] feature are in the same syllable, the prenuclear one fail to surface out. (see 4.1.2) (iv) A mid vowel is inserted between two adjacent high vocoids. (see 4.1.3) These results can almost explain the presence and the absence of the rhymes without a nasal coda listed in 3.1. As for the constraint ranking, we have developed the Hasse Diagrams at the end of each subsection. However, the constraint rankings should not be independent. After all, they are all evaluating the patterns of the same language, and even the same dialect. In addition, the constraints MAX and IDENT[F]-G are active