Variable Thresholds of Pattern A

In this tableau only three candidates (i.e. (50c), (50e) and (50f)) incur no trouble from the ranking [LAPSPK &LAPSED]ω » ANCHOR-L(tσ1, σ́). Most of the other candidates threaten to beat the intended winner due to gaining an L in the column of [LAPSPK &

LAPSED]ω; candidate (50g), though not favored by [LAPSPK &LAPSED]ω, threaten to tie with the intended winner. Both of the threatening situations are readily foreclosed, however, with the aid of the top-ranked ALLFTLand TROCHEE. The ranking proposed for [LAPSPK &LAPSED]ω and ANCHOR-L(tσ1, σ́) is then further borne out.

4.3.2 Variable Thresholds of Pattern A

Since the violation of [LAPSPK &LAPSED]ω begins within quadrisyllabic Pattern B, prior to the case of Pattern A, the conjoined constraint serves to filter Pattern B in words of four or more syllables. A threshold is then set for the emergence of Pattern A in four-syllable-long words. Nonetheless, as described in section 4.1.3, older native speakers seem to have a different threshold for Pattern A compared to younger ones.

H L

‧ 國

立 政 治 大 學

‧

N a tio na

l C h engchi U ni ve rs it y

The intra-linguistic variations of TSYA with such different thresholds are repeated in the tables in (51).

(51) = (8) Intra-linguistic variations of TSYA a. Old Shanghai

Initial σ σσ σσσ σσσσ σσσσσ

Pattern B Pattern A

Yangru LMʔ

Lˀ-LM Lˀ-L-LM Lˀ-L-L-LM Lˀ-M-L-L-L

b. New Shanghai

Initial σ σσ σσσ σσσσ σσσσσ

Pattern B Pattern A Yangru LMʔ

Lˀ-LM Lˀ-L-LM Lˀ-M-L-L Lˀ-M-L-L-L

Clearly, what we have been dealing with so far is the case of New Shanghai, in which the threshold for Pattern A is set in four-syllable words, as in (51b). The emergence of Pattern A in four-syllable words is not the case in the other variation, Old Shanghai, however, in which case Pattern B continues to surface in a quadrisyllabic word, with the threshold of Pattern A retracted to much longer words, as in (51a). It follows that [LAPSPK &LAPSED]_ω would be too severe on Pattern B in Old Shanghai – it wrongly punishes quadrisyllabic Pattern B.

Therefore, a less stringent constraint is called for to obtain the later threshold of Pattern A in Old Shanghai. We posit for this purpose the self-conjunction of [LAPSPK

&LAPSED]_ω in the domain of PrWd – written here as [LAPSPK &LAPSED]² – which is violated once by any instance of the PrWd that contains at least two distinct violations of [LAPSPK &LAPSED]_ω. With this locally self-conjoined constraint crucially domina- ting ANCHOR-L(tσ1, σ́), which in turn dominates [L^APSPK &LAPSED]ω, we can derive the case of Old Shanghai in which the retraction of Pattern A is observable. The later

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threshold of Pattern A is illustrated in the tableaux in (52), in which candidates (a) are all Pattern A and candidates (b) all Pattern B. It is obvious from these tableaux that Pattern B survives in quadrisyllabic words because it only incurs a single instance of the offending lapse, which is tolerated by the less stringent self-conjoined constraint, as in (52.i). When there is another offending lapse added to Pattern B in five-syllable words, however, Pattern B turns out to fail on [LAPSPK &LAPSED]² and thus Pattern A takes its place, as in (52.ii).

(52) Old Shanghai: [LAPSPK &LAPSED]² » ANCHOR-L(tσ1, σ́) » [L^APSPK &LAPSED]ω

i. Quadrisyllabic TSYA: Pattern B as the winner σ_μσσσ [LAPSPK &

ii. Pentasyllabic TSYA: the emergence of Pattern A σμσσσσ [LAPSPK &

Note particularly that in Old Shanghai, ALLFTL is required to dominate ANCHOR-L(t_σ1, σ́) lest there is any undesired candidate that fails to be eliminated by the top-ranking [LAPSPK &LAPSED]². Tableau (53) offers an example with the case of pentasyllabic TSYA, where the otherwise threatening candidate (53c) is ruled out by ALLFTL. This tableau validates the ranking proposed.

M

‧

Overall, the two variations (i.e. Old Shanghai and New Shanghai) differ only in qua- drisyllabic TSYA: Old Shanghai surfaces as Pattern B and New Shanghai as Pattern A.

In pentasyllabic TSYA, they turn out to converge on Pattern A. Since the emergence of Pattern A is subject to the higher-ranking [LAPSPK &LAPSED]_ω, then setting up the threshold of Pattern A is simply a matter of whether [LAPSPK &LAPSED]ω is ranked higher or lower than ANCHOR-L(t_σ1, σ́), all else being equal. This alternative leads to the ranking permutation in (54): when [LAPSPK &LAPSED]ω is crucially dominated by ANCHOR-L(t_σ1, σ́), we attain the variation of Old Shanghai, as in (54a), and conversely, when [LAPSPK &LAPSED]ω crucially dominates ANCHOR-L(tσ1, σ́), we attain the vari- ation of New Shanghai, as in (54b).

(54) Ranking permutation in two variations

/σμσσσ/ /σμσσσσ/

‧ 國

立 政 治 大 學

‧

N a tio na

l C h engchi U ni ve rs it y

Two comments on the ranking relationship of (54) are in order here. First, Note that the self-conjunction is always ranked higher than ANCHOR-L(tσ1, σ́) to guarantee that both of the variations converge on Pattern A in pentasyllabic TSYA. Thus, [LAPSPK

&LAPSED]² happens to be unranked with respect to its original version, [LAPSPK &

LAPSED]_ω, in New Shanghai, as in (54b), suggesting that there is no need to conjoin [LAPSPK &LAPSED]ω with itself in this variation. In other words, the self-conjoined constraint and its original version merge when they are unranked with respect to each other. This merger is not unreasonable because any constraint and its self-conjunction are in a stringency relation (Prince 1997b, 1997c, de Lacy 2002). Formally speaking, the violations of the less stringent self-conjunction are a proper subset of the viola- tions of the more stringent original version. Therefore, if the more stringent [LAPSPK

&LAPSED]ω is ranked higher than ANCHOR-L(tσ1, σ́), it subsumes the effect of its self- conjunction in practice, so there is no need to distinguish the demarcation between them.

The ranking of ALLFTL is another point that merits attention here. It appears that the constraint immediately dominated by ALLFTL is different in the two variations.

Nevertheless, the ranking relation holds constant – ALLFTL invariably dominates both [LAPSPK &LAPSED]ω and ANCHOR-L(tσ1, σ́).

With all of the relevant ranking relationships taken care of, we are now in a position to explain why the ranking permutation is permitted in a single language.

Here I adopt one of the co-phonological theories that derive variation from a single grammar – the theory of Partially Ordered Grammars (see Anttila 1997, 2002a, Anttila

& Cho 1998). In terms of this theory, grammars are defined as a partial order in a set of constraints. A partial order is, in the words of Anttila (2007:527), a “binary relation (i.e. a set of ordered pairs) that is irreflexive, asymmetric and transitive.” A language with internal variations is a Partially Ordered Grammar where only some pairs are

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ordered (i.e. specified for the ranking). Variations of this language share these ordered pairs, with the other unordered ones specified variably. Re-ranking in this view then arises from the alternative way of specifying unordered pairs of constraints. Therefore, the ranking permutation in (54) can be translated into two sets of ordered pairs, with each of them crucially different in the ordering. This is spelled out in the diagram in (55), where every node stands for a grammar of Shanghai, each annotated with the derived output pattern for quadrisyllabic TSYA. The constraints included in this gram- mar lattice are only those that are concerned in the alternation of TSYA patterns.

(55) Grammar lattice of Shanghai

In diagram (55), the master grammar on the superordinate node contains a set of par- tially ordered pairs, to which the individual sub-grammars on the terminal node must conform. This is implemented by the conclusion of these pairs in both sub-grammars.

The master grammar also contains a pair of unordered constraints placed in the braces:

a. Master grammar

‧ 國

立 政 治 大 學

‧

N a tio na

l C h engchi U ni ve rs it y

ANCHOR-L(t_σ1, σ́) and [L^APSPK &LAPSED]_ω. Their ranking is variably specified in the two sub-grammars. Specifically, in sub-grammar (55a) – Old Shanghai – [LAPSPK &

LAPSED]_ω outranks ANCHOR-L(t_σ1, σ́); while in sub-grammar (55b) – New Shanghai – the ordering is inversed, with ANCHOR-L(tσ1, σ́) ranked above [L^APSPK &LAPSED]ω. The partially ordered pairs in both the sub-grammars can be incorporated into totally ranked constraint sets as those in (54), thereby deriving pattern A in one variation and Pattern B in the other. This grammar lattice then makes transparent that the variable thresholds set for Pattern A are parameterized by the partially ordered pairs of the master grammar.