108 114 .THS J.»— -. ..’ 4/ I' 4 ”D 6‘ c/L)\'4“4' k_.'\) 4‘.) NlVERSlTY LlBRARlES 111111111111111111111111111111111141 211111 11‘ .4 293 004955 LIBRARY Michigan State University This is to certify that the thesis entitled Tonal Strength in Tianjin Tone Sandhi presented by Kenneth L. Field has been accepted towards fulfillment of the requirements for 11.": ster (1f 'irt's degreein Linguistics gar/2y 1%129/ /\/ Major professor Date June 3, 1988 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution TV1ESI_J RETURNING MATERIALS: Place in book drop to LJBRARJES remove this checkout from ” your record. FINES will be charged if book is returned after the date stamped below. Atria C.>(_ til. 02}. TONAL STRENGTH IN TIANJIN TONE SANDHI BY Kenneth L. Field A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Linguistics 1988 ABSTRACT TONAL STRENGTH IN TIANJ IN TONE SANDHI BY Kenneth L. Field The Tianjin dialect of the People's Republic of China is unique in that it has a complex interaction of four tone sandhi rules. In this paper, I have analyzed two and three—syllable strings. I have attempted to uncover what dictates when tone sandhi applies and what determines where it will change to. I have done this by analyzing the freedom of occurrence of tones in their respective strings and by analyzing the tones in terms of pitch frequency gain. The results indicate that the four tones of Tianjin may be a part of a strength hierarchy. All the outputs of Tianjin tone sandhi in two and three-syllable strings, limited by two constraints that I have proposed, can all be explained by the tonal strength hierarchies. The implica- tions of tonal strength and how it can explain tonal phenom- ena in other languages is yet to be determined. Copyright by KENNETH LYNN FIELD 1988 ACKNOWLEDGEMENTS I most graciously thank Dr. Grover Hudson, Dr. Ruth Brend, and Dr. Barbara Abbott of Michigan State University for their valuable insight and helpful suggestions in regards to the content of this paper. I would also like to thank Sau Kuen (Florence) Wong for her translation assis- tance and continued encouragement throughout the writing of this paper. iv TABLE OF CONTENTS LIST OF TABLES . . . . LIST OF FIGURES . . . INTRODUCTION . . . . . 1.1 Purpose . . . . . 1.2 The Tianjin Dialect . . . . . . . . . . 1.3 Background. . . . PREVIOUS ANALYSES. . . 2.1 Li and Liu. . . . 2.2 Matthew Y. Chen . 2.3 Fu Tan. . . . . . 2.4 Tony Hung . . . . 2.5 Zheng-Sheng Zhang 2.6 The Data. . . . . TIANJIN TONE SANDHI IN 3.1 Variables X and Y TWO-SYLLABLE STRINGS. 3.2 Freedom of Occurrence of Tones in the XY String 3.3 The Tone Hierarchy. . . . . . . . . . . 3.4 Tonal Contours, Frequency Gain, and 3.5 The Tone Matrix . 3.5.1 Replacement Within the Matrix . 3.6 The Tonal Matrix Graph. . . . . . . . . 3.7 Summary . . . . . TIANJIN TONE SANDHI IN THREE-SYLLABLE STRINGS. 10 11 12 13 14 18 Strength 18 22 23 25 29 30 4.8 Variables P, Q, and R . . . . . . . . . . . . . 30 Freedom of Occurrence of Tones in the PQR String . . . . . . . . . . . . . . . . . . . . . . . . . 31 Tone Hierarchies in the PQR String. . . . . . . 32 The 27 PQR Input Strings and Their Outputs. . . 33 Exceptional Surface Strings . . . . . . . . . . 39 The Three-Dimensional Tonal Matrix. . . . . . . 40 Q Position Hierarchy: B-C-A-D or B-C-D-A?. . . 47 Summary . . . . . . . . . . . . . . . . . . . . 47 CONCLUSION O O O O O O O O O O O O O O O O O O O O O 4 8 5.1 5.2 5.3 Summary . . . . . . . . . . . . . . . . . . . . 48 Statement of Rules. . . . . . . . . . . . . . . 48 Tonal Strength: Universal or Language Specific? 49 NOTES I O O O O O O O O O O O O O O O O O O O O O O O 51 APPENDIX C O O O O O O O O 9 O O O C O O O O O O O O 5 2 REFERENCES 0 O O O O O O O C O O O O O O O O O O O O 5 4 vi Table Table Table Table Table Table Table Table Table Table Table Table Table LIST OF TABLES The Sixteen Possible XY Strings. . . . . XY Surface Strings . . . . . . . . . . . Freedom of Occurrence of X in Surface XY Freedom of Occurrence of Y in Surface XY Freedom of Occurrence Hierarchy. . . . . Tonal Contour Groupings. . . . . . . . . The 64 Possible PQR Strings. . . . . . . Freedom of Occurrence Hierarchies. . . . Strings Strings Predicted Outputs of the 27 Input PQR Strings . Actual Outputs. . . . . . . . . . . . . Explanation of Replacement in Figure 4. Explanation of Replacement in Figure 5. Explanation of Replacement in Figure 6. vii 14 15 16 16 18 20 31 32 34 35 43 45 45 Figure Figure Figure Figure Figure Figure 1: The The The The The The LIST OF FIGURES Tone Matrix . . . . . . . . . . Tonal Matrix with Strength Values . . . . Tonal Matrix Graph. . . . . . . Three Dimensional Tonal Matrix. Three Dimensional Tonal Matrix: Three Dimensional Tonal Matrix: viii Second View Third View 22 24 26 41 44 46 1. Introduction 1.1 Purpose The purpose of this paper is to analyze Tianjin tone sandhi (TTS) from a new point of view. Previous analyses have concentrated solely on the issues of 1) rule direction- ality, 2) rule ordering, and 3) the prosodic domains of TTS. They have not, however, dealt with the issue of what exactly might dictate and determine TTS, but rather have dealt with what specific problems TTS presents to analysis. My hypo- thesis is that TTS is not dissimilatory in nature, as has been generally accepted in the past, but is in fact motivated (for the most part) by what I have called "tonal strength." This hypothesis, when applied to the tone sandhi processes of many other languages, may yield a new understanding of the function of tones. In this paper, I will limit my discussion to TTS in two and three—syllable strings. Rule ordering and rule direc- tionality will be discussed, but I will refer the reader to Chen (1987) and Hung (1987) for their discussion on the prosodic domains of TTS. 1.2 The Tianjin Dialect The Tianjin dialect is a dialect of the Chinese lan- guage. It is spoken in the metropolis of Tianjin, located in Tianjin province, in the People's Republic of China. 1 2 Tianjin is 120 km southeast of Beijing, the capital of China. The Tianjin dialect and Mandarin are mutually intelli- gible. They both have four tones, the major difference being that the Tianjin dialect has no high level tone [55], but. rather' has a low falling’ tone [21]. The complete inventory of the Tianjin tones is as follows: (1) [21] Low Falling Tone A [45] Rising Tone B [213] Falling-Rising Tone C [53] High Falling Tone D I will refer to these tones as A, B, C, and D in my discussion in order to remain consistent with other authors. 1.3 Background There are four tone sandhi rules in the Tianjin dialect. They are: (2) 21 ->213/_21 (3) 213->45 /_213 (4) 53 ->21 /___53 (5) 53 ->45 /_21 They can be restated as: (6) AA->CA (7) CC->BC (8) DD->AD (9) DA—>BA 3 These rules have been referred to in previous articles by their input strings, so (6) is the AA rule or AAR, (7) is CCR, (8) is DDR, and (9) is DAR. Here are some examples of TTS applying on two-syllable strings: (10) AA->CA gao shan ‘high mountain' 21 21 213 21 by AAR (11) CC->BC xi lian ‘wash face' 213 213 45 213 by CCR (12) DD->AD jing zhong ‘net weight’ 53 53 21 53 by DDR (13) DA->BA kan shu ‘read book' 53 21 45 21 by DAR Whenever the conditions for TTS are not fulfilled, TTS does not apply. From this we know the original tone of each syllable. For example, whenever ‘gao' (considered to bear tone A) occurs before a syllable bearing tones B, C, or D, ‘gao' remains tone A. There are seven three-syllable strings where either more than one TTS rule applies to the string at the same time, or where the application of one TTS rule on the string feeds another, or in other words, provides input for another 4 TTS rule to apply. When TTS rules apply to these three-syl- lable strings, their application seems to be inconsistent. Examples of each are presented below: (14) AAA->ACA kai fei ji A A A A C A (15) DDD->DAD->BAD suo liao bu D D D D A. D B A D (15) CCC->BCC->BBC 1i fa suo C C C B C C B B C (17) CAA->CCA->BCA bao wen bei C A A C, C A B C A (18) ADD->AAD->CAD xin dian shi A D D A A D C A D (19) DDA->ADA->ABA zuo dian che D D A A D A A B A (20) DAA->DCA zi zun xin D A A D C A ‘fly airplane’ by AAR ‘plastic sheet’ by DDR by DAR ‘barber shop’ by CCR by CCR ‘thermo cup’ by AAR by CCR ‘new television’ by DDR by AAR ‘take tram’ by DDR by DAR ‘self respect’ by AAR In (14), it appears that AAR is applying from right to left because its input is the last two syllables of the AAA string. DDR also appears to be applying from right to left because in (15), its input is the last two syllables of the DDD string. DDR also feeds, or in other words, provides input for DAR to apply. In (16), CCR appears to be applying iteratively from left to right. In (17), AAR feeds CCR. In (18), DDR feeds AAR. In (19), application appears to be from left to right, or another interpretation would be that DDR precedes DAR. Finally, in (20), AAR applies preventing DAR from applying. One might argue that this shows that AAR precedes DAR. In any case, the problems of rule directionality and rule ordering presented by the data above have been the main issues of discussion in previous articles. I will touch on these issues but the main focus of this study will be tonal strength and how it dictates and determines Tianjin tone sandhi. 2. Previous Analyses 2.1 Li and Liu Li and Liu’s 1985 article in Zhongguo Yuwen, "Tone Sandhi in the Tianjin Dialect," was the first to introduce the Tianjin tone sandhi phenomenon to the linguistic world. 6 In the article, Li and Liu present the four TTS rules, (6)-(9), together with a fair amount of data showing TTS applying to two, three, and four-syllable strings. The two and three syllable strings are not subdivided but the four- syllable strings are. They are subdivided into 2+2 word groupings, 1+3 word groupings and 3+1 word groupings dependent upon the internal structure of the strings. The data that Li and Liu present shows that in the 2+2 word groupings, TTS applies as it does in two-syllable strings to each two-word group, but that TTS does not apply between these two two-word groups, in other words, TTS does not apply to the second and third words in these four-syllable strings. They go on to show that TTS applies to three-word groups of both 1+3 and 3+1 word groupings the same as it does in three-syllable strings and furthermore that TTS does apply between the first and second word in the 1+3 word groupings and the third and fourth word in the 3+1 word groupings. 2.2 Matthew Y. Chen Chen has published two articles on the Tianjin tone sandhi phenomenon. The first was a 1986 article, "The Paradox of Tianjin Tone Sandhi," and the second was a 1987 article, "A Symposium on Tianjin Tone Sandhi: Introductory Remarks." In his 1987 article, Chen remarks on his 1986 article, saying: "In Chen . . . 1986 . . . I reached the unhappy and inelegant conclusion that no con- ceivable mode of rule application seemed to be compatible with Li-Liu’s (1985) data. I demonstrated that neither cyclic application (obeying Strict Cyclicity Condition), nor simultaneous or iterative application in any direction (L to R, or R to L) is capable of generating the attested sandhi patterns (205)." He goes on to say that the reason that this was so was that. he ‘was treating* the four' TTS rules (6)-(9), as a unified system that applied in a unified way. In his 1987 article, the rules of TTS are presented as individual rules with different modes of application. The major contribution of the 1987 article is its dis- cussion of morphosyntax and how it relates to TTS and the author’s analysis of the prosodic domains of TTS. Chen gives Phrasing/Foot—Formation rules for dividing up longer utterances (of more than three syllables) into feet and phrases that TTS can apply to. Chen shows how different derivations of longer strings can be explained by alterna- tive divisions of the utterance. 2.3 Fu Tan Tan has also published two articles on this subject. The first was a 1986 article in Zhongguo Yuwen entitled, "More on Tone Sandhi in the Tianjin Dialect." The second was a 1987 article entitled, "Tone Sandhi in the Tianjin Di- alect." This was a revision of an earlier 1986 unpublished manuscript. 8 Tan, in her 1987 article, proposes that all the rules have a specific directionality: (21) AAR CCR DDR DAR R to L L to R R to L unspecified She also proposes that these rules are ordered in rela- tion to each other: (22) AAR>CCR and AAR>DDR>DAR She also claims that morphosyntax does not change the way that TTS rules apply. She shows this by giving examples of left and right branching structures with identical tone patterns and showing that the outputs are the same: (23) [suo liao] bu D D D D A _D B A D (24) ya [re dai] D D D D___A__D B A D ‘plastic sheet’ by DDR by DAR ‘subtropics’ by DDR by DAR On the other hand, she claims that emphasis blocks TTS: 9 (25) gai + tai duo ‘there is too much yegetable Di. + D .A (not meat)’ D + B A by DAR (+ indicates blocking of TTS) The expected output of DDA is ABA, but in (25) , the first word, ‘vegetable’, has contrastive emphasis with ‘meat’. This blocks DDR from applying to the first two words, so DAR applies to the last two words. Li and Liu also give a few examples where emphasis blocks TTS. I will not be covering this issue in my analysis. Read Tan (1987) for her arguments and Chen (1987) for his counter arguments against this position. 2.4 Tony Hung In a 1987 article, "Tianjin Tone Sandhi: Towards a Unified Approach," Hung attempts to explain the TTS phe- nomenon in a different manner. This consists of a surface phonotactic constraint called simply, the Tianjin Phonotac- tic Constraint (TPC), "... which discourages identical low tones [tones A and C] from surfacing in juxtaposition within the same tone group... (279)." Hung makes no comment on directionality, but rather says TTS rules apply whenever their condition is met subject to TPC. The only ordering that he proposes is that DAR is ordered last. A rather large portion of the article deals with the domains for TTS which he specifies as the tone group which is mainly conditioned by prosodic structure but is condi- 10 tioned less by syntactic structure. I have chosen to ignore the prosodic domains for TTS in this paper because I feel that Chen’s (1987) and Hung’s (1987) hypotheses are suffi- ciently viable. If the reader is interested in this aspect of TTS, then I refer the reader to the above analyses for a more complete understanding of TTS. TPC does not, in my opinion, threaten the validity of my discussion. This constraint cannot fully account for the way TTS operates. It accounts to some extent for the moti- vation behind CCR and AAR, but it does not account for DDR which Hung says is a product of dissimilation or DAR which is not explained in terms of why it occurs at all. 2.5 Zheng—Sheng Zhang Zhang’s 1987 article, "The Paradox of Tianjin: Another Look," does not draw any conclusions very different from those I have already discussed. The main difference between Zhang’s and Tan’s proposal is that Zhang avoids the extent of Tan’s extrinsic ordering just by stating that AAR and DDR precede DAR. He agrees with Tan on directionality, that AAR and DDR apply right to left and CCR applies left to right. He also shows that TTS rules do not apply cyclically on morphosyntactic structures. The only other thing of major importance in Zhang’s article is a refutation of Hung’s TPC (see section 2.4 above). He states that TPC must be "global" in order for it to do the work that Hung wants it to do and is therefore too 11 powerful. He shows that Hung’s TPC does not disallow low tones in juxtaposition in ADD->AAD->CAD derivations and it does not disallow AAA->CCA alternative derivations (see section 4.4). 2.6 The Data The data available for the study of TTS is limited. I have pooled all the data from the above mentioned studies of TTS for my data base. However, in many cases, the data is not consistent. For instance, Li and Liu neglect to give any examples of TTS applying to DAA strings as in example (20). Further- more, their output for TTS applying to DDD strings is DAD, thus DDD->DAD->*BAD. This means that DAR doesn’t apply after DDR in their data. Hung’s data agrees with Li and Liu’s in this instance. Tan’s and Chen’s data, on the other hand, give the out- put for TTS applying to DDD strings as BAD as in example (15). Moreover, Tan gives her output for TTS applying to ADD strings as AAD and not CAD, as in example (18). Thus ADD—>AAD->*CAD. This means that AAR does not apply after DDR in her data. Zhang has no data of his own, but rather uses both Li and Liu’s and Tan’s data. But the cited examples for PQR strings DDD and ADD are from Li and Liu’s data because his final output for DDD strings is DAD (same as Li and Liu’s) and his output for ADD strings is CAD (same as Li and Liu’s). This apparent split in the data base is most likely due to different variants of the Tianjin dialect. Tan admits that there is another dialect of Tianjin where the CAD output for ADD is an alternative. As regards to the output of DDD strings, I have chosen to use the 2-part derivation DDD->DAD->BAD in agreement with Chen and Tan. The conflicting data does not affect my discussion of Tianjin tone sandhi. The only difference is that. the derivations are not carried out to their full extent. It is still true that each string changes to a stronger string, according to my hypothesis. It is interesting to note that the major difference in data concerns whether DAR applies after DDR. DAR is the only rule whose output is 3 strength relation values stronger than its input. See discussion in section 4.4 below. Also see Appendix for complete listing of data sources. 3. Tianjin Tone Sandhi in Two-Syllable Strings In my discussion of Tianjin tone sandhi (TTS), I will propose a strength hierarchy of tones. I will show that this hierarchy is supported by two criteria: 1) freedom of occurrence of tones and 2) frequency gain. I will also show that these strength hierarchies dictate when TTS occurs and that they determine where and how the input string changes. 12 13 3.1 Variables X and Y Before I discuss TTS in three-syllable strings, I want to discuss Tianjin tone sandhi in its most limited domain, that is, in two-syllable strings. The four basic TTS rules operate minimally in two-syllable strings. The four basic TTS rules are restated below: (26) 21 ->213/___21 or AA—>CA AAR (27) 213->45 /___213 or CC->BC CCR (28) 53 ->21 /___53 or DD->AD DDR (29) 53 ->45 /___21 or DA->BA DAR In order to represent Tianjin two-syllable strings, I want to introduce two variables, X and Y. Let X and Y each represent a mono-syllable. Secondly, let X and Y each rep- resent a maximum of one morpheme. And finally, let X and Y each represent a tone bearing unit (although it is possible in Tianjin for the syllable to bear no phonemic tone at all). Next, it is important to understand the relationship of X and Y to each other. Let X always represent the first syllable of a two-syllable string and Y the last syllable in a two-syllable string; therefore the order of these two variables is always XY, never YX. It follows that there can be no other syllables between variables X and Y. They are always adjacent to each other. These variables were designed so that I can more easily refer to the two-syllable string as the XY string and so that I can refer to the first 14 and last syllable of a two-syllable string as X and Y respectively. 3.2 Freedom of Occurrence of Tones in the XY String The Tianjin dialect has four tones. They are restated below: (Contrastive Tonal Patterns) (Tone Labels) (30) [21] Tone A [45] Tone B [213] Tone C [53] Tone D In the discussion that follows I will refer to the tone labels (A, B, C, and D) and not the contrastive tonal patterns of each tone. Therefore X, of the XY string, can bear four possible tones (A, B, C, and D), and Y can also bear four possible tones (A, B, C, and D). That means that there are sixteen possible XY tonal combinations. Table 1 The Sixteen Possible XY Strings AA BA CA DA AB BB CB DB AC BC CC DC AD BD CD DD Since linearity is inherent in my description of the XY string in section 3.1 above, none of the strings in Table 1 are redundant. In other words, an XY string bearing tones A 15 and D in sequence is not equal to an XY string bearing tones D and A in sequence i.e. AD+DA. Of these sixteen possibilities, four of them are input strings for TTS rules (26)-(29). They are AA, CC, DD, and DA. This means that when the conditions for tone sandhi are met, these four input strings do not appear as surface strings but rather appear as CA, BC, AD, and BA respec- tively. Tone sandhi does not occur with any other XY strings. Therefore, in surface strings, AA, CC, DD, and DA do not occur. Table 1, therefore, can be modified to include only those strings that occur as surface strings: Table 2 XY Surface Strings BA CA AB BB CB DB AC BC DC AD BD CD Looking at the X position in surface XY strings, tone B occurs four out of four possible times. In other words, tone B may occur in the X position with any other tone including itself, without becoming part of an input string for tone sandhi. I will refer to this as "freedom of occur- rence." Therefore, tone B has a high freedom of occurrence because it occurs four out of four possible times. Additionally, tone C (occurs three out of four possible 16 times, tone A occurs three out of four possible times, and finally tone D occurs two out of four possible times, as shown in Table 3: Table 3 Freedom of Occurrence of X in Surface XY Strings BY CY AY DY BA CA BB CB AB DB BC AC DC BD CD AD Now looking at the Y position in the surface XY strings, tone 8 occurs four out of four possible times, tone C occurs three out of four possible times, tone D occurs three out of four possible times, and finally tone A occurs two out of four possible times, as shown in Table 4: Table 4 Freedom of Occurrence of Y in Surface XY Strings XB XC XD XA AB AC AD BB BC BD BA CB CD CA DB DC In Table 3 above, both tones C and A occur three out of four possible times in the X position. With only this information, the tones in the X position could be ranked 17 either B-C-A-D or B-A-C-D in terms of freedom of occurrence. In addition, in Table 4, both tones C and D occur three out of four times in the Y position. So in the Y position, the tones could be ranked either B-C-D-A or B-D-C-A. In order to arrive at a ranking for tones regarding freedom of occur- rence, one must either concede that there are two possible rankings for each position in the string, or use some addi- tional data to decide upon a ranking. I have decided upon the latter. If the results of both Tables 3 and 4 are combined, one sees that tone B occurs eight out of eight possible times, tone C occurs six out of eight possible times, tone A occurs five out of eight possible times, and finally tone D also occurs five out of eight possible times. This data shows that, overall, tone B has the greatest freedom of occur- rence. In fact, tone B never undergoes tone sandhi. Tone C follows tone B in terms of freedom of occurrence, because it occurs six out of eight possible times in either the X or Y position. This is greater than either tone A or D which both occur five out of eight possible times (see Table 5.0). On this basis I have ranked tone C above tone A in the X position and tone C above tone D in the Y position. The ranking of tones A and D has already been determined by their freedom of occurrence in their respective positions in the XY string. 18 3.3 The Tone Hierarchy Table 5 Freedom of Occurrence Hierarchy a. X Position b. Y Position 0. Overall High B B B Freedom of 1 1 1 Occurrence C C C l 1 / \ Low A D A D Freedom of 1 1 Occurrence D A Table 5 above shows the hierarchy of tones as deter- mined by freedom of occurrence. Table 5.a shows that in the X position, tone B has the highest freedom of occurrence and tone D has the lowest. Similarly in Table 5.b, tone B has the highest freedom of occurrence while tone A has the lowest. We will see that there is a criterion other than free- dom of occurrence for this ranking of the tones. 3.4 Tonal Contours, Frequency Gain, and Tonal Strength In the Tianjin dialect, there are five phonological pitch levels, [5] being the highest and [1] being the lowest. If the phonological pitch levels within each tone are examined and compared, some interesting results come to light. For example, the phonological pitch levels of tone B are [45]. The tone starts approximately at pitch level [4] and rises to pitch level [5]. This tone has a rising contour. Another way of describing this is that there is an increase in pitch frequency. 19 The phonological pitch levels within tone C are [213]. It starts at approximately pitch level [2], dips to pitch level [1], and then rises to pitch level [3]. This tone begins with a falling contour but ends with a rising one. There is first a decrease in pitch frequency followed by an increase in pitch frequency. The phonological pitch levels within tone A are [21]. It starts at approximately pitch level [2] and falls to pitch level [1]. This tone has a low falling contour. Note that the only significant difference between tone C and A is that tone C rises to pitch level [3] after its fall to pitch level [1] and tone A doesn’t. The phonological pitch levels within tone D are [53]. It starts at approximately pitch level [5] and falls to pitch level [3]. Tone D has a high falling contour. Both tones A and D can be described as having a decrease in pitch frequency. The reason that tones A and D remain distinct, even though they both have a decrease in frequency, is because they are maximally different within the context of a falling tone. Tone D starts at the highest possible pitch level in a five pitch level system, [5], and then falls approximately two pitch levels. Tone A, on the other hand, starts on pitch level [2], the lowest possible starting position for a falling tone and falls to the lowest pitch level, [1]. In Table 6, the tones have been grouped according to their contour. From the discussion above concerning the 20 phonological levels within each tone, it was seen that tonal contours are actually increases or decreases in pitch frequency. Instead of referring to each tone as having an increase or decrease in pitch frequency, I want to propose a single feature which I will call "frequency gain." So any tone that has an increase in pitch frequency will have a positive [+] frequency gain and any tone that has a decrease in pitch frequency will have a negative {-1 frequency gain. Table 6 Tonal Contour Groupings Rising Contour Falling-Rising Contour Falling Contour Tone B Tone C Tone A Tone D [+] Frequency Gain [- +] Frequency Gain {-1 Frequency Gain Therefore, since tone B has an increase in pitch frequency, it can be understood as having a positive [+] frequency gain. Tones A and D, on the other hand, can be understood as both having a negative [-] frequency gain since both have a decrease in pitch frequency. Tone C, however, is a combination of both a decrease and increase in pitch frequency in that order. 80 to accurately represent tone C, it can be understood as having both negative and positive frequency gain represented as [-+]. Therefore tone C is ranked between tone B and tones A and D because it shares features with both. If it is understood that the tones shown in Table 6 (left to right) are in descending order ([+] to [-]} in terms of frequency gain, then the 21 result is an ordering equivalent to that of freedom of occurrence (Table 5). Another ‘way' of understanding ‘this. ordering' is that freedom of occurrence directly correlates with frequency gain. Therefore, if atone has a positive [+] frequency gain (tone B for instance), then it will have a high freedom of occurrence. In other words, a tone that has a positive [+] frequency gain resists change and is therefore stronger than a tone that has a negative [-] frequency gain (tones A or D for instance) which are most subject to change. I will refer to this as "tonal strength." Tone C falls in between these two extremes because it has both negative and positive ['+] frequency gain. The fact that both tones A and D have negative [-] frequency gain correlates with the ordering of these two tones in the strength hierarchy which can either be A-D (X position) or D-A (Y position). Their ultimate ordering is dependent upon their position in the XY string. This will be explained in detail in section 3.5. This phenomenon of tonal strength may be related to perception, in that increases in pitch frequency are often perceived as being stressed. This factor may account for why increases in pitch frequency are stronger than decreases in pitch frequency. 22 3.5 The Tone Matrix It was shown in section 3.2 that freedom of occurrence ordered the tones as B-C-A-D in the X position and B-C-D-A in the Y ‘position. These tones were placed in freedom of occurrence hierarchies in section 3.3. In section 3.4, it was shown that pitch frequency gain ordered the tones in the same way. These hierarchies, presented in Tables 5 and 6 can now be understood as strength hierarchies, tone B being the strongest and tones A and D being the weakest. To further illustrate this, I will use the X hierarchy for the horizontal axis in a matrix, and I will use the Y hierarchy for the vertical axis in a matrix. I will also show by using strength relation values how tonal strength dictates and determines tone change. x B c A D Y B BB CB AB DB c BC <fi— 9; AC DC D BD CD AD < DD A BA <—r—‘ CA <—— AA L1— 125 Figure 1 The Tone Matrix Figure 1 above shows the sixteen possible XY tonal com- binations. Those underlined, AA, CC, DD, and DA, do not occur as surface strings, but rather undergo tone sandhi. 23 XY string AA becomes CA by AAR, CC becomes BC by CCR, and DD becomes AD by DDR. In Figure 1 above, output strings CA, BC, and AD all appear immediately to the left of their input strings AA, CC, and DD respectively. DA does not become AA as might be predicted by Figure 1, but rather becomes BA. Before this can be explained, replacement within the matrix must be discussed. 3.5.1 Replacement Within the Matrix I have proposed that tonal strength both dictates and determines Tianjin tone sandhi: (1) an XY string will change if the XY tonal combination has a low strength rela- tion value and (2) the input string will change to an output string that is stronger than the original input string. To show this, in Figure 2, I have assigned number values to each tone in each hierarchy ranging from 4 to 1, 4 being the strongest and 1 being the weakest. The strength of each XY string is then determined by the sum of the values of the X and Y tone. In the tonal matrix, strings that undergo tone sandhi may only be replaced within the horizontal row which they occupy. This is because the tone in the X position is the one that changes. The tone in the Y position always remains the same. In other words, replacement occurs along the X hierarchy and not the Y hierarchy because the tone in the X position is the one that changes, not the tone in the Y position. See Figure 2: 24 X B C A D Y 4 3 2 1 B BB CB AB DB 4 8 7 6 5 C BC <—r cg AC DC 3 7 6 5 4 D BD CD AD <-—— 212 2 6 5 4 3 A BA <——‘CA CA is a change from 3 to 4, DD->AD is a change from 3 to 4, and DA->BA is a change from 2 to 5. The output of XY input string DA does not change to the next strongest string as do the others, but this can be explained in the following manner. If DA’s output were the next strongest string, then the output would be XY string AA which is also an input string. AA would also undergo tone sandhi and the final output of DA would be CA, the same output string for AA. Therefore input strings DA and AA would have the same output, CA. In fact, if DA were to 25 become CA, then tone D of the input string DA would undergo tone sandhi twice. First it would change to A and then it would change to C. I propose the following constraintl: (31) TTS Constraint 1: A tone may only undergo tone sandhi once. This constraint would prohibit DA from becoming CA through AA. However, it would not prohibit DA from becoming CA without any transition through AA. But the problem would still remain that DA and AA ‘would both have the same outputs, namely CA. Although this situation is not at all impossible, a language would reasonably avoid this merger if there were a feasible alternative. The only alternative left is for DA to become BA, which is in fact the case. This means that the output string of DA is three strength relation values higher than its input string, but the fact remains that the output string has a stronger value than the input string. Moreover, the fact that DA becomes BA doesn’t violate TTS Constraint 1 because there is no transition through other tones. TTS Constraint 1 will be discussed in more detail in section 4.4, below. 3.6 The Tonal Matrix Graph The Tonal Matrix Graph (see Figure 3) is a graphic representation of each tone and each of the XY string tonal combinations. It is presented in the same 'manner as the 444]”. . v31... 1.331.... 411.1... a! n 4.. <~ BC tone sandhi rule is applicable in all Mandarin dialects,2 which may be true, but it is still important to realize that CC 28 still changes to the next strongest XY tonal combination. One explanation of why this XY string is an input for tone sandhi, even though it has a strength relation value of 6, is that it is the most complex of all the XY tonal combina- tions in that there is a lot of information packed in a small amount of time. In a relatively short time span, there is first a decrease in pitch frequency immediately followed by an increase, then another decrease immediately followed by another increase. The intuitions of most native speakers support this explanation of complexity in that two C tones in a row are simply difficult to pronounce. Finally moving in another layer on the matrix which consists of XY strings AA, AD, DD, and also including DA, these XY tonal combinations only consist of falling tones, or in other words, only those that have negative [-] frequency gain. This is the weakest section of the matrix (see Figure 2) and the three weakest XY strings are indeed input strings for tone sandhi, AA, DD, and DA. AD is not an input string for tone sandhi although it consists of two falling tones. This is because tone A is stronger in the X position than in the Y position and because tone D is stronger in the Y position than in the X position. The XY string DA, the weakest of all the strings having a strength relation value of 2, is actually a continuous decrease in frequency starting at pitch level [5] and falling to pitch level [1]. The XY string AD, on the other hand is not a continuous decrease in frequency. Tone A ends at pitch 29 level [1] and then tone D starts at pitch level [5]. Although this juncture is not voiced, in fact, none of them are, there is a difference of 5 pitch levels. It has also been suggested by Chen3 and Hung“ that Tianjin tone sandhi is dissimilatory in nature. If this is true, then why doesn’t the XY string BB change? And furthermore, why does the XY string DA change at all? My explanation of tonal strength is consistent with these facts. 3.7 Summary I introduced two variables, X and Y, to represent the two-syllable string in TTS. Then I proposed a strength hierarchy for tones supported by two criteria: 1) I showed the freedom of occurrence of each Tianjin tone in the X or Y position in the XY string. These tones were then placed in a hierarchy in regards to freedom of occurrence. 2) Then I compared the phonological pitch levels of each Tianjin tone and placed them in a hierarchy in regards to frequency gain. Then I showed that the freedom of occurrence and the frequency gain hierarchies were consistent with each other and could be referred to as strength hierarchies. Then I constructed a matrix using the X and. Y position tonal strength hierarchies for variables and I showed that each XY string changes to a stronger XY string and that the weaker strings (excluding CC) were the XY strings that changed. This matrix was then reformulated in the form of a tonal graph matrix where it was apparent that the weakest XY strings (those with strength relation values of 3 and 2) were combinations of falling tones. In the next section, I will discuss how tone sandhi operates in three-syllable strings. 4. Tianjin Tone Sandhi in Three-Syllable Strings 4.1 Variables P, Q, and R In this section I want to discuss how TTS operates in three-syllable strings. In order to represent the three- syllable string, I need to introduce three new variables, P, Q, and R. The variables P, Q, and R represent the same thing as variables X and Y (see section 3.1). However, the relationships among these three variables are different in that P always represents the first syllable of a three- syllable string, Q always represents the medial syllable of a three-syllable string, and R always represents the final syllable of a three syllable string. Again, these variables are only used so that I can more easily represent the three- syllable string as the PQR string and so that I can refer to the first, medial, and final syllables of a three-syllable string as P, Q, and R respectively. I decided to use three different variables rather than add just one variable, Z, to the XY string because I wanted to make it clear when, for example, I am referring to the 30 31 first syllable in a three syllable string: this is P and not X. 4.2 Freedom of Occurrence of Tones in the PQR String Since there are three positions in the PQR string, there are 64 possible tonal combinations as in Table 7: Table 7 The 64 Possible PQR Strings AAA DAA 9AA DAA AAD BAB CAB DAB AAQ BAC CAC QAQ AAD BAD CAD DAD ABA BBA CBA DBA ABB BBB CBB DBB ABC BBC CBC DBC ABD BBD CBD DBD ACA BCA QQA DCA ACB BCB QQB DCB AQQ DDD 999 DDD ACD BCD QQD DCD ADA DDA DDA DDA ADB BDB CDB DEB ADC BDC CDC DDQ ADD DDD DDD DDD Of the 64 possibilities, 27 are input strings for TTS. Therefore, these 27 PQR strings do not appear as surface strings. These are underlined in Table 7 above. The free- dom of occurrence for each tone can be figured in the same manner that it was in section 3.2 above. 32 4.3 Tone Hierarchies in the PQR String The hierarchies that result are as follows: Table 8 Freedom of Occurrence Hierarchies a. P Position b. Q Position c. R Position d. Overall B 12/16 B 16/16 B 12/16 B 40/48 c 9/16 c 9/16 c 9/16 c 27/48 A 9/16 A 6/16 D 9/16 A 22/48 D 7/16 D 6/16 A 7/16 D 22/48 To the right of each tone in the hierarchies are the freedom of occurrence ratios for that tone. The highest freedom of occurrence possible for each tone in a given position is 16; therefore the overall ratio is 48 because there are three positions. To understand the hierarchies above, it is necessary to remember that the input for any TTS rule is a two-syllable string, thus in the PQR string there is an overlapping of two two-syllable strings. (32) xy xv The hierarchy for the P position (Table 8.a) of the PQR string is the same as that for the X position in an XY string. Moreover, the hierarchy for the R position (Table 8.c) is the same as that for the Y position in the XY string. But the hierarchy for the Q position (Table 8.b) is 33 indeterminate. Where tones A and D were clearly ordered depending on their position in either X or Y of the XY string, the freedom of occurrence of tones A and D is the same in the Q position of a PQR string. This is because the Q position, example (32), is both the X and Y position at the same time. If the overall hierarchy (Table 8.d) is referred to, tones A and D still have the same freedom of occurrence. It would appear that an arbitrary decision needs to be made regarding the ordering of the Q position hierarchy. For the moment, I will use the hierarchy as listed in Table 8.b, B—C-A-D, without explanation. However, it will be explained in section 4.7. 4.4 The 27 PQR Input Strings and Their Outputs If two assumptions are made, then the output of each PQR string can be predicted. The first assumption is that all the rules apply uniformly from left to right. The second assumption is that in TTS, whenever the condition for a rule is met, then the rule applies. Therefore, in a PQR string where both PQ and QR meet the condition for tone sandhi, then it is predicted that TTS will apply first to the PQ string and then the QR string, if possible. By the second assumption, it is also possible for a QR string to feed, or in other words, provide input for a PQ string. A PQ string, however, cannot provide input for a QR string because it is the tone that occupies the P position that changes and P is not part of the QR string. 34 It is also possible that after tone sandhi operates on the PQ string that QR is still an input string for TTS, in which case TTS occurs. In Table 9.a below is a complete listing of the 27 PQR input strings and their predicted outputs according to the two assumptions: Table 9.a Predicted Outputs of the 27 Input PQR Strings (*: Incorrect Outputs) 1.*AAA->CAA->CCA->BCA 2. BAA->BCA 3. CAA->CCA->BCA 4.*DAA->BAA->BCA 5. AAB->CAB 6. DAB->BAB 7. AAC->CAC 8. DAC->BAC 9. AAD->CAD 10. DAD->BAD 11. CCA->BCA 12. CCB->BCB 13. ACC->ABC 14. BCC->BBC 15. CCC->BCC->BBC 16. DCC->DBC 17. CCD->BCD 18. ADA->ABA 19. BDA->BBA 20. CDA->CBA 21. DDA->ADA->ABA 22. DDB->ADB 23. DDC->ADC 24. ADD->AAD->(CAD)5 25. BDD->BAD 26. CDD->CAD 27.*DDD->ADD->AAD->CAD 35 Of the predicted outputs for the 27 PQR strings, only three of them are incorrect, numbers 1, 4, and 27. Their actual outputs are: Table 9.b Actual Outputs 1. AAA->ACA 4. DAA->DCA 27. DDD->DAD—>(BAD) The data in Table 9.b seem to indicate that AAR and DDR operate from right to left in three syllable strings, because these strings (AAA and DDD) are the only strings where AAR and DDR have the opportunity to operate on PQ and QR of the PQR string at the same time, and the outputs show that it is the QR string that TTS applies to. But this, in fact, does not prove conclusively that AAR and DDR operate from right to left. TTS Constraint 1 (introduced in section 3.5.1) can explain this. TTS Constraint 1 says that a tone may only undergo tone sandhi once. If AAR and DDR were to operate on PQ of AAA and DDD respectively, then the tone in the P position would undergo tone sandhi twice (see Table 9.a, 1 and 27). This is an unacceptable output, so to prevent this, AAR and DDR operate on the QR string instead. There is more data to support TTS Constraint 1. In fast speech, these alternative outputs have been attested (see Appendix): 36 (33) AAA->CAA->CCA ->*BCA kai fei ji ‘fly airplane’ A A A C A A C C A (34) ji guan qiang ‘machine gun’ A A A C A A C C A (35) fei ji shi ‘airplane expert (pilot)’ A A A QL__A__A C C A These outputs show that AAR is applying left to right, that is, on the PQ position first and then the QR position. The resulting CCA strings in (33), (34), and (35) above, appear to be able to undergo TTS again, but that there is no change may be attributed to TTS Constraint 1. That is because tone A in (33), (34), and (35), has already become tone C and therefore they cannot change again. Hung(1987) gives the following example: (36) DDD->ADD->AAD ->*CAD fu jiao shou ‘associate professor’ D D D A__D____D A A D It is unclear in Hung’s discussion whether this is an alternative output for a DDD string or not. He labels it with a question mark [?], but he has also labeled the previ— ous example (an AAA->CAA->CCA output) in the same manner although he has just stated that this reading is acceptable in fast/casual speech. He may have been referring to (36) 37 above as unacceptable in normal speech, but not in fast/casual. If this is the case, then there is evidence that DDR applies left to right in fast casual speech also and that it also follows TTS Constraint 1. We may understand the results as follows. In normal speech, the speaker looks further ahead than in fast casual speech. In AAA->ACA of normal speech, it is possible that the speaker realizes, obviously not in a conscious way, that if he accepts PQ for tone sandhi, then the output will be a violation of TTS Constraint 1, so the speaker skips PQ and accepts QR. But in AAA->CAA—>CCA of fast/casual speech, the speaker does not take time or is not careful to look that far ahead and accepts PQ as an input string for tone sandhi. When the speaker reaches CCA of the derivation, he realizes that if he continues, he will violate TTS Constraint 1, so he accepts CCA as the surface string. This shows that. TTS Constraint. 1 is stronger than assumption two, in other words, prohibiting tone sandhi from applying twice to a given tone is more important than that a string undergo tone sandhi, even when the condition for tone sandhi is met. The fact that DAA becomes DCA rather than BAA->BCA can be explained in the following manner. AAR, CCR, and DDR all produce outputs which are one strength relation value stronger than their input strings. DAR, however, is the only TTS rule which produces an output string that is three strength relation values stronger than its input string. 38 All the previous analyses agree that DAR is ordered last. This may be understood as a consequence of the strength relations as follows: those rules that produce outputs one strength relation value stronger than their input strings (AAR, CCR, and DDR) must apply before a rule (DAR) that produces an output three strength relation values stronger than its input string. Granted, this is another way of say- ing DAR is ordered last, but it is an explanation of why this is so. I will call this TTS Constraint 2: (37) TTS Constraint 2: A rule that produces an output string one strength relation value stronger than its input string must apply before a rule that produces an output string more than one strength relation value stronger than its input string. Tan (1987:232) provides the following example: (38) DAA->DCA dian deng guan ‘electric light turn-off’ D, A A D C A by AAR The application of AAR in (38) has prevented DAR from applying. But Tan (1987:232) also provides another derived ‘form: (39) DAA->BAA ->*BCA dian deng guan D .A A B A A by DAR 39 In (39), DAR has applied first, AAR cannot apply now due to TTS Constraint 2. This also shows that TTS Constraint. 2 is stronger than assumption two, in other words, it is more important that no other rule apply after DAR (which strengthens its output string by three strength relation values) than that a string undergo tone sandhi, even when the condition for tone sandhi is met. 4.5 Exceptional Surface Strings In section 2.6, I discussed the inconsistency of the data. There is another type of inconsistency in the data, which I did not mention before, which I will refer to as "exceptional." These are examples given by the various authors of surface strings that do not seem to follow the previously discussed patterns. These exceptional surface strings are idiosyncratic in nature in that they only appear in specific lexical items. Some examples are given below: (40) DDA->*ADA->*ABA xia dian che ‘descend tram car’ D, D A D B A by DAR (41) ADD ->*AAD->*CAD yi yuan jin ‘hospital is near’ A D D no change In (40), the PQ position of the PQR string DDA has been skipped and the QR position has been accepted. In (41) , 40 there is no change where one would expect it to occur. There are a few other examples similar to these but they are idiosyncratic in nature as well. The unproductiveness of these patterns, in that they are limited to a few specific lexical examples, indicates that they do not invalidate the present analysis, which seems to hold for the vast majority of the data. These could be considered in the same category as idioms. 4.6 The Three-Dimensional Tonal Matrix In order to represent TTS in three-syllable strings, a three-dimensional matrix (in other words a matrix with three sets of variables) may be used. The variables are the tonal hierarchies for the P, Q, and R positions. See Table 8. Figure 4 is a three-dimensional representation of all the PQR strings and their relationships to each other. The P position of the PQR string is represented by the vertical axis of Figure 4. The R position of the PQR string is represented by the horizontal axis that is perpendicular to the P position axis. The Q position of the PQR string is represented by the horizontal axis that is perpendicular to the R position axis. The lightly shaded areas in Figure 4 (and in Figures 5 and 6) are PQR input strings. The darker shades areas are also PQR input strings, but they are the seven input strings presented in section 1.3. That means that they are subject FPosilion 41 Figure 4 The Three-Dimensional Tonal Matrix 42 to more than one TTS rule or that after application of the first TTS rule, the output feeds another TTS rule. The BBB string, in the uppermost corner of Figure 4, has the strongest strength relation value, 12, if values form 4-1 are assigned for each place in the hierarchy, 4 being the strongest. ‘The DDA string, in the lowermost cor— ner, is the weakest with a strength relation value of 3. In Figure 4, any replacement of an input string by an output string leftward or upward of one space represents an increase in tonal strength of one value. In any PQR string where only PQ fulfills the condition for tone sandhi, replacement will be upward within the vertical plane and row in which the input string exists. In any PQR string where only QR fulfills the condition for tone sandhi, replacement will be leftward within the horizontal plane and row in which the input string exists. If both PQ and QR fulfill the condition for tone sandhi, then PQ will undergo tone sandhi first (vertical plane replacement-which I will refer to as VPR in the tables below) and then QR will undergo tone sandhi (horizontal plane replacement-HPR) except in cases where TTS Constraints 1 and 2 apply. In Figure 4, 13 PQR input strings and their outputs are visible. They are listed below. The numbers refer to the strings as listed in Tables 9.a and 9.b: 43 Table 10 Explanation of Replacement in Figure 4 1. AAA->ACA TTS Constraint 1/HPR 2. BAA->BCA HPR 3. CAA->CCA->BCA HPR and VPR 4. DAA->DCA TTS Constraint 2/HPR 11. CCA->BCA VPR 14. BCC->BBC HPR 18. ADA->ABA HPR 19. BDA->BBA HPR 20. CDA->CBA HPR 21. DDA->ADA->ABA VPR and HPR 22. DDB->ADB VPR 23. DDC->ADC VPR 25. BDD->BAD HPR A violation of TTS Constraint 1 would be represented in Figure 4 by an ‘S’-like replacement path. This can be seen in Figure 4 by looking at the AAA string. Instead of HPR, it would first have VPR, thus *AAA->CAA->CCA->BCA. A violation of TTS Constraint 2 would be represented in Figure 4 by a DAR input string being replaced by another input string. This can be seen by looking at the DAA string if it first had VPR to BAA instead of HPR to DCA. Figure 5 is the same as Figure 4 except that it has been split open in order to see the inside. In order to get the correct orientation, compare the BBB string in Figure 5 to the BBB string in Figure 4. 44 PPofllion Figure 5 The Three Dimensional Tonal Matrix: Second View 45 In Figure 5, 9 more PQR input strings and their outputs are visible. They are listed in Table 11 below: Table 11 Explanation of Replacement in Figure 5 5. AAB->CAB VPR 6. DAB->BAB VPR 7. AAC->CAC VPR 8. DAC->BAC VPR 9. AAD->CAD VPR 10. DAD->BAD VPR 12. CCB->BCB VPR 15. CCC->BCC->BBC VPR AND HPR 17. CCD->BCD VPR Figure 6 is also the same as Figure 4 except that it has been split open in a different manner. Again, in order to get the correct orientation, compare the BBB string in Figure 4 to the BBB string in Figure 6. In Figure 6, the remaining 5 PQR input strings and their outputs are visible. They are listed in Table 12 below: Table 12 Explanation of Replacement in Figure 6 13. ACC->ABC HPR 16. DCC->DBC HPR 24. ADD->AAD->(CAD) HPR and (VPR) 26. CDD->CAD HPR 27. DDD->DAD->(BAD) TTS Constraint 1/HPR and (VPR) 46 Figure 6 The Three-Dimensional Tonal Matrix: Third View 47 4.7 Q Position Hierarchy: B-C-A-D or B-C-D-A? Now that the three-dimensional matrices have been presented, it will be easier to explain why the Q position ordering must be B-C-A-D rather than B-C-D-A. The last tone in each string, Y of the XY string and R of the PQR string, never changes. In the AAA string, for example, if PQ of this string were accepted (I have shown, however, that this is not the case), then replacement would be vertical along the P hierarchy, because the P tone changes. If, on the other hand, QR were accepted, replacement would be horizon- tal along the Q hierarchy. There is never replacement along the R hierarchy because the last tone in every string remains the same. So in a PQ string that shows vertical replacement, the Q position does not change. But in a QR string that exhibits horizontal replacement, the Q position does change and replacement takes place along this hierar- chy. And since Q is in the first position of a QR string, the hierarchy must be the same as that for the P position. 4.8 Summary I introduced three more variables, P, Q, and R, to represent the three-syllable string in TTS. Then I showed the freedom of occurrence of tones in the PQR string and arranged these in strength hierarchies for each position in the PQR string. Then I took the 27 PQR input strings and explained all of their outputs showing that all the TTS rules apply left to right but that TTS Constraints 1 and 2 limit the position (PQ or QR) of the PQR string that they can apply to. After I discussed exceptional surface strings, I used the tonal strength hierarchies for each position in the PQR string to construct a three-dimensional tonal matrix. Finally, I showed why the ordering of the Q hierarchy must be B-C-A-D and not B-C-D-A. 5. Conclusion 5.1 Summary In this thesis I have discussed Tianjin tone sandhi in two and three-syllable strings. I have shown that an inde- pendently motivated notion of tonal strength may be the explanation for the occurrence of tone sandhi, and I have shown, according to this understanding, that the TTS rules all apply from left to right, and given two constraints which limit the position of the string that TTS rules can apply to. 5.2 Statement of Rules One implication of this study is that rules (42) and (43) are not restatements of the same phenomenon, as is generally accepted. A rule, for example, like (42) below does not seem to state the facts as accurately as (43) when stating the rules for Tianjin tone sandhi. 48 49 (42) x->y/___z (43) xz->yz Rule (42) can be restated informally as: x becomes or appears as y in an environment where it occurs before z. In this rule, x changes because it occurs before 2. Example (43), on the other hand, can be restated informally as: when x and 2 occur immediately adjacent to each other, they become or appear as yz. In this rule, x changes because it occurs with 2. Rule (43) is a more accurate statement of Tianjin tone sandhi because it is the combination of the two tones e.g. two falling tones occurring in an XY string (excluding AD), that makes the string subject to TTS. It is not the fact that a falling tone occurs before another falling tone that causes it to change as (42) would indicate. 5.3 Tonal Strength: Universal or Language Specific? That tones may have strength in relation to one another to my knowledge has never been proposed before. To show this empirically is to say something about tones that might be found to have further implications in other languages. It goes without saying that much more research needs to be done on this subject. Tonal languages from different language groups need to be studied and the data needs to be analyzed along the lines I have shown. Only in this way can we find if tonal strength is a parameter for other tone 50 languages or even universal, or if it is in fact only a phenomenon specific to the Tianjin dialect. NOTES 1 Chen (1986:109) refers to a Non-Derived Environment Constraint that is mentioned in Hung (1985): " . . .no TS [tone sandhi] rule of Tianjin may apply to the same syllable more than once in the course of a derivation." Although this is very similar to my TTS Constraint 1, Hung does not mention it in his more recent 1987 paper. 2 Zhang mentions (1987:260) that Chen told him this through personal communication. 3 Chen (1986:105). 4 Hung (1987:278 and footnote 4). 5 Parentheses are used to indicate that there is conflicting data for the final outputs of these strings. See section 2.6. The parentheses are also used in Tables 9.b and 12. 51 APPENDI X used in this paper. APPENDIX followed by the author, year number. (10) Chen:l987:205. (11) ibid. (12) ibid. (13) ibid. (14) Zhang:1987:248. (15) Tan:1987:234. (16) Zhang:1987:249. (17) Chen:1987:208. (18) ibid. (19) Zhang:1987:255. (20) ibid. (23) Tan:1987:234. (24) ibid. (25) Tan:1987:243. (33) Zhang:1987:269. (34) Hung:1987:278. (35) Hung:1987:283. (36) Hung:1987:278. (38) Tan:1987:232. (39) ibid. 52 of publication, This Appendix provides the sources for all the data I will give the number of the example and page (40) (41) Zhang:1987:261. ibid. 53 LI ST OF REFERENCES LIST OF REFERENCES Chen, Matthew Y. 1986. The paradox of Tianjin tone sandhi. Chicago Linguistics Society 22.98-114. . 1987. A symposium on Tianjin tone sandhi: Introductory remarks. Journal of Chinese Linguistics 15.203-26. Hung, Tony T.N. 1987. Tianjin tone sandhi: towards a unified approach. Journal of Chinese Linguistics 15.274-308. Li, X.J. and S.X. Liu. 1985. Tianjin fangyan de liandu biandiao [Tone sandhi in the Tianjin dialect]. Zhongguo Yuwen 1: 76-80. Tan, Fu. 1986. Yetan Tianjin fangyan de liandu biandiao [More on tone sandhi in the Tianjin dialect]. Zhongguo Yuwen 6: 447-50. . 1987. Tone sandhi in the Tianjin dialect. Journal of Chinese Linguistics 15.228-45. Zhang, Zheng-Sheng. 1987. The paradox of Tianjin: another look. Journal of Chinese Linguistics 15: 247-72. 54 "71111111111111.1111