2.1 Vowel nasalization

Between the two nasal rhymes, only one undergoes vowel denasalization in r-suffixation. In the stem forms, both /n/ and /ŋ/ nasalize the preceding vowel. During r-suffixation, the nasal coda is deleted to make way for the addition of the /-r/ suffix, in order to avoid a complex coda (Zhang 2000). The conditioning environment for vowel nasalization is therefore lost. Indeed, in a nasal rhyme that ends in /n/, the preceding vowel loses its nasalization, and surfaces as an oral vowel in [päɻ] (3d&g). But in a nasal rhyme ending in /ŋ/, the vowel retains its nasalization, as seen in (3f&i) [pɑ̃ɹ]. This is true for both Liaoning and Beijing. Why is the process of vowel denasalization sensitive to the place of articulation of the deleted nasal coda? In other words, why does vowel denasalization only target alveolar nasal rhymes?

Zhang (2000) pointed out that the answer can be found in the stem forms of the nasal rhymes. In an aerodynamics study, Zhang measured the duration of nasal airflow in nasalized vowels in the stem forms produced by two Beijing speakers. The durational ratio of nasal airflow to oral airflow in the production of a nasalized vowel is taken as an indication of the degree of nasalization. The higher the nasal-to-oral airflow duration ratio is, the more nasalized the vowel is. It was found that /CVŋ/ rhymes show a much higher nasal-to-oral airflow duration ratio than /CVn/ rhymes do, which suggests that the velar nasal triggers more nasalization on a preceding vowel than the alveolar nasal does. Zhang used double tilde to mark the highly nasalized vowels in [CV͌ŋ]. I adopt this notation. The data in (3) are updated in (4) to reflect the notational change in vowel nasalization.

According to Zhang, it is the strength of the nasal trigger that determines whether the vowel surfaces as a nasalized or an oral vowel in the r-suffixed form. The strong nasalization triggered by a velar nasal is perceptually more salient, and therefore more likely to surface in the absence of the triggering nasal. Whereas the weak nasalization triggered by an alveolar nasal is less salient, and therefore more easily deleted when the environment for nasalization is lost. Zhang used a gradient input-output Max[+Nas] constraint to capture this generalization. There is a Max[+Nas] for every nasalization-triggering segment. The Max[+Nas] associated with the stronger nasalization trigger always outranks the one associated with the weaker trigger. In the case of Mandarin, Max[+Nas]_ŋ ranks above Max[+Nas]_n. The two constraints are defined in (5), alongside a markedness constraint *V_nas, which punishes surface nasalized vowels found without a nasal trigger. The markedness constraint is ranked between the two faithfulness constraints, as seen in (5d), to derive the pattern seen in Mandarin diminutive forms. Vowels preceding /ŋ/ retain their nasalization in the suffixed forms (Max[+Nas]_ŋ » *V_nas), whereas those preceding /n/ get denasalized (*V_nas » Max[+Nas]_n). The ranking arguments are illustrated with the tableaux of (6). To put the limelight on vowel denasalization, only the subset of candidates that have undergone nasal coda deletion are considered in (6).

Zhang’s Max[+Nas] account places much importance on the preservation of individual features from input to output. The rhyme with a stronger degree of [+nasal] gets to preserve it in the output. I argue that it is actually the contrast between rhymes that is preserved in the suffixed output. The original contrast between the two inputs /CVn-ɻ / and /CVŋ-ɻ / is the place of articulation of the nasal coda. But it cannot be manifested in the suffixed output, due to nasal coda deletion. Therefore the two rhymes have to resort to enhancing their contrast in vowel nasalization, by fully nasalizing one rhyme and denasalizing the other. This is achieved in coordination with many other features of the suffixed forms, to preserve the contrast between the low vowel rhymes. A more detailed analysis is presented in Section 4.

2.2 Vowel backing

In the stem forms, the backness of the low vowel is determined by the following nasal coda (or the lack of it). After r-suffixation, the conditioning environment for rhyme harmony is lost via nasal coda deletion. The low vowel is now situated next to the suffixed rhotic coda, which has a coarticulatory backing effect. The backing effect of a rhotic has been observed in many dialects of English (see Tunley 1999; Lilienthal 2009; Chung & Pollock 2014). In Mandarin, the vowels in the stem forms [ãn] and [ä] undergo vowel backing by the rhotic coda. The stem [ɑ͌ŋ] is not affected by vowel backing, since its vowel is already back.

The coarticulatory vowel backing effect is observed in the recorded speech of a Beijing speaker and a Liaoning speaker (author). The second formant (F2), an indication of vowel backness, is measured across stem and suffixed forms. A front vowel has a high F2, while a back vowel has a low F2. It is found that for the rhymes /an/ and /a/, the F2 of the vowel is lower in the suffixed form than in the stem form. But the vowel in /aŋ/ rhymes have similar F2 for suffixed and stem forms.

The recording of the two speakers, both female, was conducted in a soundproof booth, with a sampling rate of 44.1Khz, 32 bits. Measurements were taken using Praat (Boersma & Weenink 2017). The recording materials include minimal triplets shaped as Can vs. Ca vs. Caŋ, in both stem and suffixed forms. There are 3 minimal triplets, each with a different onset. They include a voiceless stop /p/, a fricative /f/, and an affricate /ʈʂʰ/. The tones are consistent within each minimal triplet, but not controlled between triplets. All /p/-initial syllables are in the falling tone, while all syllables that begin with /ʈʂʰ/ have a low dipping tone. To elicit the diminutive forms, a disyllabic or trisyllabic noun compound was formed using the low vowel rhyme syllable as the final morpheme, where the rhotic coda is attached to. The compounds were recorded as part of a carrier sentence [wo xwej ʂwo ____ ʈʂəkə tsʰɨ ], which can be glossed as ‘I can say ____ the word’. Each compound was recorded in its stem form and diminutive form. Each sentence was repeated 4 times. There are altogether 2 (speakers) × 4 (repetitions) × 2 (forms) × 3 (rhymes) × 3 (onsets) = 144 tokens. For each token, the F2 value is taken at the visible vowel midpoint.

In the statistical analysis, the stem form and suffixed form of the same rhyme spoken by the same speaker are compared. For example, the Beijing speaker’s diminutive form /Can-r/ is compared against the stem from /Can/. A linear regression model on the vowel midpoint F2 is ran using RStudio (R Core Team 2018). Independent variables include morphological form (stem or suffixed) and onset type. Significance level is taken at p < 0.05. The results are summarized in Table 1 (Beijing) and Table 2 (Liaoning). The intercept is taken to represent the mean F2 of the stem rhymes. The estimate for “Formsuffixed” indicates the change in F2 between stem and suffixed forms. A negative change in F2 indicates that the vowel F2 is lower in the suffixed form than in the stem form.

In both Beijing and Liaoning, the p-value for change in F2 between stem and suffixed forms have reached significance for /Can/ and /Ca/ forms. This shows that vowel backing has taken place for /an/ and /a/ rhymes after r-suffixation. However, F2 is not significantly different between stem and suffixed /Caŋ/ forms, which indicates that the vowel is not backed. Onset does not appear to significantly affect F2.¹

The acoustic data support the description that the front [a] in the stem form (4a) [pãn] is backed into a central [ä] in the suffixed form of (4d&g). The central [ä] in the open-syllable stem (4b) [pä], though also backed in r-suffixation, remains categorically central in the suffixed form in (4e&h), since it has roughly the same F2 realization as the central vowel derived from the [pãn] stem (see mean F2 values in Table 3 & 4). The back vowel [ɑ] in the stem (4c) [pɑ͌ŋ] remains the same in (4f&i).

I also list the mean vowel F2 of each rhyme form in Table 3 (Beijing) and Table 4 (Liaoning). In each table, the middle block lists the stem rhyme F2 values, whereas the rightmost block has the suffixed rhyme F2 values. Each row shows the mean F2 of a minimal triplet of rhymes that share the same onset and tone. Each cell represents the mean F2 of 4 tokens of the same lexical item.

There are some unexpected F2 values² in Tables 3 and 4. For instance, in Table 3, the vowel in the /a/ rhymes are not consistently central for the Beijing speaker. In /p/-initial syllables, it has a similarly low mean F2 as the back vowel in /aŋ/. But in /ʈʂʰ/-initial syllables, it is as front as the front vowel in /an/. It could be the case that the vowel in an open syllable is not necessarily specified as central, but more likely to be unspecified in backness. Without a following nasal coda to dictate its surface representation, it can vary in its F2 value. Although such a wide range of variation in F2 is not found in the open-syllable rhyme produced by the Liaoning speaker. As to the suffixed rhymes, they usually have low F2 values across the board. But it is interesting to note that for the Beijing speaker, the suffixed /an/ and /a/ rhymes sometimes have lower F2 than the originally back vowel in the /aŋ/ rhymes. Since the vowel in /aŋ-r/ is heavily nasalized, it is possible that it might have colored the F2 measurement, thus making the comparison with other rhymes difficult.

2.3 /r/ allophones

Up to this point, I have discussed phonological processes that are common between Beijing and Liaoning in r-suffixation. They both undergo nasal coda deletion, vowel denasalization, and vowel backing. In this section, I introduce the major point of difference between the two dialect — the distribution of the /r/ allophone across the three rhymes.

The /-r/ suffix has two surface realizations: the retroflex [ɻ] and the non-retroflex, or bunched, approximant [ɹ] (Shuwen Chen et al. 2017; Hsieh et al. 2019; Jiang et al. 2019). The retroflex [ɻ] is produced with the tongue tip raised and bent towards the palate. [ɹ], on the other hand, is not a retroflex rhotic. During its production, the tongue tip is located in the lower region of the oral cavity, pointing downwards, behind the back of the lower teeth. There is no discernible upwards curving of the tongue tip.

Jiang et al. (2019) have identified two types of rhotic codas in an EMA study of the speech of Liaoning speakers. They compared the rhotic coda in two environments. One is the diminutive suffix /-r/ that attaches to a monosyllabic open-syllable stem like /a/. The other is the coda /r/ found in the monomorphemic word [ə˞] ‘child’, where it is not an affix. The tongue position of the speaker was tracked throughout the production of the rhyme in both cases. It was discovered that the affixational /-r/ found after monophthong stems mainly involves tongue-body movement, whereas the monomorphemic /r/ in [ə˞] is essentially produced with tongue-tip movement. The former is the non-retroflex [ɹ] used next to /a/ rhymes in Liaoning, while the latter corresponds to the retroflex [ɻ] found in /an/ stems. Jiang et al. suggest that the difference between the two rhotic allophones might be quite similar to that between the bunched and the retroflex rhotic found in English (see Delattre & Freeman 1968). The same group of researchers also compared the rhotic suffix between 3 Beijing speakers and 3 northeastern speakers. They found that after an open-syllable stem, Beijing speakers produce a retroflex suffix, whereas northeastern speakers have a non-retroflex suffix (Hsieh et al. 2019).

In Liaoning, /an/ rhymes select the retroflex [ɻ] as the diminutive suffix (7d), while /a/ rhymes select the non-retroflex [ɹ] (7e). But in Beijing, both /an/ and /a/ rhymes employ the retroflex [ɻ] for r-suffixation, as seen in (7a&b). When it comes the velar nasal /aŋ/ rhyme, the non-retroflex [ɹ] is used in both dialects, as shown in (7c&f).

The difference between the retroflex [ɻ] and the non-retroflex [ɹ] can be observed in formant transitions. In a production experiment, it was found that at the end of a suffixed rhyme with a retroflex [ɻ], F1 lowers and F2 rises. While in a suffixed rhyme with a non-retroflex [ɹ], F1 and F2 stay roughly the same towards the end of the rhyme.

4 female Liaoning speakers and 2 Beijing speakers (1 male, 1 female), who now live in Boston, were recruited for the experiment. They were all born in Liaoning or Beijing and have lived there for most of their childhood. They were recorded producing suffixed forms in isolation as well as in carrier sentences. The recordings were made in a soundproof booth. The sampling rate was 44.1Khz, 32 bits.

The test items include 100 disyllabic or trisyllabic words (one item has 4 syllables). Among them, 73 are of the shapes /Can/, /Ca/, or /Caŋ/, all beginning with a stop consonant. The rest are filler items. The test items consist of nouns and verb or adjective compounds that contain a noun as the rightmost morpheme. Some words are selected on the basis that they sound extremely unnatural with a diminutive suffix. For instance, [tsʰwen ʈʂɑŋ] ‘head of village’, is a title for someone in a position of authority. It is very unlikely to appear in the diminutive form. These words are placed in the experiment to make sure that speakers do not blindly judge every suffixed form to be natural sounding.

During the experiment, for each test item, the speakers are first asked to read out loud a sentence shown on a computer screen. The sentence is in the form of a question: [ni tɕɥetə ____ kʰəji tɕja ə˞xwajin ma], ‘Do you think ____ can take on an erhua suffix?’ Next, they are encouraged to attempt to produce the suffixed form. Speakers can use this opportunity to figure out whether the suffixed form is natural-sounding to them or not. During this period, isolated forms are recorded as well. Afterwards, the speakers are presented with a choice between two answer sentences displayed on the screen. The first answer reads: ‘I think ____ can take on an erhua suffix.’ ([wo tɕɥetə ____ kʰəji tɕja ə˞xwajin]). The other reads: ‘I think ____ cannot take on an erhua suffix.’ ([wo tɕɥetə ____ pu kʰəji tɕja ə˞xwajin]). The speakers are asked to make a choice based on their judgement of the naturalness of the suffixed form they have just attempted to produce, and to read that answer out loud. The answer sentence not only serves the purpose of recording suffixed forms in a carrier sentence, but also ensures that the suffixed tokens collected are actually natural sounding to the individual speaker.

The procedure is repeated for the 100 nouns. Of the 73 low vowel rhymes that are of interest, only those that pass the naturalness test are measured for their formant values.³ This means that there is no fixed number of tokens analyzed for each speaker, since there is a lot of between-speaker variation in the naturalness judgement of the suffixed forms.

Figure 1 shows the spectrograms of suffixed forms produced by the same female Liaoning speaker. The spectrograms are generated using Praat. Each spectrogram represents one of the three rhymes, /an/, /a/, and /aŋ/, in suffixed forms. They all begin with a bilabial unaspirated stop /p/, and are all in the third tone.

Figure 1

Spectrograms of low vowel rhymes produced by a female Liaoning speaker.

Figure 1.a is the spectrogram of [päɻ] (/pan-r/), and Figure 1.b displays that of [päɹ] (/pa-r/). In Figure 1.a, where there is a retroflex coda [ɻ], F1 and F2 diverge towards the end of the rhyme. F1 lowers and F2 rises. Compare this with the formant transition at the end of the rhyme in Figure 1.b, where F1 and F2 both stay around the same level for a non-retroflex coda [ɹ]. The same can be said for Figure 1.c, where [pɑ͌ɹ] (/paŋ-r/) also ends in a non-retroflex coda.

The F1-F2 gaps at the end of suffixed rhymes in isolation are measured. There are 99 Liaoning tokens from 4 speakers, and 55 tokens from the 2 Beijing speakers. Table 6 displays the mean F1-F2 gap of each suffixed rhyme produced by the Liaoning speakers. The retroflex [ɻ] has a big F1-F2 gap of nearly 900Hz, whereas the non-retroflex [ɹ] has a small F1-F2 gap at about 550Hz. This shows that F1-F2 gap is a good acoustic indicator that distinguishes between retroflex and non-retroflex rhotic codas. Table 5 shows the mean F1-F2 gaps produced by the Beijing speakers. Both /an-r/ and /a-r/ display a big F1-F2 gap at around 1000Hz, indicating a retroflex [ɻ]. /aŋ-r/ has a small F1-F2 gap below 700Hz for the non-retroflex [ɹ].

4.1 The three-dimensional rhyme space

Three auditory cues are used to distinguish between the stem SR of the low vowel rhymes: nasal stop’s oral closure duration, the degree of vowel nasalization, and vowel F2. The three cues correspond to the x-axis, the y-axis, and the z-axis in a three-dimensional rhyme space, respectively. This is illustrated in Figure 2, with coordinates for each rhyme labeled in parenthesis.

Figure 2

Three-dimensional stem rhyme space.

The z-axis has abstract values of vowel F2 expressed as integers. The bigger the integer, the higher the F2. A difference of 1 on the F2 axis corresponds to roughly 100Hz. This is based on Zee & Lee’s (2001) measurements of the low vowel produced by speakers of Beijing Mandarin in different rhymes. They report that for 10 female speakers, the mean F2 of the front low vowel found in [ãn] is 1730Hz. The central vowel in [ä] has a mean F2 of 1594Hz, while the back vowel in [ɑ͌ŋ] has a mean of 1382Hz. The difference between the front [a] and central [ä] is roughly 100Hz, and that between the central [ä] and back [ɑ], about 200Hz. This is why the central [ä] corresponds to a value of 2 on the F2 axis, 1 unit lower than the front [a] (3), and 2 units higher than the back [ɑ] (0).

The y-axis of vowel nasalization is an abstraction from Zhang’s (2000) observation that there are two degrees of nasalization in the stem forms. The number on this axis corresponds to the number of nasalization tilde marks. The weakly nasalized [ã] has a value of 1 on the nasalization axis, while the strongly nasalized [ɑ͌] has a value of 2. The oral vowel [ä] sits low at 0 on this axis.

The numbers on the x-axis of nasal stop are based on the duration of the oral closure of the two nasal codas. Li & Cheng (2014) reported that the two nasal codas of Mandarin differ in their duration of oral closure. /n/’s oral closure is proportionally shorter than that of /ŋ/, when compared to the duration of the entire nasal rhyme. Therefore I assign a higher numerical value for /ŋ/ (3) on the nasal stop x-axis, and a lower one for /n/ (2). The open-syllable rhyme has a value of 0 on the nasal stop axis. Note that the distance between /n/ and the absence of a nasal coda is 2, larger than that between /n/ and /ŋ/. This is because perceptually, the difference between a nasal coda and the total absence of any nasal segment, is greater than that between two nasal stops of different lengths. The assignment of values for each dimension is summarized in Table 8.

The choice of oral closure duration as the auditory cue corresponding to the nasal stop x-axis might be a controversial one. It could be argued that vowel-to-nasal transition F2 is a better indicator for the place of articulation of the nasal coda (see Liberman et al. 1954; Malécot 1956; Recasens 1983; Harding & Meyer 2003). Indeed, in Mandarin, vowel-to-nasal transition F2 can be used to distinguish between alveolar and velar nasals. Faytak et al. (2020) measured the formant values at the vowel endpoint preceding a nasal coda in Standard Mandarin. They found that between /n/ and /ŋ/ codas, there is approximately a 300Hz difference in F2. I concur that vowel-to-nasal transition F2 is a good auditory cue for nasal place of articulation. However, it cannot be used to model the difference between open-syllable rhymes and nasal rhymes. After all, the nasal stop x-axis is required to provide a coordinate for each of the three low vowel rhymes, /an/, /a/, /aŋ/. Had vowel-to-nasal transition F2 been used as the auditory cue for this axis, it would not be possible to represent the open-syllable rhyme /a/ on the axis. /a/ does not have a nasal coda, and therefore there is no vowel-to-nasal transition F2. It is for this reason that I have decided to use oral closure duration as the auditory cue for the nasal stop axis. The open-syllable rhyme, despite having no nasal coda, can be interpreted as having an oral closure duration of zero. Thus one can compare /a/ with the two nasal rhymes along the nasal stop x-axis.

Using the criteria of Table 8, the rhyme [ãn] has the coordinates (2,1,3) in the three-dimensional rhyme space. It has a value of 2 on the x-axis for /n/, 1 on the y-axis for one degree of vowel nasalization, and 3 on the z-axis for having the highest F2. Similarly, [ä] has coordinates of (0,0,2), and [ɑ͌ŋ], (3,2,0). The three rhyme SR’s, with their coordinates, can be found in the rhyme space of Figure 2. The locations of the rhymes are labeled with black dots. The dashed lines are drawn to help visualize their locations in the three-dimensional space. Concrete lines connect each pair of rhymes, showing their distance, which are calculated in (8).

The smallest distance between any pair of rhymes is that between [ãn] and [ä], at approximately 2.45, which satisfies a MinDist=RD:2 constraint, as defined in (9).

4.2 Suffixed rhyme space

After r-suffixation, the SR rhyme space takes on a different look, for the nasal stop x-axis ceases to be relevant for contrast representation due to nasal coda deletion. The nasal coda deletion process itself can be accounted for using the following three constraints: *ComplexCoda, RealizeAffix, and Template, adopting the analysis in Zhang (2000). Their definitions can be found in (10). In (11), *ComplexCoda rules out the faithful candidate (a) [CṼnɻ], which contains both the nasal coda and the /-r/ suffix. One of the coda consonants has to be deleted, and RealizeAffix makes sure it is the stem consonant that gets deleted. The constraint places a priority on realizing the affix over the stem, based on Lin’s (1993) Affix Manifestation Principle. Thus candidate (d) [CṼn] is ruled out. Finally, there is also the possibility of realizing the /-r/ suffix in a separate syllable, as in candidate (b) [CṼn.ɻ]. Template dictates that the diminutive rhyme should be realized as a single syllable. All 3 constraints are ranked above Max, resulting in the win of the nasal-coda-deletion candidate (c) [CVɻ].

With the deletion of the nasal coda, all three rhymes now have a value of 0 on the nasal stop x-axis. It can be visualized as all three rhymes being squashed to the yz-plane on the left hand side, as illustrated in Figure 3. The original locations of the stem rhymes are marked in gray. The movement the rhymes undergo after r-suffixation are shown in arrows, which include vowel backing along the F2 axis, and denasalization along the nasalization axis. The /-r/ suffix is written with an abstract R here, since its SR is specific to each dialect.

Figure 3

The rhyme space after nasal coda deletion.

In the suffixed rhyme space, a fourth dimension needs to be taken into consideration, to include auditory cues to the rhotic suffix. This is the F1-F2 gap dimension. Recall that the F1-F2 gap at the end of a rhyme is an indicator for whether the rhotic suffix is retroflex or not (see Section 2.3). Figure 4 shows the suffixed rhyme space with the added F1-F2 gap dimension. Figure 4.a is the suffixed rhyme space of Beijing. Figure 4.b represents Liaoning. Here, I reuse the x-axis for the F1-F2 gap dimension, since the nasal stop dimension is no longer relevant in the suffixed forms.⁴ As shown in Table 6, the retroflex rhotic suffix [-ɻ] has an F1-F2 gap of approximately 850-900Hz at the end of rhymes, whereas the non-retroflex [-ɹ] has one of about 550Hz. The two types of /-r/ allophones are separated by approximately 300Hz. Recall that each unit on the F2 axis corresponds to a difference of 100Hz. The same rule of thumb is applied to the F1-F2 gap axis as well. Therefore, the 300Hz difference is represented on the x-axis as a difference of 3 between the non-retroflex [ɹ] at 0, and the retroflex [ɻ] at 3.

Figure 4

Suffixed Rhyme Space.

As shown in Figure 4.a, in Beijing, the rhymes /an-r/ and /a-r/ share the same suffixed form, occupying the same location in the suffixed rhyme space. [äɻ] has the coordinates (3,0,1), where 3 on the F1-F2 gap axis points to a retroflex suffix [-ɻ], 0 on the nasalization axis indicates that it is an oral vowel, and the 1 on the F2 axis is a slightly backed central vowel [ä]. The rhyme /aŋ-r/ surfaces as [ɑ͌ɹ], with coordinates of (0,2,0). The first 0 is for the non-retroflex [ɹ] on the F1-F2 gap axis, 2 signifies the degree of nasalization on the vowel, and the second 0 indicates a back vowel on the F2 axis. The rhyme distance is calculated in (12). Since there are only two surface forms in Beijing suffixed rhymes, there is only one rhyme distance.

Liaoning (Figure 4.b), on the other hand, retains the contrast between /an-r/ and /a-r/ in the suffixed forms. /an-r/ surfaces as [äɻ], with a retroflex [ɻ], which is a 3 on the F1-F2 gap axis. Whereas /a-r/ surfaces as [äɹ], with a non-retroflex [ɹ], corresponding to 0 on the F1-F2 gap axis. The /aŋ-r/ rhyme has a value of 0 on the F1-F2 gap axis, just like its counterpart in Beijing. The rhyme distance between each pair of suffixed rhymes in Liaoning is calculated in (13).

4.3 Contrast preservation constraints

As seen in the calculations of suffixed rhyme distances in (12) and (13), neither Beijing nor Liaoning violates MinDist = RD:2. The smallest rhyme distance in Beijing is 3.74, and 2.24 in Liaoning. However, the number of contrasts remaining in the suffixed forms differ between the two dialects. In Beijing, the /an/ and /a/ rhymes are neutralized after r-suffixation. Therefore, there are only two contrastive suffixed rhymes in Beijing (Figure 4.a). Liaoning, on the other hand, retains all three contrastive rhymes in the suffixed forms, as shown in Figure 4.b. There is no neutralization between any of the three rhymes.

PreserveContrast-BD, as defined in (14), rewards Liaoning for retaining all three contrastive rhymes in the suffixed forms, while penalizing Beijing for its neutralization. It is adapted from Flemming’s (1995) MaximizeContrasts, to evaluate mappings from stem forms to suffixed forms.

Similar to MaximizeContrasts, the constraint assigns checkmarks instead of violation marks. But PreserveContrasts-BD departs from Flemming’s constraint in that it evaluates the number of contrasts in the derived forms in relation to the base forms. Instead of saying “have as many contrasts as you can”, PreserveContrasts-BD says “keep as many contrasts from the base forms as you can in the derived forms”.

PreserveContrasts-BD has a different ranking in Beijing and Liaoning. In Beijing, it is ranked below MinDist=RD:2 and Ident[Retroflex]-IO (more on this constraint in Section 4.4), for the dialect ensures that the rhyme distance between each suffixed rhyme is big enough, at the expense of losing contrasts between rhymes. This is shown in the tableau of (15a). In Liaoning, however, PreserveContrasts-BD is ranked as high as MinDist=RD:2. This is because Liaoning puts as much importance on retaining rhyme contrasts as maintaining rhyme distances. The ranking of Liaoning is shown in (15b).

The candidates of the tableaux in (15) are not individual output forms, but sets of output forms. Each candidate represents a suffixed rhyme space, illustrated separately in Figure 5. They are evaluated against the stem rhyme space. In each candidate, the suffixed rhymes, from left to right, correspond to /an-r/, /a-r/, and /aŋ-r/. This is the way to read tableau candidates throughout this paper.

The five candidates are the same in (15a) and (15b). Candidate (a) is Beijing, with neutralization between the /an-r/ and /a-r/ rhymes into [äɻ] (see Figure 5.a). In terms of notation, the neutralization output form [äɻ] is written twice, to show their one-to-one mapping with the stem rhymes. Between the two instances of [äɻ], an equality sign “=” is used instead of a dash, to emphasize that the output forms are identical. Candidate (b) is Liaoning, where the /a-r/ rhyme surfaces as [äɹ], with a non-retroflex coda, and every contrast is kept (see Figure 5.b).

Candidate (c) also maintains the three-way contrast, but violates MinDist=RD:2. Here, the /an-r/ rhyme retains its nasalization, surfacing as [ä̃ɻ], and reduces its distance from the /a-r/ rhyme to a mere 1, as shown in the calculation in (16a). Candidate (d) has all three vowels maintaining their stem values in F2 and nasalization, while employing identical retroflex [-ɻ] suffix. It is ruled out by MinDist=RD:2, for a rhyme distance of 1.41 between /an-r/ and /a-r/, as shown in (16b). Candidate (e) displays complete neutralization between all three suffixed rhymes, converging at [äɻ] (see Figure 5.e). It is disfavored by both dialects, due to losing too many contrasts.

Figure 5

Candidate rhyme spaces in tableaux (15a&b).

In both dialects, MinDist=RD:2 is ranked high, ruling out candidate (c). The remaining two candidates, the neutralizing candidate (a) and contrast-preserving candidate (b) both satisfy MinDist. Liaoning (15b) ranks PreserveContrasts-BD as high as MinDist=RD:2, and therefore favors the contrast-preserving candidate (b) over the neutralizing candidate (a). In Beijing, however, PreserveContrasts-BD ranks below MinDist=RD:2 and Ident[Retroflex]-IO. The neutralizing candidate (a) has one less violation of Ident[Retroflex]-IO than the contrast-preserving candidate (b), and thus is chosen by Beijing as the optimal candidate. The lowly-ranked PreserveContrasts-BD does not get a say on the matter.

Beijing satisfies MinDist=RD:2 at the expense of violating PreserveContrasts-BD. This can be observed in the candidate pair (a) and (c). The two candidates are equally acceptable according to Ident[Retroflex]-IO, incurring one violation each. But MinDist=RD:2 favors the neutralizing candidate (a), whereas PreserveContrasts-BD favors candidate (c). For the dialect, MinDist=RD:2 is ranked higher, thus the neutralizing candidate (a) wins, despite not preserving all contrasts from the stem forms.

In Liaoning, on the other hand, the two constraints are equally high. Therefore, neither candidate (c) nor the neutralization candidate (a) can surface. The dialect places as much priority on preserving the three-way contrasts from the stem forms, as making sure each contrast is salient enough.

4.4 /r/ allophony constraints

Up until now, I have used the constraint Ident[Retroflex]-IO without explanation. This section provides the reasoning behind this constraint, arguing against an alternative markedness constraint account. I argue that the retroflex [-ɻ] is the default diminutive suffix. I also address why the /aŋ/ rhyme would opt for the non-default [-ɹ] as its suffix.

4.5 F2 constraints

The vowel backing of the front [a] and central [ä], triggered by the addition of a rhotic suffix, can be accounted for with the markedness constraint F2<2/_R, as defined in (20a). The front vowel [a], with an F2 value of 3, violates the constraint. So does the slightly more front central vowel [ä] seen in the open-syllable stem. By stipulating that before a rhotic suffix, a vowel cannot have a value bigger than or equal to 2 on the F2 axis, the constraint explains why both the front [a] in the /an-r/ rhyme and the central [ä] in the /a-r/ rhyme undergo coarticulatory backing.

A markedness constraint is often the triggering force behind modifications in the output form that departs from the input form, or another output form. But its power needs to be checked by a counterforce: the faithfulness constraint, which requires the output form to be identical to the input form, or another output form. This is why I propose the BD faithfulness constraint Ident[F2]-BD (defined in (20b) to ensure that the backing process triggered by F2<2/_R does not push the vowels all the way to 0 on the F2 axis. The markedness constraint is ranked above the BD faithfulness constraint, as shown in (20c).

The relative ranking between the two F2 constraints and the contrast preservation constraints are illustrated with the tableau for Beijing in (21a), and the tableau for Liaoning in (21b). Between the two tableaux, candidates with the same letter share the same F2 values for each suffixed rhyme, differing minimally on the choice of /r/ allophone. For instance, candidate (a) of (21a) [aɻ-äɻ-ɑ͌ɹ] and candidate (a) of (21b) [aɻ-äɹ-ɑ͌ɹ] have the same values on the F2 axis: [3-2-0]. Figure 7.a illustrates the position of each suffixed rhyme in candidate (a) on the F2 axis, with R as an abstracted rhotic suffix. Every pair of near-identical candidates in (21a) and (21b) corresponds to an F2 diagram in Figure 7. Figure 6 shows the stem rhyme F2 values for comparison.

In order to focus on F2 constraints, I only include candidates that have the same nasalization pattern and choice of rhotic suffix as the winning candidate for each dialect. Only F2 values vary between candidates.

Therefore, /r/ allophony constraints and nasal constraints can be omitted from the tableau.

In (21a), candidate (a) has F2 values that are completely faithful to the base forms. It incurs two violations of the markedness constraint F2<2/_R. Candidate (b) (Figure 7.b) has partial backing, where the front vowel in the /an/ rhyme moves from 3 to 2 on the F2 axis, and the central vowel in /a/ from 2 to 1. One violation of F2<2/_R is incurred by /an/. Candidate (c) has both front and central vowels moving back to the position of 1 on the F2 axis (see Figure 7.c). The requirement of F2<2/_R is satisfied. Candidate (d) has the central vowel in /a/ moved back one step further, showing up at 0 on the F2 axis in Figure 7.d. But this causes a violation of the equally highly ranked MinDist=RD:2, for the rhyme distance between the suffixed /an-r/ and /a-r/ rhymes is only 1. Candidate (e) violates neither F2<2/_R nor MinDist=RD:2, by having a back vowel [ɑ] in all three rhymes, and neutralizing the contrast between /an-r/ and /a-r/. But it violates the gradient BD faithfulness constraint Ident[F2]-BD 5 times, whereas candidate (c) only causes 3 violations of this constraint. Therefore, candidate (c) is the optimal candidate. Both F2<2/_R and MinDist=RD:2 are highly ranked, for the winning candidate cannot violate either.

Figure 6

Stem rhyme F2 values in tableaux (21a&b).

Figure 7

Candidate rhyme F2 values in tableaux (21a&b).

The F2 constraints derive the same vowel F2 values for Liaoning, as shown in tableau (21b). Here, the candidates are minimally different from the Beijing tableau in their choice of rhotic suffix for the open syllable rhyme, while all F2 values remain the same as the Beijing candidates. The difference in constraint ranking lies in the fact that Liaoning ranks PreserveContrasts-BD as high as MinDist=RD:2. Candidates (a) and (b) are ruled out for violations of the markedness constraint F2<2/_R. Ident[F2]-BD stops candidates (d) and (e) from surfacing, both of which have incurred too many violations of the BD faithfulness constraint. Candidate (c), where both the front vowel and the central vowel are backed into the position of 1 on the F2 axis, wins, just like they do in Beijing.

4.6 Nasal constraints

As previewed in Section 2.1, I argue that vowel denasalization is not motivated by the markedness constraint *V_nas, but by contrast preservation. In the stem forms, the varying degrees of nasalization seen in the two rhymes [ãn] and [ɑ͌ŋ] serve to enhance the contrast in place of articulation of the nasal coda. But in the suffixed forms, the nasalization trigger is deleted for both rhymes. What is left are two nasalized low vowels that still need to maintain a salient contrast between each other. However, for the listener, perceiving the difference between the two nasalized low vowels is a difficult task. There are two reasons for this.

First of all, the difference in degree of nasalization between *[ä̃] and [ɑ͌] is simply not big enough to be perceptually salient. It is true that two degrees of nasalization are licensed in the stem forms, but they are a byproduct of a contrast elsewhere, namely the nasal coda. The degree of nasalization cannot manifest a contrast on its own, when the nasal coda is deleted. Therefore, only one degree of nasalization is allowed in a context without nasal codas.

A second problem with having *[ä̃] and [ɑ͌] in the suffixed forms is that the nasalization would get in the way of the F2 contrast. With backing of the front vowel, the F2 distance between the two vowels is already reduced from 3 to 1 on the F2 axis. It is universally more difficult for a speaker to distinguish between two nasalized vowels than between two oral ones (see Bond 1976; Wright 1986; Krakow et al. 1988; Beddor 1993; Stanton 2018). Retaining the nasalization in both vowels makes it harder to maintain an F2 contrast between them.

To capture the objective of the language to maximize the contrast in degree of nasalization, I include a single-dimension MinDist constraint in my analysis. This is MinDist=VND:2, as defined in (22a).

The suffixed rhymes *[ä̃ɻ-äɻ-ɑ͌ɹ] (/an-a-aŋ/) violate MinDist=VND:2, for their distance along the vowel nasalization axis is a mere 1 between the pair *[ä̃ɻ-äɻ] and between the pair *[ä̃ɻ-ɑ͌ɹ]. This is shown in the tableau for Beijing in (23a), as candidate (a).

A gradient BD faithfulness constraint for the nasalization axis (22b) is also included. Ident[Nasal]-BD works in a similar fashion as Ident[F2]-BD. It helps rule out candidate (c) of (23a), where instead of denasalizing the vowel in the /an-r/ rhyme, it denasalizes the vowel in the /aŋ-r/ rhyme and raises the degree of nasalization in /an-r/. While satisfying MinDist=VND:2, candidate (c) causes 2 more violations of Ident[Nasal]-BD than the winning candidate (b).

In (23a), I only include candidates with the optimal F2 values and rhotic suffixes, in order to put the limelight on nasal constraints. A diagram of the vowel nasalization dimension of each candidate is illustrated in Figure 9 (also applicable to (23b)), so that the evaluation of the nasal constraints is more transparent to the reader. Figure 8 shows the vowel nasalization dimension of the stem rhymes.

(23b) shows the tableau for Liaoning, where the distribution of /r/ allophony in each of the candidates is adjusted for the dialect. The open-syllable stem /a/ takes a non-retroflex [ɹ] as suffix. Liaoning also differs from Beijing in its ranking of the PreserveContrasts-BD constraint. In Liaoning, it is ranked as high as MinDist=VND:2 and MinDist=RD:2, ruling out any neutralization candidate. In addition, candidate (c) is ruled out by a different constraint in Liaoning than in Beijing. It incurs a fatal violation of MinDist=RD:2, due to the small rhyme distance of 1 between [äɹ]_(0,0,1) (/a/) and *[ɑɹ]_(0,0,0) (/aŋ/).

Figure 8

Stem rhyme nasalization values in tableaux (23a&b).

Figure 9

Candidate rhyme nasalization values in tableaux (23a&b).

Note that stem forms are not subject to MinDist=VND:2, due to the presence of nasalization triggers. Therefore, varying degrees of nasalization are licensed in the stem forms, allowing [ãn] and [ɑ͌ŋ] to surface at the same time.

The full ranking of all constraints in Beijing is shown in (24), with candidate rhyme spaces illustrated in Figure 10. (25) displays the full ranking in Liaoning, accompanied by candidate rhyme spaces in Figure 11.

Figure 10

Candidate rhyme spaces in tableau (24).

Figure 11

Candidate rhyme spaces in tableau (25).

5.1 The role of BD faithfulness

In Flemming’s (1995) original description of Dispersion Theory, faithfulness constraints have no place in the framework. But in this study, it can be seen that BD faithfulness constraints play an integral part in deriving the distribution of the rhotic suffix allophones in the two dialects of Mandarin. The BD faithfulness constraint Ident[FormantTransition]-BD works alongside the contrast preservation constraints, to dictate which rhotic allophone the nasal rhymes /an/ and /aŋ/ should use. BD faithfulness constraints are not necessarily incompatible with a contrast preservation analysis. In Liaoning, the suffixed /a/ rhyme is instructed by MinDist=RD:2 and PreserveContrasts-BD to enhance its contrast from /an/ by resorting to a different rhotic suffix. But without a BD faithfulness constraint dictating which rhotic allophone /an/ should take, /a/, solely with the goal to be distinct from /an/, would have received no instruction on which rhotic allophone itself ought to use. In both Beijing and Liaoning, the BD faithfulness constraint Ident[FormantTransition] requires the /aŋ/ rhyme to use a non-retroflex rhotic suffix, so that the suffixed form is more faithful to the stem form. BD faithfulness constraints play an important role in deriving the allophonic distribution of the rhotic suffix, and are therefore not at odds with the overall objective of contrast preservation.

Interestingly, PreserveContrasts-BD is itself a BD faithfulness constraint. Unlike Flemming’s MaximizeContrasts, it does not generate a set of contrastive phonemes to form an inventory, but draws upon the contrasts already existent in a set of base forms, making sure that the contrasts are still present in the derived forms. PreserveContrast-BD evaluates the mapping between base forms and derived forms, and can therefore be considered a BD faithfulness constraint. But unlike a regular BD faithfulness constraint, where the similarity between a specific base form and its derived form are evaluated, PreserveContrasts-BD is not concerned with the specific segments or features in the derived form. Instead, it requires that the number of elements in the set of derived forms match the number of elements in the set of base forms. In the example of low vowel rhymes in Mandarin, the set of base forms contains 3 elements: [ãn], [ä], [ɑ͌ŋ]. PreserveContrasts-BD requires that there be 3 elements in the set of suffixed forms as well. As to how the derived forms individually map onto the base forms, PreserveContrasts-BD has no say in the matter.

5.2 Alternative analyses

The two key ingredients of my contrast preservation analysis are contrast enhancement and output-output mapping. I argue that neither are dispensable. In this section, I consider three alternative analyses. The first alternative analysis is one without reference to either contrast enhancement or output-output mapping. The second alternative analysis considered has elements of contrast enhancement, but no output-output mapping. The third alternative analysis contains output-output mapping, but no contrast enhancement. I provide arguments against each of the three analyses, and show that both contrast enhancement and output-output mapping are crucial to the analysis of Mandarin r-suffixation.

5.3 Diachronic sound change

Beijing and Liaoning are two concurrent dialects of Mandarin that display different r-suffixation patterns. There is reason to believe that they might represent two stages in diachronic sound change as well. Wang & He (1985) reported a generational difference among Beijing speakers. According to them, older speakers tend to have the contrast between /an/ and /a/ after r-suffixation, whereas younger speakers at the time have neutralized the two suffixed rhymes. The observation was supported by a perceptual study conducted on 50 speakers under the age of 35, who overwhelmingly could not distinguish between /an-r/ and /a-r/, with a confusion rate at 96.4%. However, the same group of young speakers had less trouble distinguishing between the mid vowel rhymes /ən-r/ and /ə-r/, displaying varying degree of identification rate. Wang & He suspected the neutralization was a sound change in progress, that somehow affected low vowel rhymes more than mid vowel rhymes.

Wang & He (1985) did not provide any acoustic data for the older speakers, so it is hard to see how they realized the contrast between /an-r/ and /a-r/. It is possible that the older speakers of Beijing in the 1980s had a similar r-suffixation pattern as present-day Liaoning speakers. Exactly how the sound change took place is an interesting question for future research. One relevant study is the Bidirectional Phonetics and Phonology learning algorithm proposed by Boersma & Hamann (2008). The algorithm uses the same set of gradient constraints in the process of perception and production. It is capable of modeling the non-teleological sound changes across generations that eventually arrives at a stable state of dispersion. The learner can predict the sound changes of the three Polish sibilants across centuries. However, Boersma & Hamann admit that their learner cannot replicate the process of contrast neutralization across generations. Therefore, it is not capable of modeling the recent sound change in Beijing that results in contrast neutralization.

5.4 High vowels and diphthongs

The high vowel rhymes suffixation patterns reported by Chao (1968), Wang & He (1985), Duanmu (2007), and Lin (2007) for Standard Mandarin are similar to those of the low vowel rhymes in Beijing. The alveolar nasal rhyme /Vn/ neutralizes with the open-syllable rhyme /V/, while the velar nasal rhyme /Vŋ/ maintains contrast with some degree of nasalization. The /i/ and /in/ rhymes neutralize as [iər], whereas /iŋ/ is realized as [iə̃r]. /y/ and /yn/ neutralize as [yər]. /u/ becomes [ur], while /uŋ/ becomes [ũr] (or [uŋʳ] according to Duanmu 2007).

The low vowel diphthong rhymes: /aj/ and /aw/ also display interesting suffixation patterns. /aj/ is reported to have neutralized with /an/ and /a/ in Standard Mandarin, surfacing as [ar]. Suffixed /aw/, on the other hand, is variably transcribed as [aur] (Chao 1968; Wang & He 1985) or [auʳ] (Duanmu 2007; Lin 2007). The rounding feature of the offglide is retained in the suffixed form.

The neutralization facts reported about Standard Mandarin, or Beijing, is not surprising, given the dialect ranks MinDist=RD:2 above PreserveContrasts-BD. It remains to be seen how Liaoning realizes the high vowel and diphthong rhymes in the suffixed forms. It is possible that /r/ allophony and other additional acoustic cues are recruited to preserve the contrasts after suffixation. More production and perception data from both Beijing and Liaoning speakers need to be collected, in order to extend the contrast preservation analysis to account for these rhymes. I leave this as an open question for future research.