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CantoneseA data pattern similar to Thai is documented by Gordon (1998) for Cantonese. Possible syllable types in Cantonese are the same as Thai: CV, CVN, CVVN, CVO, and CVVO (N=/m, n, N/, O=/p, t, k/). With both vowel length contrast and the checked/non-checked distinction, the distribution of contour tones in Cantonese is also only affected by the latter factor. In CV, CVN and CVVN, seven different tones, including four contour tones, can occur: 53, 35, 21, 23, 55, 33, 22. But in CVVO and CVO, only level tones 5, 3, and 2 can occur, even when the syllable contains a long vowel. Gordon’s duration data for different syllable types of Cantonese are graphed in (0). Again, the grey portion in the bars for /a:m/ and /am/ indicates sonorous duration contributed by the nasal coda. Similarly to Thai, even though there is no vowel length contrast in open syllables, vowels in open syllables are phonetically long—considerably longer than the phonemic long vowel in CVVO. Also, the sonorous portion of the rime in CVR is considerably longer than that in CVVO. (0) Cantonese sonorous rime duration (ms): 
Cantonese may differ from Thai in one respect. In Thai, CVN has a longer sonorous rime duration than CVVO, largely due to the overly long nasal coda, and vowel shortening in checked syllables plays a minor role. But in Cantonese, it is probably the combination of both factors that gives rise to this durational pattern: in (0), we can see that the nasal coda in /am/ accounts for more than half of the sonorous rime duration, and the long vowel in /a:p/ is considerably shorter than that in /a:m/ (150ms vs. 208ms). The more prominent vowel shortening in Cantonese maybe due to the vowel quality differences that accompany the vowel length distinction. For example, in Kao (1971), the long and short versions of /a/ are transcribed as [A…] and [å] respectively. This may give the long vowel more freedom to shorten before an obstruent coda, as the long/short contrast is still safely maintained by their quality difference. Thai, however, does not have quality differences between long and short vowels, and thus must more faithfully preserve the durational distinction between them before an obstruent coda. I further conjecture that in all languages that favor contour tones on non-checked syllables regardless of the contrastive vowel length status, either a prolonged sonorant coda, or shortening of vowel nucleus in checked syllables, or both, are at play, and this results in non-checked syllables having a significantly longer sonorous rime duration than checked syllables, even when the former has a phonemic short vowel and the latter has a phonemic long vowel. Just like Standard Thai, Cantonese can be used as another language in our search of an appropriate a value for the definition of CCONTOUR. The relevant syllable types are again CVN and CVVO, and the relevant duration values are summarized in (0).
Dur(V2)=150ms, Dur(R2)=0. Substituting the variables in 1<a<  with the duration values in (0), we get the a range 1<a<3.451. Therefore, the a range that we have obtained from the Thai data (1<a<1.695) should be able to account for the Cantonese data; i.e., it will predict that CVN has a greater contour tone bearing ability than CVVO in Cantonese.
NavajoHypothesis and MaterialsThe two factors that influence the sonorous rime duration in Thai and Cantonese—phonemic vowel length and coda sonorancy—are also at play in Navajo. The only difference is that in Navajo, vowel length is contrastive in both open and closed syllables, which results in six syllable types: CV, CVO, CVR, CVV, CVVO, and CVVR. But the tonal distribution in Navajo is very different from Thai and Cantonese. Navajo syllables can have four possible tones: High (H), Low (L), Fall (H°L), and Rise (L°H), with the contour tones H°L and L°H restricted to long vowels and diphthongs, i.e., CVV, CVVO, and CVVR syllables. Therefore, unlike Thai and Cantonese, the factor that determines the contour distribution in Navajo is phonemic vowel length, not coda sonorancy. The tonal distribution in Navajo is summarized in (0). (0) Tonal distribution in Navajo:
The crucial phonetic comparisons for contour tone bearing ability are between CVR and CVV, and between CVR and CVVO: CVR benefits from having a sonorant coda, while CVV and CVVO benefit from having a long vowel. Given that a vowel is a better tone bearing segment than a sonorant consonant, we will know that CVV and CVVO have greater contour tone bearing ability than CVR as long as their sonorous rime duration is no shorter than CVR’s (see §2.1 and §3.1). Thus, the hypothesis for the sonorous rime duration in Navajo under the direct approach crucially differs from that in Cantonese and Thai, as shown in (0). (0) Hypothesis (Navajo): Syllables with a long vowel or diphthong have a longer sonorous rime duration than syllables with a short vowel. In particular, CVV≥CVR, CVVO≥CVR. One data source of Navajo is two analog audio tapes in the UCLA Language Archive made by Joyce McDonough in the Navajo Mountain area in 1993. Fourteen speakers read a word list after a lead speaker. The dialect they speak was categorized as Western Navajo by McDonough. For each word, there were five tokens from the lead speaker and one from each of the other speakers. The words extracted for use in the durational study included two representative words for each of the following syllables types: CV, CVO, CVR, CVV, CVVO, and CVVR. All words were disyllabic except one. The target syllable was always the second syllable in the disyllabic words and had the vowel /i/ as its nucleus. It was always level-toned. The word list is given in (0). Both practical orthography and IPA transcription are given. High tone is marked with an acute accent / !/. Low tone is not marked. The target syllables are in boldface. (0) Navajo word list 1 (McDonough tape, 15 speakers):
I also collected phonetic data from another native Navajo speaker—EN, who was from the White Horse Lake in New Mexico and speaks an Eastern Navajo dialect. The word list used for EN is given in (0). For each syllable type, two words with /i/ and two words with /a/ were used. All except one target vowels/rimes were in the second syllable of a disyllabic word. The only exception was ’adidiil ‘snowstorm’, which was trisyllabic. All target syllables were low-toned. The speaker read each word with eight repetitions. (0) Navajo word list 2 (data collection, 1 speaker):
ResultsThe rime duration results obtained from McDonough’s tape are plotted in (0). The darker portion in the bars for CVR and CVVR indicates sonorous duration contributed by the sonorant coda. A one-way ANOVA shows that syllable type has a significant effect on the sonorous duration of the rime (F(5, 222)=208.8, p<0.0001). Fisher’s PLSD post-hoc tests show that the difference between CVR and CVVO is not significant (p>0.05), but the difference between CVR and CVVO is (p<0.0001). (0) Navajo sonorous rime duration (ms) (McDonough’s tape): 
Therefore, the duration data support the phonetic hypothesis in (0): there is no difference in sonorous rime duration between CVR and CVV, and the sonorous rime duration of CVVO is significantly greater than that of CVR. And if we look at the vowel duration in CVR, we can see that it is the shortest of all syllable types—a mere 95ms. More than half of the sonorous duration in a VR rime is contributed by the sonorant coda. The difference in tone-bearing ability between CVR and CVV therefore lies in the difference between a sonorant consonant of 228-95=133ms and a vowel of 209-95=114ms. Although I have no perceptual study to support the hypothesis, it is quite plausible that the winner is the latter. The duration results obtained from McDonough’s tape are confirmed by data collected from EN. The average sonorous duration of the rime and vowel duration for each syllable type are shown in (0). Again, the gray portion in the bars for CVR and CVVR indicates sonorous duration contributed by the sonorant coda. A one-way ANOVA shows that the syllable type has a significant effect on the sonorous rime duration: F(5, 162)=596.7, p<0.0001. From the plot in (0), we can see that CVR has a comparable sonorous duration in the rime to CVV and CVVO: it is not significantly different from CVVO (Fisher’s PLSD post-hoc tests, p>0.05); and even though it is marginally greater than CVV (Fisher’s PLSD post-hoc tests, 0.01 (0) Navajo sonorous rime duration (ms) (EN data): 
I therefore conclude that the hypothesis in (0) is supported by phonetic data. CVR in Navajo has comparable sonorous rime duration to CVV and CVVO. In light of the fact that the vocalic duration plays a more important role than the duration of the sonorant coda in the definition of CCONTOUR (see §3.1, CCONTOUR = aDur(V)+Dur(R), a>1), the direct approach, which uses the CCONTOUR value of a syllable to predict its contour bearing behavior, correctly predicts that CVV and CVVO are better suited for contour tone bearing than CVR. A traditional faithfulness approach again does not in principle rule out the possibility that CVR is a better contour tone bearer. But the results here are consistent with the moraic approach, since one may simply posit that only vowels are moraic in Navajo. Comparing Navajo with Thai and Cantonese, we observe a crucial difference: in Thai and Cantonese, the sonorous rime duration in CVR is considerably longer than that in CVVO, while in Navajo, the two durations are comparable. I further conjecture that the Navajo pattern characterizes the durational pattern for all languages that restrict contour tones to long vowels. In these languages, the sonorant codas do not have a prolonged duration as in Thai, nor do obstruent codas considerably shorten the duration of the nucleus vowel as in Cantonese. Therefore the sonorous duration in CVR is comparable to that in CVVO. SomaliA preliminary study of Somali (data from UCLA Language Archive), an Afro-Asiatic language, supports the conjecture made at the end of the last section. Somali has vowel length contrasts in both open and closed syllables. Both sonorant and obstruent consonants can occur in coda position. The single contour tone—falling (H°L)—can only occur on long vowels (Saeed 1982, 1993). Compare the two spectrograms in (0a) and (0b), which depict words ban ‘plain’ and naak’ ‘woman’ respectively: the coda nasal in ban does not have an excessively long duration, and the coda /k’/ in naak’ obviously does not shorten the preceding vowel; in fact, the sonorous portion of the rime for these two words has a duration of 257ms and 264ms respectively. (0) Somali spectrograms: (a) ban ‘plain’ (b) naak’ ‘woman’  
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