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Let me ask a question of an usage of schwa as a phoneme and [r]. This [r] is the sound which is used in English and generally expressed with R and not [r] expressed with IPA.

Schwa can be regarded as an independent phoneme, apart from weak forms of other vowels, I heard. And here, I treat this idea as true.

Then my question is: Is this schwa phoneme can be followed by consonant [r] in the same syllable?

If so, I think that this schwa phoneme can take two forms, one just the ordinary schwa or little bit rhotic schwa, the other completely rhotic schwa, that is rhotacized schwa, because other vowels can take these two forms when being followed by consonant [r] in the same syllable.

Please think about it.

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    What language is this question about? English? German? Any?.. – Yellow Sky Mar 2 '17 at 4:27
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    It probably can, but it would probably be better to analyse it as a syllabic [r] instead. – curiousdannii Mar 2 '17 at 8:04
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    Perhaps -- in "liqueur". Wiktionary gives /lɪˈkɝ/ as the "General American" pronunciation. (I'm just talking about pronunciation -- don't know about the phonemics. I agree with @curiousdannii.) – Greg Lee Mar 2 '17 at 11:42
  • And Wikipedia gives US /lɪˈkɜːr/. I also agree with @user6726's answer, largely. – Greg Lee Mar 2 '17 at 12:02
  • It is clear that English has a phoneme /r/. But that is all that is clear. The allophones and other phonological strategies used in various English dialects to exemplify the phoneme /r/ have just about no common center (nor centre). Sometimes /r/ is expressed by vowel neutralization or centralization or lengthening, sometimes by consonantal flap or trill, sometimes by just about anything you can do with your mouth. So, to say "This [r] is the sound which is used in English" is to make a category mistake. The /r/ which is used in English is not a sound but a set of sounds, i.e. a phoneme. – jlawler Mar 2 '17 at 22:57
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It is hazardous to ask questions about sound system of English without saying what dialects you mean, and what kind of analysis you are assuming, because the answer is "It depends...". The observable facts are "how things are pronounced", i.e. the phonetics of English, so you should start there. The vowel [ə] does not appear before [ɹ] (the English version of r) within the syllable, at least in most American dialects. Things get even more complicated and under-reported when you look at other dialects, so I will only talk about the main patterns of American English.

In words like "pervert" (noun or verb), "burn", there is a vowel-like thing in each syllable, which can be transcribed as [ɹ̩] (or [ɚ], also [ɝ]). Distributionally speaking, [ɹ̩] is in complementary distribution with [ə.ɹ], where [ɹ̩] occurs when the sequence is within a syllable, and [ə.ɹ] occurs when the vowel and consonant are in separate syllables (e.g. parade [pəɹɛɪd] – I'll come back to this form). A common phonemic analysis of [ɹ̩] is that it derives from əɹ, thus ɹ̩ is not an autonomous vowel, and derives from reduction of əɹ within the syllable.

Reduction is actually somewhat more general, since "parade" is also pronounced [pɹ̩ɛɪd] or [pɹ̩ɹɛɪd], that is, the "in the same syllable" condition is often dropped from the requirement of the reduction rule, and this is widespread, but dialect-dependent (it's a feature of more-western US dialects, though widespread throughout US English). The extended rule is optional, though very likely to happen (whereas phonetic [pəɹvəɹt] in American English is either extremely rare or unattested).

Cross-syllable reduction of əɹ can happen at the phrasal level, so that "a rabbit" can be realized as [ɹ̩ɹæbɪt]. This is much less likely, and this can lead to semi-minimal pairs like "a rest" [ə ɹɛst] vs. "arrest" [ɹ̩ɹɛst]. It is likely that if one were to extract examples of such words from a corpus of casual spoken English that there isn't really a difference between the two-word and one-word structures, but I don't believe a systematic study of this has been undertaken. An interesting and unanswered question is whether the more-casual form of "a rest" ever becomes phonetically indistinguishable from "arrest", or is there always some distinction.

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If you look at the phonological level, it can. E.g. water is pronounced /wɔdər/ or /wɑdər/ in US English according to the Oxford English dictionary. [The answer above, that looks at the question from the phonetic level, states it is not possible. Though I do wonder for the rationale behind that!]

Right now I am assuming you define schwa as the [ə] sound; people may define it differently (Backley, 2011, defines schwa as an ɨ I believe, though in that case it is quite probable that an [ɹ] can follow this sound too).

To answer this question you may also want to look at the phonotactics of English and other languages: there are rules about which consonants and vowels are possible at which positions in the word and the syllable, based on feature theory, for example.

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