According to the answer of @what to the question Pronunciation of “lernst” there are 3 different ways to pronounce the alphabet r in German:
voiced uvular fricative [ʁ] (splattne's sample)
uvular trill [R]
alveolar trill [r]
(Regarding "splattne's sample" see his answer.)
My question is regarding the uvular trill. Which region is this pronunciation associated with? Is this the pronunciation in Hochdeutsch? And which of these is the most common in Germany?
The voiced uvular fricative [ʁ] is nowadays the common pronunciation of "r" in High German.
The uvular trill [R] is used if you want to emphasize the "r", or if you want to achieve a clear pronunciation in a more formal speech or conversation. In most contexts it is harder to speak and thus avoided.
Both originated from a weakening of the alveolar thrill and got used in educated speech out of convenience and because of the reputation of French where its use was also spreading.
The alveolar trill [r] is commonly used by older speakers but it got deprecated because of its association with rural, uneducated people. Educated people in the cities and the nobility of the various German states were Francophile for a long time and adapted a lot of French habits. It loses ground to [ʁ] and [R], but is still very common in the southern areas of German.
voiced uvular fricative [ʁ] being common in High German?
According to german wikipedia] uvular trill [R] is used as the standard pronounciation in Schweiz, Siebenbürgen, Bayern, Österreich, Südtirol and part of Norddeutschlands.
http://de.wikipedia.org/wiki/Stimmhafter_alveolarer_Vibrant
I'm from austria myself and only use it in classical singing or in very formal public speech: its used in "stage german" for acoustic reasons.
(A question was closed as duplicate of this question, but the answers to this question do not even mention vocalic "r" !? So I write my answer here.)
The pronunciation of German "r" depends on whether it is in front or after a vowel. In regional dialects, "r" is famously pronounced differently from the standard in Germany, but I won't touch on that, because there are already other answers on that and I am not too familiar with Southern accents. For Standard German German, the rules are as follows:
If "r" is in front of a vowel, it is typically pronounced as a voiced uvular fricative [ʁ] or approximant [ʁ̞].
If "r" is not in front of a vowel and after a long vowel, it is pronounced [ɐ] and forms a diphthong with the preceding vowel, so Rohr is /ʁoːɐ̯/.
If "r" is not in front of a vowel and after schwa, the entire sequence "er" is pronounced [ɐ] except for in careful speech, so roher is /ʁoːɐ/.
If "r" is not in front of a vowel and after a short vowel, it can be both a voiced uvular approximant [ʁ̞] or the vowel [ɐ], so "Herz" would be [hɛʁt͡s] or [hɛɐ̯t͡s].
There are some variation possible in front of [j] and [ən]. So words like "Ferien", "führen" can both have consonantic or vocalic "r". If "r" is in between vowels, is can also be both, [ɐʁ], for example [ˈlɛɐ̯ʁɐ] for Lehrer.
Other things to note: Length is often neutralized in front of vocalic "r" (Wiese (1996), via https://en.wikipedia.org/wiki/Standard_German_phonology). The vowel [ɐ] is not always distinguished from [ä], so "Oper" and "Opa" are pronounced the same for some speakers. In my personal observation, the pronounciation of vocalic "r" after "i, u, ü" is closer to [ə] than to [ɐ], so that "Karls Ruhr" might actually sound closer to "Karlsruhe" [u:ə] than to "Karlsruher" [u:ɐ].
