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According to the wiki page:

[x] occurs after /uː oː/ (for instance in Buch [buːx] 'book') and [χ] after /a aː/ (for instance in Bach [baχ] 'brook'), while either [x] or [χ] may occur after /ʊ ɔ aʊ̯/, with [χ] predominating.

When pronouncing the [χ] sound I end up trilling, otherwise no sound really comes out. So, it ends up sounding like a voiceless 'r'. Is this a mistake and would native speakers notice, or does it really not matter?

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up vote 3 down vote accepted

When I say 'Bach', I also trill the [χ] sound very slightly, and I have no accent at all. It's important how prominent your trill is. As mentioned, a prominent trill will make you sound like someone from Eastern Europe. Can you upload a speech example for us to analyze? For me, it depends on the speaking volume. The louder I pronounce the [χ] sound, the more I trill it.

Here example from Wiktionary:

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How sure are you about your producing a trill? – The Eastern European accent is not a trill, however, it’s just a fricative [x] in places where a native speaker would use [χ] (or [ç], as well). – chirlu Jun 30 '13 at 8:18

That’s difficult to tell without conducting some kind of study (e.g., play back recorded words like [baʀ̥] to native speakers and ask them whether they hear /bar/ or /bax/). I’d guess there would be a tendency to interpret it as /x/, but chiefly because /r/ in /bar/ would be represented as a vowel in standard pronunciation, not as one of the four possible consonantic forms (ʁʀɾr).

If you can produce [x] but not [χ], you might consider using [x] everywhere. It will give you an Eastern European accent (Poland/Russia), however.

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