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"ch" is pronounced as /x/ or /ç/ depending on the vowel in front of it, and "s" is pronounced /z/ before a vowel, how come then that the sequence "chs" in the words wachsen and Wechsel is pronounced as "ks"?

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Interesting question. I have no idea, but I would guess that it would be too difficult to combine a "ch" with an "s", so the "ks" sound developed... – Anke Apr 20 '13 at 17:04
    
related: german.stackexchange.com/questions/4519/… – Takkat Apr 20 '13 at 18:27
    
Although there is the letter 'x' in German, it's mainly used for loadwords (only few exceptions, like "Axt", "Hexe"). Most German word with a /ks/ sound are either written as 'chs' or 'cks' (iirc the difference was how they were derived from medieval German, 'hs' was the origin of 'chs', but I don't have any source at hand). That said, just because there is a word written with 'chs' doesn't mean it has to be spoken as /ks/. In word combinations or when a base word with 'ch' gets mutated the original sound stays ("Dachstube", "du sprichst", "des Bachs") – hoffmale Jan 12 at 6:39

"ch" has been developed out of the greek chi. This character has been pronounced in different ways throughout it's development. Even in German, in some words "ch" is pronounced as /k/ (the set of these words depends on the region). So the combination "chs" is pronounced as /ks/. This is a sensible way, as "ch" might be pronounced /k/ and /xs/ or /çs/ are difficult sound combinations for Germans.

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Most ch have no relation whatsoever to Greek χ or Greek at all, and it is those that form part of the question. – Jan Jan 19 at 13:55

"wachsen" is pronounced with /x/ if you mean "(to) grow" and with /ks/ if you mean "(to) wax". Usually, /ks/ is used except when "chs" are part of two different compounds or an comparative/superlative of an otherwise normally pronounced word. In my opinion, using the actual phenom like in "sechs" /ç/ can help avoid disambiguities with identical sounding ones such as "Sex" which is why I tend to pronounce it accordingly except for when I speak quickly.

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Welcome to German Language SE. Unfortunately, I fail to see how your answer addresses the question, which was asking why chs is pronousced /ks/, not when this happens or whether this is actually a good idea. – Wrzlprmft Jan 11 at 18:11
    
Furthermore, /vaxsn/ for wachsen is quite far from the standard pronunciation, which is /vaksn/. Are you from Western Germany maybe? – chirlu Jan 11 at 21:52
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»Wachsen« wird immer mit [ks] ausgesprochen, egal ob damit »to grow« oder »to wax« gemeint ist: [ˈvaksn̩]. Und »sechs« wird immer gleich wie »Sex« ausgesprochen: sechs = [zɛks]; Sex = [zɛks]. Im Süden des deutschen Sprachraums wird [z] generell als [s] ausgesprochen, daher klingen sechs und Sex dort wie [sɛks] und [sɛks] (aber eben auch dort genau gleich). Allerdings gibt es tatsächlich Leute, die aus lauter Angst, man könnte glauben, sie hätten die Absicht zweideutig zu sein, das Zahlwort falsch aussprechen. – Hubert Schölnast Jan 12 at 8:34
    
Ich nehme an, dass wir es mit einem südwestdeutschen oder einem Schweizer Gast zu tun haben, denn außerhalb dieser Gegend ist wachsen, wie oft genug erwähnt, als /waksn/ auszusprechen. – Jan Jan 19 at 13:56

Pronouncing "chs" as "ks" is just a simplification that has been made official over the original /çs/ and /xs/ pronounciation, akin to pronouncing -ig as /iç/ instead of /ik/ for the Auslautverhärtung (https://en.wikipedia.org/wiki/Final-obstruent_devoicing#German) or /ik~g/ as fortis and lenis (https://en.wikipedia.org/wiki/Fortis_and_lenis) The proto-germanic "*fuhsaz" still had the /x/: see Wiktionary

Also, many people over here in the south do make the distinction between / ˈvaksn̩/ (to wax) and /ˈvaxsn̩/ (to grow) and also say Dachs, Fuchs, Luchs, with /xs/ and Wechsel, Deichsel and similar words with /çs/. It's just when speaking fast or when you need to be better understandable that one uses the standard simplifications of modern High German in standard federal republic German variety.

You can see the decay of proper German pronounciation the best with words that have a "Ch-" at the beginning like China or Chemie. There's the question though whether either "Schina/Schemie" in the north or "Kina/Kemie" in the south will eventually be used as the new general standard.

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I would upvote this for the etymologic information in the first paragraph and the first half of the second which demonstrates differences I assume to be of Swiss origin. However, the last paragraph, about ‘decay of pronunciation’ and the example Chemie is really putting me off … – Jan Jan 19 at 13:59

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