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In Danish, the pair /ø/ and /ø:/ are distinguished from the pair /œ/ and /œ:/. In Swedish, the phonemes /ø:/ and /œ/ are treated as a short-long pair.

In Danish, the pair /ɔ/ and /ɔ:/ are distinguished from /o/ and /o:/. In Swedish, /o:/ and /ɔ/ are treated as a short-long pair.

How did Danish develop a length distinction for the qualities /o/, /ɔ/, /ø/, and /œ/?

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    I think you’re asking this the wrong way around – without looking up the developments specifically, I think it’s rather that Swedish lost the distinction. Old Norse had both ø/ǿ and ǫ/ǫ́ (later ö/ö́), as well as both a/á (later a/å) and o/ó, with length later redistributed by syllable weight. Danish has /ø, øː/, /œ, œː/, /a, aː/, /ɔ, ɔː/ and /o, oː/; the only pair Swedish has is /a, aː/. Note that, much like English, Swedish has virtually no tense short vowels – only /e/ remains, and only in some dialects – so it’s not surprisingly that there are no /ø/ and /o/ phonemes. Commented Jan 12 at 11:27
  • So Swedish lost some pairs while Danish retained them? Commented Jan 12 at 19:50
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    It’s probably a bit more complicated than that, but essentially yes. Consider that historically, Danish /ɔː/ (written å) is equivalent to Swedish /oː/, while Danish /oː/ (written o) is equivalent to Swedish /uː/, and Danish /uː/ (written u) is equivalent to Swedish /ʉː/ – the phonemes don’t match up neatly, but it’s clear that Danish and Old Norse both have tense and lax short vowels, while Swedish (almost) only has lax ones, so by Occam’s Razor you’d assume that Swedish lost phonemes along the way. Commented Jan 12 at 23:31

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