The correct answer is (2): a short ü (notated [ʏ] and found in ‘Rücken’ or ‘gefüllt’ or ‘fünf’) is pronounced like (obviously except in duration) a long ö ([ø]/‘schön’ or ‘Löhne’).
The vowels /øː/ and /ʏ/ are very similar except in duration, as can be demonstrated by artificially manipulating their duration using Praat or some similar software:
- When the duration of an /øː/ (e.g. in Höhle) is artificially shortened, it will be perceived as a perfectly cromulent /ʏ/. A shortened Höhle will be perceived as Hülle.
- Likewise, when the duration of an /ʏ/ is artificially lengthened (e.g. in Hülle), it will be perceived as a perfectly cromulent /øː/. A lengthened Hülle will be perceived as Höhle.
Artificially manipulating the respective lengths of the vowels /yː/ and /ʏ/ gives a very different result:
- When the duration of an /yː/ (e.g. in Hüte) is artifically shortened, it sounds like something halfway inbetween /yː/ (because of the quality) and /ʏ/ (because of the duration). A shortened Hüte sounds neither quite like Hüte or Hütte.
- When the duration of an /ʏ/ is artificially lengthened (e.g. in Hütte), it will not be perceived as an /yː/, but rather as a perfectly cromulent /øː/. A lengthened Hütte will not be perceived as Hüte, but rather as *Höte.
Nevertheless, it is natural for people to believe or feel that the two vowels have different qualities, even though they are virtually identical except for their duration. This is because the short /ʏ/ patterns with /yː/ in orthography and (to some extent) in morphology, whereas the long /øː/ patterns with the short /œ/ (incidently, I believe that this is the only reason why the IPA has the signs [ɪ ʏ ʊ] at all).
Three-way minimal pairs (or triplets)
The contrasts can be observed best by comparing three-way minimal pairs (or triplets). The question is: Does the word in the middle (the one with the short near-close vowel) resemble more the word on the left (the one with the long closed vowel) or the word on the right (the one with the long close-mid vowel)?
- Flüge – flügge – flöge
- biete – bitte – bete
- Mus – muss – Moos
Manipulated vowel length minimal pairs for all near-close vowels
The long close-mid vowels /eː øː oː/ have virtually the same quality as the short near-close vowels /ɪ ʏ ʊ/:
- /eː/ and /ɪ/
- /øː/ and /ʏ/
- /oː/ and /ʊ/
The long close vowels /iː yː uː/ have a noticeably different quality from the short near-close vowels /ɪ ʏ ʊ/:
- /iː/ and /ɪ/
- /yː/ and /ʏ/
- /uː/ and /ʊ/