Trying to figure out the difference between pronouncing short o and short u

Question

According to this video, the [u] letter as in Hund [hʊnt] is the short version of [o:] instead of [u:], but as I know, there is another letter [o] as in Millionär [mɪli̯oˈnɛ:ɐ̯] being the short version of the same letter [o:].
So my question is, what's the difference between [o] and [u], if they're the same thing why do they use two different IPA letters to represent one single vowel?

EDIT: As the video mentioned above doesn't use the standard IPA script, I have to clarify my question here. What confuses me is these two letters in IPA script [o] and [ʊ]. Some would say that the short o sound is denoted by [ɔ] as in Nonne [ˈnɔnə] , but there is another one letter [o] as in this video.

Answer 1

One problem (but not the only one) with this video is that it uses its own notation for sounds which makes it confusing for people who know IPA.

The short u in German is pronounced like the oo in English foot. The IPA symbol for this vowel is ​[⁠ʊ⁠]​.

While the German long o (IPA [oː]) may sound very similar when spoken short, I would not consider them the same sound. So I think it is correct that them IPA symbols are different. In some regional variants the sounds may be identical, but this is not generally true.

The short o is IPA ​[⁠ɔ⁠]​. Like the short u, it is a pronounced more open than its long German counterpart. It is pronounced much like the British English short o in lot or bot. This is not 100% true as the former is IPA [ɔ] and the latter is [ɒ], but the difference is IMHO not important in practical usage.

So we have four sounds:

Short u [ʊ] rounded centralized almost closed short back vowel

Long u [u:] closed rounded long back vowel

Short o [ɔ] half-open rounded short back vowel

Long o [o:] half-closed rounded long back vowel

Millionär is a bit of a special case since the o is pronounced like the long o but short. If the vowel in Hund were the same vowel (as in Boot but short, as the video claims) Millionär would be homophonous to Milliunär, but I would deny that.

Answer 2

This video is nonsense. The speaker himself said at the beginning (0:11 to 0:15):

Dafür verwende ich meine eigene phonetische Umschrift.
For that I use my own phonetic transcription.

This means nothing else but:

You can't compare the symbols that I invented without any scientific background with any standard phonetic symbols.

In fact the pronunciation of the examples in this video in the standardized international phonetic alphabet is:

• [oː] (long close-mid back rounded vowel)

  Oma = [ˈoːma]
  Boot = [boːt]
  froh = [fʀoː]

• [ʊ] (short near-close back rounded vowel)

  Hund = [hʊnt]
  Butter = [ˈbʊtɐ]
  Luft = [lʊft]

• [ɔ] (short open-mid back rounded vowel)

  Post = [pɔst]
  Tonne = [ˈtɔnə]
  voll = [fɔl]

• [uː] (long close back rounded vowel)

  U-Bahn = [ˈuːˌbaːn]
  gut = [ɡuːt]
  Ruhm = [ʀuːm]

Answer 3

The difference between the German vowels /eː øː oː/ and /ɪ ʏ ʊ/ lies primarily in their quantity. The difference in their quality is tiny at best. If you record /eː øː oː/ and then shorten it, the result will be perceived as /ɪ ʏ ʊ/ (see Thomas Becker: Das Vokalsystem der deutschen Standardsprache, Frankfurt a. M.: Lang, 1998, S. 33).

The traditional explanation is that there is a difference in tenseness between /eː øː oː/ and /ɪ ʏ ʊ/: the former are said to be tense, the latter are not. However, it is debated whether there is any acoustic correlation to the difference in tenseness.

An important reason why we use different signs in spite of virtual identical vowel quality lies in the spelling. It is because of the spelling that we perceive the vowel of a word like Beet as an ‘e’ sound, and the vowel of a word like Bit as an ‘i’ sound. I guess this is ultimately the reason why there are the non-cardinal vowel signs [ɪ ʏ ʊ] in the International Phonetic Alphabet. The cardinal vowel [e] is obviously an ‘e’ sign, and it corresponds to a French ‘e’ sound in words like été. In English, however, it would correspond to an ‘i’ sound in words like bit. I guess representing the English ‘i’ sound by the ‘e’ sign [e] like in French felt inadequate (even if it would have been perfectly possible), so the International Phonetic Association created the non-cardinal ‘i’ sign [ɪ] instead.

Coming back to the words Millionär and Hund

As I have said, a shortened /oː/ will be perceived as a /ʊ/. So if you record the word Million which has a stressed long /oː/ and cut out that sound and shorten the recording, you will get the sound of /ʊ/ as in the word Hund. This basically means that the video is right: there is no audible difference between the sound of the ‘o’ in the word Millionär [mɪljoˈnɛːr] and the sound of the ‘u’ in the word Hund [ˈhʊnd].

How come the other answers insist there should be a difference? Three reasons:

1. The different spelling influences the perception of the sound: the sound in the word Millionär is perceived as an ‘o’ sound and the sound in the word Hund is perceived as an ‘u’ sound because of the spelling.
2. If there is a difference in tenseness, the articulation of the sound might feel different to the speaker even though there is no audible difference for the hearer.
3. The unstressed /oː/ in Millionär may be lowered to an [ɔ], resulting in a pronunciation [mɪljɔnˈɛːr], and [ɔ] is obviously different from [ʊ].