Students of phonetics in Britain have to learn to recognize the Cardinal Vowels established by Daniel Jones: at least the primaries (i e ɛ a ɑ ɔ o u) and four of the secondaries, namely y ø œ ɯ. Masters’ students have to learn not only to recognize them but to produce them, too.
Some readers may be surprised to learn that the cardinal vowel that generally proves most difficult for English and Scottish students to produce is primary number 8, u. These students have to learn to make a vowel sound that is considerably backer and rounder than their English GOOSE vowel.
This is also the cardinal vowel that Japanese students find most difficult.
If simple imitation failed, I generally found that the most helpful technique was to start from the English word wall. The BrE vowel in this word is reliably back. More importantly, so is the close and rounded w at the beginning. If you prolong this w instead of immediately gliding away from it, the result may be an acceptable cardinal-style u — properly close, back, and rounded. It may need to be made a little “tighter” (i.e. with a greater degree of tongue raising). Once the learner has produced that satisfactorily, you just need a few fluency and catenation exercises. Then you can compare and contrast English boot with cardinal but and moon with cardinal mun. (NB cardinal vowels have no inherent length. They can be prolonged or not at will.)
Here’s Daniel Jones’s demonstration of cardinal 8, from the recording he made in 1956.
The same difficulty faces the English-speaking learner of German. German long uː is just about cardinal. You can hear some authentic examples here, on Paul Joyce’s German Course site (the URL mentioned for this site in my blog for 10 July 2009 is no longer valid).
(Warning: to my ear the sound clip for this vowel on the Univ. of Iowa site sounds extremely odd and un-German. To hear it, go to Vokale, Monophthonge, hinten, and select /u/.)
Here’s Wikipedia’s sound clip for the word Fuß fuːs.
If I were teaching German uː I would apply the same technique. I’d emphasize the difference in sound between German du duː and English do, German Hut huːt and English hoot. And of course learners of German also have to master the front-back distinction in Brüder — Bruder ˈbryːdɐ — ˈbruːdɐ. (Both tend to get mapped onto English brooder.)
One of Joyce’s examples, Stuhl ʃtuːl, is particularly interesting. For many English people the vowel in this word, because of the following dark lateral, is not all that different from that of their English stool: the initial ʃ is no problem, but the final clear lʲ is strikingly different from the usual English ɫ used in this position.
My picture shows an eagle owl, German der Uhu ˈuːhu. Its name is onomatopoeic. It hoots in a cardinal way.