I think Hindemith gets very close with 'Gebrauchmusik', Peter. His works, while stylistically innovative, are fun to perform and his respect for the musical traditions which preceded him is always plain. On the other hand, music lovers have generally been been unable to play the role of Aaron to Schoenberg's Moses.

The Bauhaus means a lot of things, however (and it depends on which era of Bauhaus you're talking about). It could mean a particular style/relation to form and materials, in which Schoenberg may not be far off; it could mean a particular artistic engagement with leftwing politics, in which case maybe Cardew and the Scratch Orchestra come closest, or conversely the Brecht–Weill collaborations; it could be a model of integrating art, craft, business and pedagogy, in which case Hindemith, Orff or even the Bartók of Mikrokosmos (which spawned a whole tradition of its own in Hungary) might be close.

Or it could be a model of collaboration in which the institution or brand overtakes the face of the artist, in which case the perfect example is probably Tamla Motown. (And on much smaller scale in classical music perhaps Bang On a Can.)

... although, thinking about this some more, the real Bauhaus example is the electronic studios that sprang up around Europe and the US in the 1950s. A combination of art, technology, craft, pedagogy and collaboration that the Bauhaus would surely have recognised. Moreover, since many were sponsored by state broadcasters they had a role in producing utility music for radio, TV, theatre etc. The classic example is the BBC Radiophonic Workshop.

To take all this back a generation or so, the relationship between Arnold Dolmetsch and the Arts and Crafts movement is an interesting parallel. Like Bauhaus, the Arts and Crafts ethos of justifying visual aesthetics through social practicality was an important ethical dimension for William Morris and his gang. Obviously, the anti-industrial dimension separates the Arts and Crafts ideology from that of the Bauhaus, and that was also probably its most important legacy to Dolmetsch, in that it offered a cultural context in which his period performance movement could flourish.

Why is it that music always seems to be playing catch up to artistic movements in other media? Could it be a product of simplistic historiography? Debussy was sceptical about the relationship between his work and visual impressionism. The early atonality of the Second Viennese School now seems more closely related to Einstein's relativity than it does to Expressionism. And Romanticism in literature has more in common with the work of the 'Classical' Schubert and Beethoven than it does to the later generations of 'Romantic' composers.

My feeling is that it is a combination of historiography, and the relative strengths of music, literature and art criticism.

One only gets an impression of 'catching up' if one buys into the connections between, say, Impressionism in music and in art. On closer inspection it's a pretty thin connection; likewise Expressionism, etc. I suspect that music critics started using terms from the arts simply because the art critics got there first, and their terms seemed good (and always useful as critical shorthand and/or for promotional reasons). Moreover, art and literary criticism tends to predominate over musical criticism in public discussion of the arts, so the terms those critics come up with will carry greater weight and tend to be more imitated than vice versa.

Fortunately, I think it's something that criticism has largely grown out of in more recent decades. Despite the close personal relationships between Rothko, Pollock, Guston etc and Cage, Feldman, Wolff etc (and shared aesthetic values, locations, etc), no one seriously describes the music of the latter as 'Abstract Expressionism' despite the popular currency of that term wrt to the painters.

I have enjoyed this discussion very much and only wish I had a broader knowledge of 20th century music!

I wonder if the links between the visual arts and music are actually made after the event, when critics and commentators have the value of hindsight? Sometimes it seems to me a little too easy to link art to music - Debussy and Impressionism is the most obviously example, I suppose. Learning Debussy, as I am at the moment, I cannot help but think of the misty, blurred colours and images of Monet, Pissarro et al - and the piece I am learning ('Voiles') is most definitely trying to create an "impression" of wind or veils. Yet not all of his music is impressionistic; it is also infused with many, many other things - Indonesian music, Gregorian chant, figures which hark back to Bach and the baroque, or look forward to the minimalists such as Glass or Adams.

It is worth bearing in mind that these analogies can be very useful, even if they are usually cooked up after the event. Pace Mahler and Stravinsky, I don't think music loses any of its power by being directly linked to other media, and it is certainly not lazy thinking to equate the more pictorial of Romantic music with visual imagery.
It is quite frustrating though, how rarely the process works in the other direction. There are one or two examples of literature being based directly on music, Tolstoy's Kreutzer Sonata and that Strindberg play that has the Chopin E minor Prelude playing in the next room throughout. But the only two composers who have had a significant influence on other art forms have been Wagner and Cage. Why should that be? I'm struggling to think of any other connection between the two of them.

Agreed, Gavin. And there's a whole 'nother discussion to be had about literature and music - and music in literature.

And film....