Vienna is not the first place one associates with jazz, but, enthuses Phil Johnson, some work compares favourably with America.

Imagine how jazz might have developed had it had begun in the pastry- shops of Vienna rather than the bordellos of New Orleans. In this Kurt Vonnegut-style alternate world, the history books of jazz would be filled with sepia portraits of raffish blond men wearing snap-brim Tyrolean hats, clutching their alpen-horns to their breasts while in the background Jelly Roll Schoenberg plays with old Doc Freud. Cake-abuse would certainly have been a problem, too.

One thinks of some flaxen-haired Billie Holiday running down the hillsides thick with spring flowers singing "Gimme a Pig Foot and a Bottle of Beer". At least the lyrics wouldn't have to change ...

In reality, however, the Oris London Jazz Festival is featuring a mini- festival called Jazz From Austria - a series of concerts by the very best of the Viennese jazz school - which provides a timely opportunity to revalue the hip heritage of Habsburgsville. And it is quite a heritage. On Sunday, the wonderful flugelhornist and composer Franz Koglmann - whose utterly distinctive music blends post-serialism with cool jazz and film-noir soundscapes - plays the Purcell Room, in tandem with Christoph Cech's group Striped Roses, described by one critic as sounding as if Glenn Miller had taken LSD, while the Max Nagle Quartet play the RFH and QEH foyers. The great sax player Wolfgang Puschnig has already presented his Alpine Aspects - a fusion of Tyrolean folk music and jazz - at the QEH, alongside the world-class guitarist Wolfgang Muthspiel. But the high point (you could almost say the feather in the hat) of Jazz From Austria begins tonight, when the excellent Vienna Art Orchestra begins a national tour for the Contemporary Music Network at the QEH.

Now celebrating their 20th anniversary, the orchestra - which is led by the composer, arranger and conductor Mathias Ruegg - is presenting a programme entitled An Echo From Europe, featuring arrangements of works by a whole gallery of European jazz artists, from Django Reinhardt to Django Bates. The Orchestra has also recently released a three-CD set (on Verve) which is so good that it forces one to reverse the usual formulation and ask whether there is anything on the other side of the Atlantic that can compete with this.

All three CDs act as a kind of homage to American masters and American models. One album, Powerful Ways, re-interprets some of the most famous compositions of the late Eric Dolphy. Another, Quiet Ways: Ballads, features some of the greatest of all American female vocalists, including Betty Carter, Helen Merrill and Sheila Jordan, on a series of standards such as "Lush Life", while the third, Unexpected Ways, adapts John Cage's text "... Mureau" into a "Concerto for Voice and Silence".

The interplay between original compositions and rearrangements, between jazz and classical forms, and between notation and improvisation is what makes the work so distinctive. "The re-arrangements depend very much on the material," Ruegg says. "On the Dolphy set I stuck very closely to his album Out to Lunch and used the whole of his solo for `Out There', so it comes pretty close to the original. Some pieces are totally notated because I prefer to write everything down, while with jazz musicians I generally don't."

As a writer-arranger, Ruegg sees himself as operating within a well-established jazz tradition. "I would say that for every piece I compose, I arrange another one," he says. "How you use the material of other people is part of jazz. You think of Coltrane and My Favourite Things, of Miles Davis and Some Day My Prince Will Come, or of Gil Evans, who arranged everything from Gershwin to Hendrix. As an arranger, the material is always interesting; there is no milieu, no social context any more - you just have the pure music, and music paper is pretty abstract. Between Schoenberg and Scott Joplin, there is no difference."

If European jazz developed in the shadow of its American counterpart, Ruegg thinks this is no longer the case. "The level is much higher now and young musicians don't have the hang-ups of the previous generations, but still American musicians are more respected. After all, America is where jazz comes from and it will take a lot of years until things change.

"Some very big influences are coming from Europe, especially from those musicians who mix jazz with classical or folk music. People like Jan Garbarek or Albert Mangelsdorff have created a special kind of language for European jazz. And Django Reinhardt? He was a genius."

So where, I asked Ruegg, who is Swiss by birth, does the Austrian-ness of the music come in? "Er, it doesn't, or not very much," he says. "It's just a fact. When we started we were Austrian, but now we are international, European." Not entirely. The alp-horn, you will be reassured to hear, still plays an occasional role in their performances.

The Vienna Art Orchestra plays the QEH, SE1 (0171-960 4242) tonight; The Anvil, Basingstoke (01256 844244), Sat; Adrian Boult Hall, Birmingham (0121-236 5622), Sun; RNCM, Manchester (0161 907 5278), Mon; Sallis Benney Theatre, Brighton (01273 709709), Tues; Lawrence Batley Theatre, Huddersfield (01484 430528), Wed; Durham University (0191-374 3210), Thurs; Kingswood Theatre, Bath (01225 463362), Fri 21.