There was a time when, to some critics, everything of substance in jazz came from black musicians; at best, the white boys simply listened, envied, copied and stole; at worst, they were like Dr Johnson's comment on the dog that could walk upright on two legs - it was not done well, but then one was surprised to find it done at all. The truth, as Sudhalter's marvellously detailed book confirms, was infinitely more complicated than that.
For a start, there is no such thing as musical purity anywhere; people and circumstances are too various, their minglings too inevitable, for either their DNA or cultures to escape mutual contamination. Just as well; without it we wouldn't have the great Gormenghast castle of musical architecture that is jazz today, where you can hang around in a room or two of your choice, or wander all over the place and catch whatever piece of exotica takes your fancy.
If the building wasn't quite as extensive in 19th century New Orleans, where it all began, the cultural mix was anything but monochrome. French, Italian, Irish, Spanish - they set the relatively relaxed Catholic ethos of the place to which the black underclass and the mixed race, middle class Creoles of colour brought their own contributions. And the names of the first two great jazzmen, both from the city, Louis Armstrong and Sidney Bechet, epitomise this.
But there were others. For most of its history, jazz, as the author succinctly puts it, "has been profoundly pluralist" and in New Orleans the social scene was too fluid from the beginning to maintain complete cultural apartheid.
Sudhalter's meticulous research demonstrates that in New Orleans alone there was a huge body of white jazzmen, players such as Emmett Hardy, Leon Roppollo, Nick LaRocca (of the Original Dixieland Jazz Band, which made the first jazz recordings in 1917), Tony Parenti, Arnold Loyacano, to set beside better known early black musicians like the Dodds brothers, Honore Dutrey, Johnny St Cyr and Freddie Keppard. And that remained true elsewhere, when jazz spread upriver to Chicago and then to New York.
Implicit in this is an acceptance of the historical eminence, early on, of blacks such as Armstrong, Bechet and, later, of Ellington, saxophonists Coleman Hawkins, Lester Young, Johnny Hodges, Benny Carter and, eventually, Charlie Parker. Equally implicit is an acknowledgement of differences caused by social background, education, race and dominant cultures. Sudhalter makes both considerations explicit - and one of the key points of his book is that all these musicians, black and white, chose jazz themselves and, having chosen, listened to each other to a greater or lesser degree according to their inclinations.
The respect and, sometimes, the influence were therefore mutual. Armstrong admired the first great white soloist, the doomed Bix Beiderbecke, a hauntingly poetic, harmonically intriguing player completely unlike Louis' baroque, blues-drenched utterances. Young was influenced by two whites, Frankie Trumbauer, who played the now archaic Cmelody saxophone, and Bud Freeman, a Chicagoan who developed his own style on tenor saxophone at a time when Hawkins was given sole credit for making sense of the instrument.
If this makes the book sound like a scoring of musical and historical points, forget it. Sudhalter, a cornettist himself in the Bixian mode - years ago he co-wrote a superb, still definitive, moving biography of Beiderbecke - is too intelligent and scrupulous for polemics. What concerns him is to rescue from neglect and misunderstanding the vast body of white musicians who, just as much as their equally numerous black counterparts, had a vital role to play in making early jazz what it was.
Does the black/white thing still need to be pursued? Any common-sense listening to today's jazz suggests not. Young white American musicians like the trumpeter Dave Douglas, or the pianist, Brad Mehldau, are as likely to take their artistic stimulation from white or black, American or European, sources. And the adventurous young black tenor, Mark Turner, has been influenced by a great white saxophonist, Warne Marsh. So why write such a book as Sudhalter's? At the very least, it's an adjustment to the critical view that, for the early jazz generations, blacks led and whites followed. But it's also a reminder of something else integral to the nature of the music and the life of a jazz musician. Sudhalter, who can write beautifully, says the early history of jazz is "a litany of arrivals and departures. Arrivals of new populations and heroes, new ways of thinking and wanting and doing. And departures, leavetakings, mass flights of people and music to other germination points."
What he does is to put historical flesh on an under-appreciated part of those arrivals and departures - at least in an American, if not a European, context. And he asks a question which, ultimately, takes us on to Gormenghast. As centres of population shifted, he says, so did the music, "leaving behind - what? A ghost town, populated only by those too unimaginative, too faint-hearted, too conservative to take the big risk?" Well, as he shows brilliantly and exhaustively here, not so.
Ray Comiskey is an Irish Times staff journalist