When I was first converted to listening to jazz as a boy in the 1950s, the music was not so very old. It had been around in some form since the turn of the century, but it was never recorded at all until 1917, and didn't really penetrate Europe until the mid-1920s, so when I first had my ears bent and burnished by the music, it was still comparatively young - it was only 30 years previously, after all, that it had crossed the Atlantic on its crusading mission to convert the dancing public and turn Ravel's head.

Of course, I didn't see it that way. I didn't think that jazz was a recently arrived music. The 1920s and 1930s, separated from me by the burnt-out years of a long World War, seemed a long way off to a young lad in the 1950s, and when I read Eddie Condon's glamorous and funny account of life under Prohibition (or H L Mencken's pyrotechnics from the same era), it seemed as far away to me as George V or the people in funny clothes who jerked about in Laurel and Hardy shorts - impossibly far off, in other words - even though these people who played this wonderful music were no older, many of them, than my parents.

My mother, in fact, could have met and seen many of them. She was American and she had grown up in New York in the 1920s. I never associated my mother with jazz (the only time I played records of the stuff to her, she came out with the maddening line that all mothers use on such occasions, "Very nice, dear") and I found it quite hard to associate her housewifely status with the Roaring Twenties, but as I was fingering a Louis Armstrong record one day, it occurred to me that it was recorded in New York at the very same time that my mother was a teenager there. I reeled at the thought.

"Did you ever go and see Louis Armstrong when he was playing in a club in New York?" I asked innocently.

She inquired who Louis Armstrong was.

"Oh, no!" she said, when better informed. "My father would never have let me go to a place like that."

Nor did there seem to be any regret in her voice. What a waste of a youth, I thought ...

Over the years I have seen musicians who were not much older than my mother but nevertheless in almost at the birth of jazz, from Louis Armstrong to Duke Ellington, and Red Allen to Benny Waters, so I have come round to thinking of jazz as rather all within living memory. So it has come as a shock this week to find jazz celebrating a centenary.

Centenaries, after all, happen in classical music, not in jazz. This year, for instance, is Brahms's centenary. He died 100 years ago. He deserves a year to himself. Fair enough. Bring on the concerts, let off the fireworks. But Brahms-time is a long time ago, a long time before jazz, surely?

Wrong. The same year Brahms died, one of the great jazz improvisers arrived. Sidney Bechet was born in New Orleans on May 14 1897, a hundred years ago (and died, oddly, on exactly the same day in 1959). I never saw him in the flesh, but I came across his searing soprano saxophone on record 40 years ago, so searing that I have never become indifferent to it and still sweat faintly when I hear it. He came from a French-patois-speaking black family in New Orleans, and in his last years, he settled down in France as their grand old man of jazz, even though as a young man he had spent a year in prison in France after letting a pistol off in a musicians' brawl ...

You'd think that a brown Creole boy from New Orleans would grow up playing rather elegant music, as all the other brown-skinned Creole musicians with French names tended to (Achille Baquet, Omer Simeon, Albert Nicholas, Leon "Barney" Bigard and so on) but Bechet was too passionate to be elegant. As the excellent Russell Davies pointed out in his current Radio 3 series on him, Bechet liked to dominate his surroundings both musically and personally, which is no doubt why he ended up playing with lumbering French trad bands who accompanied him like porters accompanying a VIP traveller, but when he was delicate, nobody could be more delicate. The first time I went to France I found a lovely Sidney Bechet record on a jukebox, not to mention a bit of Mozart, which was my first inkling that France takes culture too seriously, but in retrospect it's hard to see who else they could have included on their roster, unless perhaps Django Reinhardt.

And now you are a hundred years old in your absence, Sidney. Well, happy birthday, old man. I shall get your records out tonight and toast you in something intoxicating.