Like most music fans, I suppose, I occasionally go through phases of listening a lot to one particular artist. Sometimes I even get a weird feeling that that artist is calling to me, across time and space, even from beyond the grave.

I grew up knowing Louis Armstrong as a somewhat comical figure on TV, sweating and grinning and singing What A Wonderful World in a gravelly voice. People liked to imitate that voice, which was a sort of musical equivalent to saying 'you dirty rat' and thinking you sounded like Jimmy Cagney.

The judgments of youth can be harsh and unforgiving. Even when I became interested in jazz as a teenager, I was more drawn to things like Miles Davis' Bitches Brew or Coltrane's Love Supreme. Anything before Charlie Parker sounded corny to me: smarmy Big Bands fronted by the Something-or-other Sisters, and some nonsense called Trad Jazz, which was played by wankers in matching waistcoats and bowler hats.

But one of the really great things about getting older is letting go not just of plain ignorance, but of peer pressure, snobbery and inverted snobbery, and fashionable or anti-fashionable prejudice, and learning to appreciate art within its own context and its own frames of reference. And when you can do that, I think you can sometimes pass through to an even higher plane, where it just is what it is, and what it is, is great art and a joy.

For reasons I can't explain, Louis Armstrong has lately become a presence in my life. I seem to keep hearing him in shops or restaurants, and a few weeks ago at a flea market, a gorgeous 1935 photo of him seemed to jump into my hand and demand to be framed. It's actually a page from a glossy magazine, promoting his upcoming shows at Connie's Inn in Harlem. By that time, he was a big star, and yet the accompanying text (under the heading 'Jazz Dazzler!') makes it clear that he was still seen as a cutting-edge, pretty much unprecedented figure. It's an intriguing paradox that his music was seen as on the one hand, 'savage' or 'primitive', and on the other, disturbingly – or excitingly - abstract and modernistic.

He was certainly more ahead of his time than I ever suspected until a few years ago. One small example: I always thought Frank Sinatra was the first singer to figure out that a microphone enabled you to sing in a new, softer style, and to create a feeling of intimacy, while still reaching a lot of people. Later I learned that Bing Crosby did it earlier, but now I realise that Louis Armstrong did it first – at a time when a singer couldn't even count on having a microphone, and had to be able to sing loud (which he could do too). As it turns out, there isn't much, in the field of jazz and popular music, that Louis didn't do first.

I've also just finished reading Thomas Brothers' monumental Louis Armstrong – Master of Modernism, which explores in meticulous detail the period of Armstrong's life which most interests me, roughly from his move from New Orleans to Chicago in 1924, to his creative and commercial breakthroughs of the early 1930s. There's so much in here that I never knew: for instance, that throughout the 1920s, the word 'jazz' had several different meanings, depending on context; and that in his Chicago years Armstrong didn't just play and sing but also danced, took part in comic skits, and even appeared in drag. He never saw any contradiction between being an artist and an entertainer, and he remained as seriously committed to giving the audience a great time as he was to being the greatest trumpet player in the world. This put him at odds with a lot of later jazzmen. He would never have understood Miles Davis playing with his back to the audience.

Another surprise to me in Brothers' book was that improvisation was not as big a factor in early jazz as I had supposed. Sure, Armstrong and his contemporaries improvised, and could be very good at it, but they tended to gradually refine a solo until they felt it had reached an ideal form, which they would then stick to. I always thought some of Armstrong's classic solos were just too perfect to have been spontaneous. Again, the more existential, experimental ethos of later musicians puzzled those of Armstrong's generation, who saw them as - rather unprofessionally – just putting jam sessions in front of an audience. (Hmm, what do you suppose they made of Ornette Coleman?)

It was also nice to have the mystery of Armstrong's birth date cleared up once and for all. He always said he was born on the Fourth of July, 1900, which might be fitting for a showman and/or patriot, but which makes him, Astrologically, a Crab. His real birth date has been established as August 4th, 1901, and he was therefore a Lion, and a King. That's more like it.

I could go on, but I'll end up writing a book which has already been written a thousand times. Here are a couple of Armstrong essentials for anyone interested in taking a first, or second, listen. Or a hundredth.

LOUIS ARMSTRONG: The Complete Hot Fives and Hot Sevens; or, if you prefer, The Best of the Hot Fives and Hot Sevens

Some of the most important documents in the history of music (I'm not kidding) these recordings from 1925-28 show Louis in funky New Orleans mode but already transcending that tradition with one dazzling innovation after another. One of the standouts, West End Blues, seems to have become the Citizen Kane of jazz, so often cited as a perfect piece of music that a recording is even widely believed to have been sent into outer space by NASA on Voyager 2. (That was actually Melancholy Blues. It was still Louis, though).

LOUIS ARMSTRONG: The Big Band Recordings, 1930-1932

There are plenty of compilations of this material, but this one on the JSP label is a gem, re-mastered by the near-legendary John R. T. Davies, who makes it sound better than music nine decades old has any right to sound.

I would say the Hot Fives and Hot Sevens were overrated if only they weren't so damn brilliant. But this second important phase of Armstrong's career is sometimes underrated. Now a fast-rising star, ambitious for success with white audiences, he was playing less blues and more popular songs, and with bigger bands which have struck some critics as slicker and less 'authentic' than the earlier, rougher small groups.

I think this is missing the point. It's the contrast between the instrumental background and what Louis is doing in the spotlight that made these records accessible to a wider audience and yet, at the same time, made his own originality more obvious. A track might start out sounding kind of corny, but when Louis starts to sing or play, it suddenly becomes incredibly hip. He's not 'crossing over' to mainstream America: he's making a bridge.

One of the many great solos here is on Chinatown, My Chinatown. The band starts at a surprisingly fast tempo, and when I first heard it, I wondered what Louis could possibly do with it. A Bebopper would try to rise to the occasion and play streams of fast 8th notes, but Louis does something in a way even more radical. His solo is effortlessly relaxed, and contains as much silence as sound, as he plays around the beat almost mockingly, for instance playing one note, leaving a couple of bars of nothing, then playing the same isolated note, and then constructing a line from three-note figures going against the 4/4 beat. The effect is extraordinary: the band seem to be huffing and puffing while Louis floats free of them, defying gravity, while at the same time swinging more than they are.

Louis and his 1930s bands are sometimes like a comedy duo in which the band plays the straight man, while Louis is the subversive, outrageous and ingenious trickster. Vocally, he seems to pull every song apart and put it back together in a new form, reinventing not only the melody but sometimes the words too, or combining words and scat singing. On the first chorus of Up A Lazy River, all he has to do is say 'Yeah' and then, a few bars later, 'All right', to establish himself as pretty much the coolest guy alive.

Which he was.