“He can't play lady, what are you doing up here? The guy has two left hands” – record store owner in Harlem gives his verdict on Thelonious Monk.

It’s a sunny afternoon and I’m sitting in a classroom in one of those classes that isn’t really a class. The teacher has asked us to bring in a piece of music that we really like or that means something to us.

We’ve had the usual fare, Stairway To Heaven, Thunder Road, some punk, a Stones track. It’s Phil’s turn. The teacher puts the cassette in the tape deck and presses play. The sound that comes out is completely unlike anything that has gone before it. I’ve never heard anything like it. I know that it’s music but this is music where all the angles are “wrong”, off-kilter.

Sometimes, the tune seems to lurch rather than flow. The notes are strange and they’re landing in different places from where you expect them to be. It’s like the player is hitting black notes where your ear expects there to be white ones and he’s hitting them too early or too late.

That was the first time I heard Thelonious Monk.

Thelonious. What kind of name is that?

Down the road from the classroom is the house where Barney and Jon Hill live. Often, during the lunch break, we go there and listen to records in the living room. We cover a wide range of music: acoustic blues, electric blues, rock and jazz. When it comes to jazz, we’re all big Charlie Parker fans. There is not much Monk being played.

For my birthday, Barney puts together a compilation tape of jazz recordings for me. Two of the tracks are by Thelonious Monk, taken from the album Thelonious Monk plays Duke Ellington. A year or so later, at Bristol university, I take the album out from the record club and make a copy of it. It’s a good late night album when I’m sitting up reading a book to three in the morning, usually one that has nothing to do with my English course.

I buy a cheap compilation cassette. It has a few of his most famous tunes: Blue Monk, Round Midnight, Straight No Chaser, Ruby My Dear, Well You Needn’t. And the entrance fee to this strange but wonderful musical world inhabited by a truly unique musician and composer, a real one of a kind? £2.99.

The first thing that needs to be said about Monk is that he writes great tunes. If he didn’t, most of his music would have been forgotten. He would probably have been remembered as an idiosyncratic bit part player in the history of jazz, a wrong turn or cul de sac in the jazz journey. His most memorable contribution would likely have been that he refused to testify against pianist Bud Powell after drugs were found in his car. Monk lost his cabaret licence which meant he couldn’t perform live for several years but Powell avoided prison.

As selfless acts go, that’s way up there and definitely noteworthy. But there’s a reason why he’s the second most covered jazz composer of all time behind Duke Ellington. It’s because he writes great tunes. He might have only written 70 or so in his lifetime but they’re tunes that musicians want to play and that people want to listen to. That’s not what I thought when I first heard the recording of him back in the classroom but all it takes is a little time to familiarise yourself with his universe.

The playing is so inventive. It’s as if he looks at a piano differently from the rest of us. When he sits down at the piano and prepares to play, it’s probably the only time when you could say he is just the same as anyone else sitting in front of a piano. Then he puts his fingers on the keys and starts to play and any similarity with the rest of us shatters with the first note. That’s when the adventure begins.

His music swings. There’s a great rhythm to everything he plays, even if sometimes it feels different to what you expect. People have remarked that he has a very percussive and angular style, that he will sometimes hammer down on single notes. Repeat them. Then he’ll throw in a run, a fill or a flourish that quickly disabuses you of any notion that he can’t play the piano.

There’s also a real sense of excitement in the music. Joy sometimes. He can make you laugh out loud when he hits a particular note or plays a flourish of notes because they’re not where you’d expect them to be but you feel a childish glee in hearing them precisely because they’re not where you expect them to be. I don’t think it’s overstating things to say that listening to Monk can sometimes be the closest a listener gets to feeling real unvarnished delight at hearing music.

The great thing about Monk is that he’s not a po-faced performer that we all have to sit and listen to attentively and quietly, pretending to be intellectuals. There is playfulness, humour and mischief in his music and his playing. You don’t have to be “serious” or clever” or “cool” to like him. You just have to like music.

It’s exhilarating to hear someone upending your expectations with nearly every note he plays. It’s not done as a display of virtuosity. Far from it. That’s why people used to claim he couldn’t play or that he was a very poor piano player. He’s not just hitting notes because he can or to show off. He’s hitting notes because they’re the ones he thinks should be played at that moment.

I have a feeling he didn’t really care if people were critical of his playing because he knew he could play and that he was a very good piano player. He just played piano his own way. But the most important thing was that it was always in and around the tune. It’s just that they were his tunes and he took his own way in and around them.

One of the most famous quotes by Monk goes like this: “The piano ain’t got no wrong notes.” In all his performances, he made it his mission to prove that statement. In one sense, he was probably the most complete jazz piano player because he showed there were lots of other notes you could play that nobody else would. He opened up possibilities across the 88 keys that even the greatest virtuoso and most technically gifted piano player could never have found. The notes had always been there but nobody else had thought to play them! “When you look at the keyboard, all the notes are there already,” he once said. “But if you mean a note enough, it will sound different. You got to pick the notes you really mean!”

His playing was almost as much about the notes he didn’t play as the ones he did, along with the gaps and pauses in places no one else would think of putting them. As he himself said: “Don't play everything (or every time); let some things go by… What you don't play can be more important than what you do.”

There is no doubt in my mind that he was a complete one-off, a genius, but always himself. And he was very good at being himself. To quote his own words: “Everyone is a genius at being themselves.” Not many people get to prove it.