It's a selfish notion, but one of the glorious aspects of the comedy circuit is the many brilliant comics who we get to keep for ourselves. There are countless comics who consistently storm gigs for years, yet don't disappear into TV Land, never to be seen again at the coal face. It's like having your own favourite band no one else knows.

One such beautifully kept secret is Robert White. White will be the comic who sticks on your brain after the show, while the omnipresent straight, middle-class 29-year-olds form an indistinct blob. And this year, White, "the only Asperger, dyslexic, cross-lateral, gay, quarter welsh, webbed toed comedian", will be breaking from the London circuit for his debut Edinburgh Fringe show.

Buzzing around behind his keyboard like an agitated TinTIn, he fires out gag after gag, punctuating the onslaught with short musical ditties that are equally rammed with jokes. His one-liners veer from the cheesy to the crass, and coupled with the relentless pace, they bludgen the audience into submission. It's a little bit Les Dawson, a little bit Tim Vine and a little bit something else we've not seen before. Self-deprecating yet full of self-belief; eccentric yet accessible; semi-chaotic yet, you suspect, very tightly rehearsed. And all performed in an absolutely splendid tank top.

White pulls off the clever trick of being a throwback to old-fashioned entertainers while feeling like something shiny and new. How has White become such a unique and memorable act? Largely because he appears to operate and exist outside the usual parameters of stand-up comedy. There's nothing wrong with obsessing over videos of Richard Pryor, Bill Hicks, Billy Connolly, Eddie Izzard, Stewart Lee and so on, but it's a machine that spews out the same kind of sausage.

When White talks influences, he reveals his priorities by citing musicians before comedians (Victor Borges, Rodgers and Hammerstein, George Gershwin), and even when he does mention comedians, you get Blackadder, Just A Minute and the Marx Brothers, and that's about it. Unless you count his sister taking the rise out of his Dad's crushingly mundane anecdotes about the world of insurance, which he will have prefaced with "this will make you laugh". White hypothesises that his sister's gentle mockery set an early anti-establishment tone that White has run with (we also have his father to thank for his penchant for the cheesy pun – test case: "I grew up in a very musical house. It was A flat.")

White evangelises about the stand-up circuit, but there is a healthy wariness of it too, keeping it at arms-length – an approach that will help White keep his individuality. He observes (without superiority) that some comics fall into the trap of apeing their heroes such as Stewart Lee and Noel Fielding. In fact White's refrain while being questioned is "I'm just being me". That may sound like the sort of thing a Miss World entrant would say, but in fact that's the platform on which great, honest comedy flourishes. Not to mention a fair answer in the face of possibly irritating journalistic deconstruction.

"People who are a product of lots of comics maybe become reviewers or something like that. I think you can learn lots from other comedians but I don't want to do anything that's copying, I've never been like that. So I deliberately don't watch much stand-up, except for my friends and then it's laughing at things that go wrong, it's more like being at work.

"I liked Blackadder when I was younger but a lot of my time was spent in my own little world. I don't read much, music was always my main thing, especially 1920s music, like Irving Berlin, early Gershwin, and I performed in bands like junior orchestra.

"A lot of my performance has come through wanting to make a show of myself. Music was something I found important because it took a lot of my time and I didn't connect to other people as a kid. Then in your teens music becomes social, and I didn't have the social skills so I communicated by playing up in the orchestra – people would laugh and maybe get annoyed as wouldn't know when to stop.

"There was so much comedy to be had in the orchestra – again an element of that was anti-estalishment – I played trumpet and I'd play a silly tune in the wrong place or wrong notes deliberately. There's a piano section in the middle of Rhapsody in Blue and the Steptoe and Son theme fits perfectly. I'd have the mute on playing into the ground, playing the trumpet upside down, putting Postman Pat into solos.

"On one occasion I was constantly playing up and making comments, people were laughing and the conductor was getting really frustrated and he told me to go up and try to conduct. He went and sat in my place while I stood there, and he started making comments like I had, and I just said "can you behave". It went quiet and everyone looked at him. He started playing and I started conducting the orchestra. It was wrong what I was doing, but his teaching was possibly wrong as well."

"Looking back at it now, I really liked the performance and mixing with people, and the connecting with people through music."

It seems unlikely that White would have become a comedian, had he not discovered music. Not just music's unnumerable joys and his talent for it, but its ability to be the glue that binds people together. The inhibited social skills that tend to come with Asperger's could easily be a barrier to a career in performance, particularly one like stand-up with its indisputable need to connect and the unwavering spotlight. But music has helped build that bridge, and Robert says his comedy career has helped in a number of ways:

"Off stage, yes, sometimes I feel lonely, and when I first started out I found new situations and experiences very hard sometimes. But doing comedy has really helped and given me confidence in things I may never have ever been able to do before. I used to be very nervous about going into new pubs and would stand outside and ring a friend to come and get me. I used to be embarrassed if people said I was funny, I'm still phenomenally embarrassed if they say that now, but I just smile and nod now, which is an improvement."

Musical comedy is a real turn-off for some of course, and few comics really make it fizz. Being technically gifted helps (see Bill Bailey, Earl Okin, Les Dawson) as does having silly conceits (see Tom Basden, Victoria Wood), and White can lay claim to these talents as well. Being a student of music, he says he has a good grasp of what makes a funny song funny – for example, retitling the Whitney Houston hit as Shaving All My Muff For You is funny in itself. Juvenile of course, but funny. It certainly doesn't need to be flabbed out with two verses and three choruses of rewritten lyrics. He says another tip is to avoid over-reliance on rhyming to crowbar in a punchline. And to find humour from tinkering with musical convention rather than the lyrics (remember Bill Bailey making any song into a cockney knees-up? That sort of thing.

"It's amazing how people see it as magic. To me and other musical people it's like another language, or breathing. Sometime it's just doing something really simple that people don't expect. It was sitting and making up funny songs that got me into comedy and touch wood I can make up songs on the spot.

"I wrote two symphonies at the age of 12 and was destined to have a career in music, but instead I got seduced by comedy at an open mic drag queen night in Soho. It was hosted by this sort of failed drag queen who would be funny then sit by the piano doing really serious songs. I would get a bigger laugh for a spontaneous musical thing than her hack washed-up opera songs – that's when I realised comedy songs should be punchy and have jokes all the way through, not just two minutes of singing followed by one punchline."

Come August, White will be migrating from his Brixton home to Edinburgh, where standing out from the hundreds of other comics is imperative. There are no guarantees of course – converting high-quality circuit material into an Edinburgh show is tricky, and White's act may be too intense or (occasionally) crude to win over everybody – but White is both unique and talented enough to stand out, and maybe go onto bigger things.