Fred Hersch is talking about the happy accident that has seen him develop his skills as a solo piano recitalist.

"I really just kind of stumbled into it, to be honest," says Hersh, who makes only his second appearance in Scotland at a solo concert in Edinburgh this weekend. "When I started playing solo there really weren't many other jazz pianists doing it. There were Cecil Taylor and Keith Jarrett but no real template, so I found my own way, discovered I liked it and seemed to have an aptitude for it."

Aptitude may be understating it. Hersch, who forms a bridge between the jazz masters he learned from and his own pupils such as leading current players Brad Mehldau and Ethan Iverson of the Bad Plus, has forged an almost separate career as a solo performer and there's no small demand for his services.

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Alongside an output that includes albums as part of a trio, concert works, tours and recordings with his Pocket Orchestra and settings of Walt Whitman poetry for singer Kurt Elling, he has released nine albums of solo piano and is the first solo pianist to be booked for a week-long engagement at New York's Village Vanguard in its 75- year history.

On his latest solo recording, Alone At The Vanguard, he pays homage to guitarist Bill Frisell and saxophonist Lee Konitz, just two of the many names he's worked with since arriving in New York in the late 1970s. Stan Getz, Joe Henderson, Art Farmer and the British singer Norma Winstone are four others who have sought out Hersch's skills.

Hersch began playing piano as a child in Cincinnati and from the age of five or six, he says, he improvised.

"It was always much more fun to make something up than to play what was on the music stand," he says. "So I'd be, I like to think, improvising in the style of Mozart or Bach when I really should have been doing my homework for my music lessons. From there I went on to discover the golden age of American pop music – Joni Mitchell, Stevie Wonder, great writers and singers like that – which was happening as I grew up, and I taught myself to play that repertoire."

In his late teens, having dropped out of Grinnell College in Iowa, Hersch returned to Cincinnati and got work on the local music scene, playing with older jazz musicians who "kicked my butt" and sowed the seeds of his obsession with knowing tunes. Being able to respond to a count-in for any tune in any key became a matter of pride – and ideal preparation for a career in jazz.

HE moved to Boston to study with former Charles Mingus pianist Jaki Byard at the New England Conservatory, where Hersch now has a part-time teaching post, and graduated with honours before hitting the New York jazz scene. This was a tough school.

One night he'd be playing with Stan Getz, the next with Art Farmer or Joe Henderson, to audiences who weren't easily impressed. However, an inner confidence, which probably wasn't hindered by Hersch having played piano on a children's TV show from the age of 10, and natural ability ensured his success.

"I was lucky," he says. "I arrived in New York when a lot of jazz's great characters were still around. You learn so much on the bandstand that you can't get from a book and that oral tradition is so important in jazz. That's why I like to pass on to students what I've learned in the same way. And if it means I'm a link between the great people I played with and learned from and the younger guys who have come up behind me and are still coming through, that's a reward in itself."

The quality of Hersch's recent work – he has just released a double CD with his trio, Alive At The Vanguard, as a companion to his similarly titled solo album – is all the more remarkable considering he almost died four years ago.

An openly gay man who made public the fact he'd been diagnosed with Aids in the early 1990s, he suffered severe pneumonia in 2007. It then transpired that the HIV had migrated to his brain, causing Aids-related dementia. He underwent a tracheotomy, was unconscious for months and, with prolonged inactivity, lost the use of his hands. But his refusal to see this as anything other than a temporary interruption to his music – along with lengthy medical treatment – has seen him make a complete recovery.

If his schedule looks like he's making up for lost time – immediately after his UK tour he returns to the US for engagements before flying back to Europe for a tour with his trio – it's hardly surprising. His playing may also have developed a greater intensity.

"I don't practise much these days because I feel I'm playing the piano as much as I need to just through my workload," he says. "There's no real plan with solo concerts, although I do like to show my love and respect for the history of jazz piano. Not in any pedantic, ordered way ... but with references to people going back to Earl Hines, who for me was the greatest, and moving forward through later masters. The important thing is that whatever I play, it connects with the listener. It's like composition. I always try to write something that's fun to play because I figure, if it keeps my attention then it'll keep others' too."

Fred Hersch plays the Queen's Hall, Edinburgh on Friday.