Josh White Junior's Scottish debut - at Celtic Connections this weekend - is long overdue. Fifty-seven years overdue, to be precise. Back in 1951, the then 11-year-old was billed to appear alongside his father, arguably the musician who did the most to introduce the blues and black music generally to a white audience, at a concert in Edinburgh. The events are slightly sketchy but as Josh Jr recalls, red tape prevented a child under 12 from performing professionally onstage in the UK at the time and he had to miss the trip.

Whether that's the official reason or not - his sister, Beverley, who was 18 months older, was able to go - Josh Jr certainly wasn't excluded owing to a lack of experience. He had already been singing with his dad in concerts and clubs for seven years by then.

"Dad used to take us along to gigs and we were meant to sit quietly and, I suppose, be seen and not heard," he says. "But there was one night in a club in New York when I was four and I started singing along a little too loudly and dad came over and picked me up and brought me on to the stage. That was it. From then on I was a gigging musician and I'm so happy that I've always followed my passion - it certainly beats the hell out of working."

The downside of starting so young is that there's so much that happened too fast, so many people he met or might have met, and he can't remember early events with certainty. Did he appear with the Duke Ellington Orchestra before his fifth birthday? He might have - Ellington and Josh Sr shared radio show stages - but lots of radio shows had orchestras in the 1940s.

His dad had a selective memory - or at least he affected one - about his own early years because there were things that happened he never talked about to his children, although they got to know about them. At the age of eight, Josh Sr became guide to a blind street singer and guitarist, Blind Henry John Arnold, in his home town of Greenville, South Carolina. They hadn't been travelling together long when, one night while sleeping under the stars, the youngster was woken up by his companion putting his hands over his mouth and asking what was happening.

A lynching was in progress: two black men were already hanging from nearby trees and a crowd of white men, women and children were celebrating, dancing around the scene and taking hot pokers to the bodies. If Josh Sr hadn't been able to lead Arnold quietly away, there might have been four black bodies. In his later life, Josh Sr would sing Strange Fruit, the song Billie Holiday made her own, which describes similar events.

"My sister, Beverley, and I always saw that eight-year-old boy's eyes when dad sang that song," says Josh Jr, "and it got so that we couldn't watch him singing it because of this. We'd slip backstage until he was finished."

The incident in question was by no means isolated. Having gone on to act as a guide to other blind blues musicians, including Blind Willie Johnson and Blind Blake, and served his guitar-playing apprenticeship with them, Josh Sr was often on the fringes of violence and brutality - he was once beaten up by police and dumped in a cell after being mistaken for a vagrant. Which made criticism of him becoming "too smooth" once he'd become established as a musician himself a little hard to take for his family.

"Coming from South Carolina and leading the life he did, dad didn't have a lot of schooling and he was always quite aware of that," says Josh Jr. "But he was also aware that audiences had to understand what he was singing. By developing the style he used, he wasn't betraying his roots or knocking any of the other blues singers. He just always told us that you have to let audiences know what you're singing so that they can believe it."

It's a lesson that Josh Jr has taken into his own career. Now approaching 68, he has enjoyed 64 years as a singer and actor. He's starred in innumerable television series and appeared on five Broadway productions - all dramas, no musicals, he says proudly - but the thing he loves above all else is doing children's concerts.

"My dad, eclectic though he was, never did children's concerts and I have to say that I avoided them for quite a long time," he says. "I think it was through the fear of losing it, to be honest. But when I started doing them, I found they were so much fun. I talk to them a lot - well, I talk to audiences a lot anyway - and I have to change the songs I sing. But for 45 minutes or so I'll sing to your children or grandchildren and I don't know who they are or what goes on at home; I can just guarantee that there'll be no negative effect on their psyche, whatever walk of life they come from."

He'll be doing one of Celtic Connections' school concerts while he's here, as well as helping to explore the links between Scottish and American songs in Tayside Tae Tennessee and playing the Friday Night Blues Session tomorrow. From children's songs to the blues involves no big change, he says. "I think whatever you sing, you have to be honest. When it comes to the blues, nobody's immune and I just sit down and let flow the feeling that we're all going to enjoy ourselves because we've all been there."

His father's influence remains strong and he wouldn't change that for anything. He's forever being asked if he gets tired of people talking to him about Josh Sr - and the answer is always "no".

He can't always answer the questions he's asked, such as did his father really influence Robert Johnson, although he's heard stuff Josh Sr played early on where a different sound to his guitar playing might suggest that a musical connection could have been made.

He can confirm, however, that House of the Rising Sun wouldn't have come to sound the way we know it without his father's contribution. "Dad, Leadbelly and I think it was Pete Seeger heard an Appalachian singer singing that song and it had no minor chord," he says. "But my old man heard it more as a lament and he added the minor chord and that's the version that became famous. It's that legacy of being an interpreter that I think he handed on. I'm not a prolific writer, so I tend to choose lyrics that, if they touch me, I know I won't be the only one to feel that way. There's always room for interpretation and we non-singer-songwriters may not have all the ideas but I believe we interpret well."

Josh White Jr appears at the Friday Night Blues Session in the Quality Hotel, Glasgow, tomorrow and in Tayside Tae Tennessee at St Andrew's in the Square, Glasgow, on Sunday.