Bill Sims wondered what the commotion was about.

His wife had taken a phone call from their daughter, Chaney, and Sims could hear the whoopin' and hollerin' at both ends of the line. The news was beyond his wildest expectations – Heritage Blues Orchestra, which father and daughter front with singer-guitarist Junior Mack, had been nominated for a 2013 Grammy for debut album, And Still I Rise.

"I'm excited," confirms Sims from New York. "But this is Chaney's first album and I'm more excited for her than I am for myself. We weren't thinking about winning awards when we made it. We just wanted to make something that showed as much of blues history as possible, make it relevant for today's audience, and it looks like we've done it."

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Heritage Blues Orchestra came from a demo Sims sent to producer Larry Skoller of Mack, Chaney and himself singing traditional blues songs, field hollers, gospel songs, folk tunes and spirituals to sparse acoustic and electric guitar accompaniment. Skoller, who is New York-born but lives in Cognac, France, loved what he heard and decided to add horn arrangements for some extra spirit of New Orleans flavour and recruit his brother Matthew on harmonica and Chicago drummer Kenny "Beedy Eyes" Smith, son of Muddy Waters's long-time drummer Willie Smith. A Franco-American blues phenomenon was born.

"We've gone over really well in Europe," says Sims. "But what's pleasing is that American audiences are digging what we're doing too. There's a real interest in roots music in America – we get all ages and they respond to the quieter songs as well as the good time side of things."

Sims began playing boogie-woogie piano, taught by his preacher father, at the age of four in Marion, Ohio – the popcorn capital of the world, he proudly announces. "Marion is a town in the middle of this huge cornfield," he says. "My father had twenty-some brothers and sisters, so there was a built-in audience. We'd play in church and gather on the back porch once work in the fields finished."

By his mid-teens Sims was playing Hammond organ and saxophone, sometimes simultaneously, at local dances, honing a vocal style influenced by Lightnin' Hopkins and Big Bill Broonzy, and a guitar technique drawn from Albert King. He went on to work in the backing band for soul singing group the Four Mints, play jazz in San Francisco and work off-Broadway before becoming a house husband for 10 years after Chaney's arrival.

"Once Chaney had grown up and I was able to go back to work, I decided I should be the one outfront because I'd always worked in other peoples' bands," he says. He's worked on the New York blues and roots scene and kept up his links with theatre by working on music for plays. He was also an advisor on the 2008 movie that charts the rise of the legendary blues label Chess, appearing as the bassist in Muddy Waters's band and as Howlin' Wolf's pianist, having sat in with both of these stars in 1960s Chicago.

Heritage Blues Orchestra's guest at Celtic Connections, Eric Bibb, whose song Don't Ever Let Nobody Drag Your Spirit Down appears on And Still I Rise, may well have provided the best endorsement of their music. "It sounds old but it sounds new and it sounds like the real deal," remarked the charismatic Bibb.

"That's exactly what we're trying to do," says Sims. "The blues never goes out of date because essentially these songs are about people telling other people what's going on – right and wrong – in their lives."

Heritage Blues Orchestra plays Glasgow Royal Concert Hall on January 31, as part of Celtic Connections.