And that range of inspiration, leading to a variety of musical approaches, will be in evidence when the saxophonist guests with the Scottish National Jazz Orchestra this weekend. Just don't ask Liebman to arrange his pieces for a band of this size.
"I love the power of a big band and to use an American football analogy, I like that feeling of being a quarterback, being well protected by having a strong team around me," he says. "But I could never cope with, never mind writing out, all these parts, thinking about what everyone's going to play; the most I can deal with is maybe four saxophone parts.
"I have the greatest respect for anyone who can orchestrate and I've been lucky to have great arrangers like Jim McNeely, Bill Dobbins and Vince Mendoza work up my compositions for big band and make me sound good when we play them."
To hear the New York-born Liebman talk, luck has played quite a part in his illustrious career. He was, he says, fortunate to be in the right place at the right time in the 1970s when first the great drummer Elvin Jones invited him to join his band and then Miles Davis hired him to pitch his soprano saxophone into the funky maelstrom of his On the Corner-Dark Magus period.
Liebman will tell you there was less competition in the jazz world back then than there is today, but the reason he was chosen by two of his musical heroes was that, even then, he had a distinctive voice on both tenor and soprano saxophones and an imagination that could keep those voices supplied with ideas that belied the spontaneity of their creation.
"Our whole lives as jazz musicians come down to getting in front of people and improvising. That's what we do and to do it well, you have to be completely focused. You can't have any distractions and that 100% commitment to being there in the moment when you're playing was something that, if I wasn't aware of it before I played with these two legends – and they were giants of this music – then I certainly carried it on into my career."
Playing with Jones, the drummer for one of Liebman's two saxophone heroes, John Coltrane (the other is Sonny Rollins), was a dream come true. He'd seen Coltrane's classic quartet with Jones countless times in his teens and was "walking in the clouds" for the first six months of the two years he spent with Jones's group. From there, joining Coltrane's former boss, Miles Davis, was like graduate school.
"One of the reasons I concentrated solely on soprano from 1980 to 1995 was down to playing with Miles," he says. "I'd be there onstage, trying to gather whatever knowledge I could from him and something about the way he held the trumpet and the way you play the soprano out in front of you had an impact. I also felt that the tenor had been such a major instrument of innovation and at the time it seemed like a blind alley. I had my own way of playing and I could tell it was me when I heard myself, but I felt an affinity with the soprano physically that I didn't feel so strongly with the tenor."
There was no shortage of opportunities for him to play post-Miles and just as his own bands illustrated his liking for different musical situations – he could switch instantly from the freely improvised side of jazz with Lookout Farm to fusion and funk with his Lighten Up team with Pee Wee Ellis – so he would fit in effortlessly with Chick Corea, Jack Bruce, imminent visitor to Scotland, Leo Blanco's African-Latina music, myriad small combos across the world and big bands including the German WDR and NDR radio orchestras and Holland's Metropole Orchestra.
"I think it's fair to say that I'm an eclectic musician. And that's reflected in the programme Tommy Smith's chosen for the Scottish National Jazz Orchestra. You have jazz standards, a Spanish influence in Port Ligat, which I wrote after a trip to where Salvador Dali had his house, and Enfin, which I wrote for Barack Obama and is very 20th century in terms of tonal colour. That's quite a left to right kind of programme but the unifying factor, the constant, for the audience will be me on soprano and hopefully I'll be able to carry them with me."
Dave Liebman joins the Scottish National Jazz Orchestra at Younger Hall, St Andrews, on Friday, June 7; Royal Conservatoire of Scotland, Glasgow, on Saturday, June 8; and Queen's Hall, Edinburgh, on Sunday, June 9