In some ways Miles Davis remains as much a presence as ever, and not just because recordings continue to be issued under his name. A book of his paintings and drawings was published last week, a biopic about him is in the works, a stamp with his image circulates, and a museum exhibition devoted to his life is traveling the world.

Overseeing those initiatives, and others, are his three heirs: his son Erin, his daughter, Cheryl, and their cousin Vince Wilburn Jr. Like those who manage the estates of Jimi Hendrix, Bob Marley or John Coltrane, they are grappling with a complicated challenge: How do you keep this trumpeter, an archetype of 20th-century popular music, in the public eye and maintain his brand, even as his original core audience is aging?

… Davis left behind an enormous body of work. But there is much more in Columbia’s vaults, in the archives of television and radio networks in countries where Davis toured, and in the family’s own collection. (Davis recorded all his shows and rehearsals once the technology became available.) The heirs, however, talk of the need to exercise restraint, to avoid the risk of diluting the value of the Davis name.

“We don’t want to rehash or saturate the market with ‘Oh, here’s another Miles record,’ ” said Mr. Wilburn, who played drums in his uncle’s ensembles in the 1980s and now leads his own band. “We don’t put things out just for the sake of putting things out. This is really thought out, from a blueprint.”

… In recent years, Davis’s heirs have stepped up their efforts to take his music to audiences at events like the indie-oriented CMJ Music Marathon in New York. At last year’s SXSW music festival in Austin, Tex., they even sponsored the Miles Davis House, described as a “genre-bending odyssey” featuring rock and pop bands that professed an affinity to his music.

“I always want the next generation to know about Miles,” Erin Davis said. “Some people figure it out for themselves. But with others, you have to show them something, and they come to it.”

… Among the heirs, a clear if informal division of labor is apparent. “They know more about music than I do,” Ms. Davis said of her brother and cousin. “They know the record keeping, the catalog and all of that,” so on strictly musical questions, she defers to them.

But on everything else, “we’ll say, ‘Let’s call Cheryl,’ ” Mr. Wilburn said. “When we get a signoff from Cheryl, then we know we’re doing something right.”

Ms. Davis was deeply involved, for example, in the new book “Miles Davis: The Collected Artwork,” for which she wrote an afterword; exhibitions of his paintings in California this year; and in the “We Want Miles” exhibition. “Cheryl has ideas for clothes, ties, scarves, QVC, and Erin and I are like, ‘Yeah, that’s beautiful,’ ” Mr. Wilburn added.

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