Texas-born pianist Robert Glasper revels in straddling the line between jazz, hip hop and R&B. His Grammy-winning Black Radio albums saw him working with the likes of Erykah Badu, Mos Def and Jill Scott, and he is among the crack squad of jazzers to play on rapper Kendrick Lamar’s album-of-the-year contender To Pimp a Butterfly. Following three albums with his electric Experiment outfit, Glasper’s new Blue Note album Covered reunites him with his acoustic trio of bassist Vicente Archer and drummer Damion Reid.

‘It was a way to come back to playing piano trio, but not in the same way I’d done it before,’ he explains. ‘After Black Radio came out I acquired a more mainstream R&B and hip hop audience. I wanted to do an album that catered to them as well as to my jazz fans.’

Glasper has been quoted as saying that Black Radio was his way of giving jazz ‘a big ass slap’. Covered is similarly motivated, bringing songs by Kendrick Lamar, Bilal, Radiohead and Joni Mitchell into an acoustic jazz idiom.

‘[I want to] loosen up, resuscitate the music, say “hey, it’s 2015, let’s make a jazz album that sounds like 2015”. So that’s why I’m doing ‘I’m Dying of Thirst’ by Kendrick Lamar. That’s why I did songs by Bilal and Musiq Soulchild: this is music from my era. That’s why I said it’s a big slap, because you have to wake it up, hello!’

Glasper does far more than simply ‘swing’ a pop tune. While retaining the melody and feel of the songs, he improvises on them with invention and flair. It’s an exciting new direction for jazz, but one that has brought accusations of selling out. He’s having none of it.

‘It’s all about connection to me. It’s not about selling out. Some people get that mixed up and say, “aw, you do all these songs, you’re trying to cross-over but you’re selling out.” No. Selling out is when you do something that you don’t naturally want to do. I naturally love what I’m doing. I loved R&B years before I even heard my first jazz song. For me it’s not selling out, it’s just me tapping into different genres I grew up with, that I love.

‘A lot of old cats can’t move forward and do anything that’s now because it’s not their generation. So they hate on it because they’re comfortable with what they are and see the music’s moving towards something that they’re not personally hip to, or don’t like. You can not like it, that’s fine. You’re not supposed to like everything I like. I don’t expect my grandmother to like Lil Wayne, you know what I mean? It’s the same thing with jazz. If you’re trying to feed jazz to a 15 year old, it’s not from their era, so they’re not gonna get that. But guess what, they get me. Why? Because I’m doing something they can actually relate to. I play songs that are recent, that they have actually heard, can understand, and can probably sing along to.’

So in a sense, you’re creating new standards?

‘That’s what it’s supposed to be. You’re supposed to create new standards. The more you play songs by your peers, they become standards, you know? Miles Davis played ‘Gingerbread Boy’ ’cos he and Jimmy Heath were cool, you know? That’s how the culture goes. I’m basically doing the same thing, like hey, I’m playin’ my boy’s tune. I just happen to know some of the most talented cats, so it really works out for me!’

Robert Glasper plays the Russian Standard Vodka Hub Sessions at the Edinburgh International Festival. The Hub, 473 2000, 10 Aug, 10.30pm, £25.