David Shrigley & Malcolm Middleton: "My wife hates his portrait of me. She says it's not very flattering. I might have to move it"

The duo met when Shrigley designed the cover for one of Middleton's albums

David Shrigley, 46

The Scottish Turner Prize-nominated artist (right in illustration) is known for his deliberately crude, mordantly humorous drawings. His sculpture 'Thumbs Up' is expected to be installed on Trafalgar Square's Fourth Plinth during 2016. He lives in Glasgow

Oddly, I was never a big fan of Arab Strap, though independently [the indie-rock band's two members] Malcolm and Aidan [Moffat] are very good, and I knew Aidan a little bit socially. In the early 2000s, one of my friends wanted to go see a solo gig by Malcolm. He had a big red beard back then, and I was totally blown away by his performance: he was a good songwriter and had a distinctive voice, which worked with his material; I became a big fan.

I think I told Aidan I was a fan, too, and he told Malcolm, so when he came to work on a new album, he got in touch and asked me to do the cover. I was in awe of Malcolm: I'd bought all of his records by then and he must have known I was a bit enthralled with him when we met. I took pictures of him near where he lived, wandering around Victoria Park [in Glasgow], hiding behind bins and playing with the swans.

After the album, Malcolm began redoing his website and he asked me to do some artwork for that, too. I'd just made my first spoken-word record. So I said, "If you compose the track for my next one, we'll call it even – no charge." And we ended up working on this track together: me recording voices first, Malcolm playing around with them and putting them to music. I was surprised when Malcolm was like, "Yeah, we should do a whole album like this!" I was like, "Hold your horses – we've only done one track." But it did eventually turn into a collaboration – though it was seven years in the making.

When we go out for lunch we're always talking music. Though I collect records, he's put me on to quite a few new things, such as Davey Graham, a late-1960s folk guitarist, who is right up my street.

The difference between the worlds of music and arts is that intellectualising is frowned upon in the music business, while you can be as pretentious as you like when you're a visual artist. But Malcolm is a literate person, not some knuckle-head rock'n'roller. I think of him as more of a poet. There's a kindness and tenderness in his songs, as well as a dark irony.

He's quite earnest. When we mixed our album, he kept asking me, "What's this lyric about?" and I'd say, "I dunno!" It became a bit of a gag. Malcolm read a lot into one track, "Sunday Morning", as if it was some church reference; his commentary on the track in the sleeve notes was… interesting. I think it was called "Sunday Morning" by the sound engineer, as that's when it was recorded!

I made a portrait of him once, which I gave to him. He tells me he loves it, but the funny thing is, his wife said it was her who liked it, and actually, Malcolm didn't. I think one rarely likes portraits of oneself.

Malcolm Middleton, 40

Middleton released six albums with Arab Strap before embarking on a number of solo projects, including, most recently, performing ambient electronica under the pseudonym Human Don't Be Angry. He lives in St Andrews

A lot of people say this, but David is massive. He must be 7ft tall. When we first met he had to stoop down low to get through my front door. I was nervous, as he was a known artist, and I was out of my depth, as I don't know much about the art world.

I'd been looking for artwork for my [2007] album A Brighter Beat and I'd come across David's photography online. I loved one image – of a tree with a painted eye on it – and the anthropomorphism of it struck me. What I didn't know, when I first got in touch, was that he was a fan of my music. We arranged to meet and speak about the album, and ended up driving round Glasgow, looking for locations to take cover photos. In the end, I featured a piece he had already done: a balloon lying in bed with a face drawn on it.

I'm quite antisocial at the best of times, so it was a bonus to meet someone I liked. A few months later I asked him to do some stuff for my website and, in lieu of payment, I gave him some music he could use on a project he was doing. A few months after that he gave it back to me, but with some actors reciting his words; the voices were quite Jackanory, but the content he'd written for them was disturbing. I mixed it for him, and it became something bigger than the sum, which made it exciting. I thought, wow, we can maybe do something more together like this.

After that we met up at pubs, curry houses, Aidan's gigs and album launch parties, with the idea just ticking away in the background: every few months he'd send me new actors' spoken-word dialogue, and between tours, albums and babies, it built up.

David says we share a love of darkness and despair. I know that with my own music and temperament, it's not that I enjoy misery and the negative but rather that I have many questions of life and death in that area. When David tackles it, it's with a lot of humour.

The strange thing about him is that he appears to have everything on display, yet he is hard to gauge. His humour is very dry, and mine is too, and sometimes when two people with a dry humour interact, no one knows who's joking and who's serious half the time.

He gave me a portrait of myself, which I've framed and it's in my bedroom. He's got my expression right, but the lines are not in the right place – and the nose is nothing like mine. My wife hates it, though – she says it's not very flattering, so I might have to move it.

Middleton and Shrigley's 'Music and Words' is released on 15 December. Shrigley's latest book, 'Weak Messages Create Bad Situations' (£25, Canongate), is out now