The animal sure comes out in the chorus which takes off on a boppy, arse-shaking groove with Byrne crooning "I am an ape, a masterpiece, a hairy beast ..."
The song is an example of the arty and clever, yet catchy pop mood of Love This Giant. Adding to the oddity of the album is the fact the pair chose a brass band as the foundation for the songs over a traditional rock set-up, but with the bouncy, playful beats offsetting the "plodding and grandiose" horn arrangements.
"I think," says Clark, "sometimes when people hear, 'Oh, collaboration. Oh, brass band' it sets off alarm bells. But this is a really strong album that's a unique intersection of accessible and artful."
For Byrne especially, who has been making music since the early 70s, his work with Clark is something special because he's never done anything like it before. "It doesn't feel like, 'Oh, another record. Strum the guitar again and do all that'. It feels like this is going to be something completely different. It's exciting."
You also get the feeling, as one of music's most willing eccentrics - his previous albums were a concept album with British DJ Fatboy Slim about the life of the former Philippines First Lady Imelda Marcos and the soundtrack to Wall Street: Money Never Sleeps with Brian Eno - he is well aware of his typecasting as an oddball. And then there's the "baggage" (that's his word, not ours) that comes with having a distinctive quirky drone as a singing voice. It's for this reason he gladly handed singing duties on the meandering and twisted mantra The Forest Awakes over to Clark.
"Well," he says, choosing his words carefully before explaining himself, "lets see how this sounds. Some of the lyrics deal with subjects that could be perceived as serious, a little bit pretentious - and there is no irony to it at all. So I thought, 'Some people are going to hear my voice and the first thing they are going to think is that I'm being ironic'. I didn't want that to happen, so, I thought Annie would sound beautiful singing it first of all, but I also thought it would free the song from the baggage people would bring to it with me singing it. It's really unfortunate," he laughs.
"No," squawks Clark. "That's not true at all."
Byrne: "But it's like being told, 'We don't believe a word you're saying'. Whatever you're singing is like you're meaning something completely different."
With this they both break out laughing. The pair have an easy way with each other, politely taking turns answering questions and then chipping in if the other needs a hand finishing their thoughts.
They dismiss the generation gap - Byrne is 60 and she is 29 - saying it doesn't impact on the collaboration at all.
"We're aware that there is an age difference. I'm aware of that," he deadpans. "But I follow a lot of music and the age of the person who plays the music I admire is completely irrelevant. Music seems to transcend that in some way."
The pair first met in 2009 at Aids/HIV charity Dark Was the Night's benefit concert at Radio City Music Hall. Byrne knew Clark's work well having followed her career since her 2007 debut, Marry Me, and he had seen her play live a number of times.
"You make me sound like a stalker," laughs Byrne. "It was a very interesting and enjoyable evolution to watch," he says of her concerts which evolved from a small "almost one-woman show" to a chamber group.
In contrast, Clark - who wasn't even born when Talking Heads released their classic fourth album, Remain In Light, in 1980 - first heard Byrne's music watching 1984 film Revenge of the Nerds. "That movie got a lot of air time in our house [during the 80s] and David's songs Burning Down the House is featured in a scene where the frat house burns down. But I've pretty much been a Talking Heads fan since I've been able to buy CDs and records."
And now she finds herself working with the man. It was soon after meeting at Radio City that another New York institution, Housing Works bookstore, approached the pair to see if they would do a collaborative concert night together.
Byrne says initially they wrote a handful of songs, sharing ideas remotely, to play for the performance "but it seemed to work out so we just kept going".
Clark's suggestion of using a brass band rather than a rock group was initially inspired by the "acoustically challenged" bookstore where they were to play. But there was more to it than practicality because over the years she had worked with woodwind, strings and rock bands. "So for me brass was the final frontier pretty much. And it has a little dimension of excitement. It also provided a neutral territory for it where it wasn't a David Byrne record, or a St Vincent record, but a third entity with a real identity," she says.
"I loved the idea," adds Byrne. "It solved the possible acoustic problem but more than that it gave the album, at least the songs we hadn't written already, a focus acoustically. But as we found out there is an awful lot you can do with brass. We didn't have to constantly ask what's the instrumentation going to be on this song, where do we go with this one. Those questions had already been answered so it was one less thing to deal with."
Juggling their various recording and tour commitments, including St Vincent playing in New Zealand earlier this year, the album came together over the course of a few years. And on Love This Giant - a title inspired by Walt Whitman's "ecstatic poem" Song Of Myself - they've come up with songs like the brassy clip clop of first single and album opener Who, the beautiful Optimist which descends slowly into dissonance, and the cooing and dancey duet Lazarus.
They worked well together because they both have, what Byrne calls a "kind of nerdy and analytical approach to music".
Although, he adds quickly, not that that consumes the music. "But you can sense the gears working a little bit," he laughs.
"Absolutely," says Clark. "We tend to both think about music in terms of architecture, form, and texture.
"David is always looking to the future of music, and he's not nostalgic about anything ... so we kept pushing each other."
Who: David Byrne and St Vincent
What: A collaboration between the former Talking Heads frontman and New York based art-pop-rock musician backed by a brass band.
Album: Love This Giant, out Friday, September 7
-TimeOut