“I LOVE the word carnal,” Sharon Olds tells me from the other side of the Atlantic in her slow, sweet American voice. “That’s such a great word. Carnal.” As she says this I am thousands of miles away from where she sits in an untidy room “full of boxes of books and poems” in lower Manhattan and I am imagining her holding the word up to the light, feeling the weight of it, how it fits into her hand.

We have been discussing the physicality of her poetry, its awareness of the blood, meat and bone of each and every one of us, the way her verse sings the body erotic and the body erratic. In her new book Odes, inspired by reading Pablo Neruda, she tells me, there are poems dedicated to (deep breath) the clitoris, the penis, withered cleavage, menstrual blood, testicles (although that’s not the word Olds uses), the female reproductive system, body fat, wattles and whiskers. There’s also one hip replacement to be found in its pages and two accounts of oral sex. (A poem entitled Blow Job Ode is pretty self-explanatory, I’m guessing.)

Olds writes poetry that is the opposite of ethereal, then. “I write better about up-close experience which is physical than I do about ideas,” she explains. “I don’t think I have any ideas.”

Well, that’s a matter of opinion. Olds is 73 years old (“73 and a half,” she points out) and possibly the greatest living poet in America (there are some critics vocal in opposition to this line but on balance I’m of the opinion they’re wrong). She’s a Pulitzer Prize winner who earlier this month was given the Wallace Stevens Award (worth $100,000) by the Academy of American Poets for her “proven mastery in the art of poetry”.

Her last collection, Stag’s Leap, won the TS Eliot award. The poems in that book address the end of her marriage in 1997 when her husband of more than 30 years left her for another woman. In the past, Olds has written about her repressive Calvinist upbringing in San Francisco. From her poems you draw an image of a childhood hemmed in by parental anger, her father’s drinking and the fear of hellfire. The fault lines of her life are written out in her verse, though she’s reluctant to play on them in conversation.

In Odes you will find anger and ecstasy, pain and pleasure and a sense of bodies in motion and bodies in trouble. Carnal is the perfect word for her work.

About that lack of ideas, though. She says she can’t do political poetry for example. And yet by writing a book from a female point of view, a view that is time and again incarnated in the female body – we’ll say hers because that’s what we want to believe – Odes is political with a small p. Because the physical is political itself. Who controls our bodies, after all? (It should also be noted that Olds once rejected an invitation from Laura Bush in the White House because of the Iraq War, so she is no political naif.)

Depending on your take on Cartesian dualism, the body might not rule the mind but it does rule Olds’s imagination. “It’s just so present to us day and night,” she says. “It’s how we live and what we are and the feelings, our physical feelings, are so intense. Our emotional ones too, of course, and the two are very bound with each other.”

There is just more of the ecstatic in the physical, she adds. “I always loved to dance. I’ve been having a little arthritis stuff so I haven’t been dancing as much but the art that I connect with most in terms of poetry is dance.”

What does this book represent to her? She’s not sure. “I have no idea of what anyone is going to make of this book. I believe in it. I got it so that it seemed right to me … But it is a wild thing.”

Oh yes, that it is. Gloriously so. “I do not want to be sugar/I want to taste sugar!" she states in Ode To The Penis. No wonder Joyce Carol Oates once described Olds as “fearless”.

Not that she quite sees it that way. I wonder, I say, when she gets up to read her Ode To The Hymen (“Not a cat flap nor a swinging door/but a one-time piñata,” she writes), does the burn of self-revelation still sting her cheeks?

“No, because I think when I’m writing it, it doesn’t feel to me as if it’s about self-revelation. I don’t think anybody is interested in me. I don’t think we’re interested in each other except in the people we really care about.

“If I’m reading a poem it is satisfactorily enough in the realm of art for me that it’s not like a diary. It’s a musical composition and almost like a dance the way the lines enjamb and step down and turn back. And the whole galloping thing that I don’t do on purpose but it just seems to be the spirit that’s behind my poems.

“It’s hard to reveal oneself. We try to do it with the ones we love the most and it’s hard. And I feel like writing a poem is very, very different from that. So, yes, that sounds like a justification, but I think it’s also the truth.”

But she must know the book will be read as self-revelation? In one poem, she talks about the time and place where she has sex for the first time, her introduction to what she describes as “the animal life of a woman”.

“Well, I don’t know. What can I do about it? I think that with people who really like poetry it won’t be read as self-revelation. I mean, I don’t care if it is. I’m not saying that I make stuff up.”

We are tiptoeing around a little here – I, because I know that she doesn’t like talking about the life behind the art, she because this is the first time she has talked about this new collection. I bring up one of the poems, Amaryllis Ode, in which the sight of dying blooms takes her back to “the female side of my genealogy”. It contains a vision of “a daughter stripped/to be punished” and possibly, just possibly, right at the end, a daughter’s sense of forgiveness.

“I’m glad it has compassion,” Olds says. “Without that last line …” She tails off.

She admits that it is a poem she can’t have imagined writing 10, 20 years ago, “because I wouldn’t have known how to or it wouldn’t have occurred to me. I think it would have been beyond my powers to control all the stuff that’s going on in it”.

Control is an ongoing issue, she admits. “I do write a lot of poems and no-one sees most of them.”

Well, what’s the percentage of poems that fail to make the grade? “I would hate to have it known. A very high per cent.”

We circle back round to sexuality and Calvinism. There’s a phrase in Odes, I say, that feels very close to home here in Scotland. At one point she writes about being “Knoxed up”.

So, is there still a puritan kneejerk reaction in the culture when it comes to discussing notions of female sexuality and female sexual pleasure? Are we still “Knoxed up”?

“I think we’re pretty Knoxed up. But I do find the subject of sexual love completely interesting, absolutely interesting. And who could write about it in a way that was at all true to the spirit of the subject. It’s important to me.

“I have been capable over my writing life of egregious errors in taste where I just went flopping around trying to write about something that I’m not really equipped to write about. And my sentimentality has got in the way of course. So it’s not that I feel I’ve been wronged by some criticism. It’s just that it’s not easy to have all the factors working together. There’s a certain luck involved and it doesn’t hit me that often that the poem will feel a little bit alive to me. I don’t mean literally. Nothing crazy. But quote alive unquote.”

Even in that answer she slips from life to art. It’s her natural trajectory. “That’s what we’re hoping for isn’t it? We want to make beauty. We want to make a dance on the page that will engage readers so the reader will dance with us for that page.”

Let the music play.

Odes by Sharon Olds is published by Cape Poetry, £12.