I've managed to catch Diana Damrau on a rest day.

She's at home in France, the morning after performing Donizetti's Lucia in Munich the night before, having travelled home in the wee hours and, thanks to a pair of enthusiastic children, had about four hours sleep. Yes, she's one of the world's top coloratura sopranos - the current darling of New York's Metropolitan Opera - but Damrau is not beyond working a gruelling schedule.

Noisy domestic goings-on are audible down the line. Damrau's husband, the French bass-baritone Nicolas Testé, is out tending the garden but the kids are very much indoors and tugging at her sleeve for attention. Our interview ends up being a hodgepodge of polite conversation in English, snippets of Verdi in Italian and pleading instructions whispered to the children in German between questions. Transcribing it later was a hoot.

When Fergus Linehan, director of the Edinburgh International Festival, announced his inaugural line-up of concerts for this summer's programme, he emphasised his aim to make the series "a platform for artists to bring their best game to the festival." He said he wanted artists "to perform material that really runs through their veins," and highlighted three events that he believes fulfil that mission: Valery Gergiev conducting Stravinsky's The Rite of Spring, the Oslo Philharmonic Orchestra performing Grieg's Peer Gynt suites, and Diana Damrau singing Verdi.

Damrau was born in Günzburg an der Donau and musically shaped in the ensemble casts of Mannheim and Frankfurt. She might not share Verdi's birthplace or native tongue, but there's no question that his music runs deeply through her veins. It was hearing Teresa Stratas sing Violetta in Franco Zeffirelli's 1982 film version of La traviata that first snared her interest in opera, she tells me, and even now she lets out a sigh at the memory. "What did it for me? Oh, the passion. The melodies. The colours. The strength of the women, too: Gilda, Violetta, Amalia, Luisa... These women find themselves in victim situations, but they have an inner strength that is radical and empowering."

She talks about her love of Verdi's orchestral textures, describing his scores as "incredibly inspiring to sing over". At the Usher Hall those textures should sound particularly vibrant in the hands of Gianandrea Noseda and the terrifically energetic European Union Youth Orchestra. It's a concert performance of various arias, not a fully staged opera, so we won't get to see much of Damrau's magnetic, charismatic acting, but she is full of enthusiasm for the opera-aria-in-concert format. "Yes! The direct communication with the audience is so gratifying. And the chance to really hear and interact with the orchestra? I love that. But most of all, for me Verdi is all about passion. It's what we're all longing for, right? And if you sing it well, it doesn't matter where you are. That passion could come across in the shower."

Damrau will be joined at the Usher Hall by her husband for a selection of duo arias from Verdi's operas Luisa Miller and I masnadieri. Over the phone I can hear her shouting to Teste to come in from the garden to discuss the collaboration. "Well," he says, seemingly having had the receiver thrust at him, "we put together a Mozart programme a couple of years ago but to be honest that was a bit boring for me." He still sounds a bit bored by the thought. "Personally I like singing Bel Canto. The voice has to be so supple and rich. I think it suits us both very well."

But it would be too simple to assume that the husband-and-wife team can simply transfer their relationship onto the stage. Their voice types mean they rarely get to be lovers - particularly in Verdi, whose tenors tend to get the girl. "Yeah, poor Nicolas usually ends up playing my father, my uncle, my priest or some kind of bad guy," Damrau jokes. "That's the fun of it. We get to work out our problems in front of the audience!"

That said, there is some love involved in the roles they bring to Edinburgh - just not love of a reciprocal nature. Arias from Luisa Miller see Damrau playing the distraught young heroine, honest and modest, while Teste plays her repugnant suitor Wurm - the name translates literally to 'worm'. In extracts from I masnadieri, Testé takes the role of Francesco, younger of two criminal brothers who are both in love with Damrau's Amalia. "She is an extremely wonderful role that Verdi wrote for Jenny Lind," says Damrau, referencing the 19th century star soprano for whom Verdi created some of his finest heroines.

"Lind was able to be so flexible and command real magic with the soft tones in her high voice. That's what I need to aim for. In Edinburgh I'll sing an aria in which Amalia dreams of true love. In my opinion it is one of the most beautiful moments in all Verdi." She sings a little, a velvet phrase that unfolds gorgeously down the phone line only to be broken by the happy shriek of a small child somewhere in the background. "Better go," Damrau laughs, and bids me a speedy goodbye. I'm looking forward to hearing the end of that phrase in August.

Diana Damrau and Nicolas Testé sing Verdi arias with Gianandrea Noseda and the European Union Youth Orchestra; Mahler's Fifth Symphony completes the programme. Part of the Edinburgh International Festival. Usher Hall, 25 August