For someone who appreciates the sound of silence so much she put 11 minutes and 11 seconds of it on the last track of her new album, singer-songwriter Melody Gardot doesn't half like to talk.

But then, with three years of new and subtly life-changing experiences under her belt since we last met, she has plenty to say – all of it eloquently and earnestly delivered, much of it profound, and some of it only comprehensible when you listen back to it and unravel it slowly.

Holding court in her London hotel room, which she has customised with shawls and rugs from her recent globe-trotting, the 27-year-old American (whom I last saw seducing an increasingly adoring audience at the Queen's Hall in Edinburgh in late 2009) has morphed from New Age femme fatale – or, as she describes herself, "modern-day dame" – into what appears to be Norma Desmond playing a North African queen. The long hair is hidden under a huge, square-ish turban and the shades are pure Gloria Swanson, but the red lipstick is vintage Gardot.

It's not just her appearance that has changed; Gardot's music has evolved into something much less readily categorisable than her previous two records, which were rooted in jazz. New album The Absence was "all about blending - about choosing the colours from the countries I went to and finding a way of putting them all together," she explains. "There's so much of myself in the music, and also of these culturally influential women from around the world – women like [Portuguese fado singer] Amalia Rodrigues, the flamenco and tango dancers, the people of the desert. So much touched me that my style just changed naturally."

During 18 months of travelling – from Portugal to Morocco, via Brazil and Argentina – Gardot soaked up inspiration. The primary new influence comes from Portugal. "Lisbon was," says Gardot, "the first place I put my bags down after that last tour." Naturally nomadic (she doesn't have one base), she says she wanted to go there and "dive into the culture". Rather than sitting somewhere else in the world listening to recordings from a culture that interested her, she was determined to get to the heart of it. "Whatever I would take into my music, if I took it from a recording, would be one thing, and it wouldn't be genuine. I realised it would be different if I went there, sat down, played with the musicians, lived it and understood it."

Once she was rested after promoting and touring her last album, Gardot immersed herself in the fado genre of music. She threw herself into learning to play Portuguese guitar. "I basically went to school there. It was a great study. I made myself rise in the morning with the intention of learning and performing and writing and observing things." She was introduced to the widow of Carlos Paredes, one of the leading Portuguese guitarists of the 20th century. "He's passed on, and his wife gave me his picks to use – with the sweat of his fingers. It was very special. I really connected to the root of what the genre of music was."

It wasn't just the music that attracted Gardot to Lisbon; she had long identified with the Portuguese concept of "saudade" (I remember her talking about it in connection with her earlier albums) which has no direct translation in English but describes a deep emotional state of nostalgic longing for an absent something or someone that one loves. It can also refer to a feeling of incompleteness and of yearning for something that might not even exist.

When asked about all the goodbyes she must have had to say during her travels and about the theme of "goodbye" which runs through the album, Gardot admits it was usually more a case of "a bientot" in reality, since she plans to revisit the new friends she's made; but she also harks back to the saudade idea. "I would leave a country but I'd never leave the people, so there's constant presence and absence. My presence was there although I had a physical absence, nothing of me left. There's still the smell of my perfume in the room, there's still the essence of what I've done in the walls, there's still the writings on the musical instruments there in the room reverberating -

"If you think about it, you give all of your heart one night on the stage to one city and then you have to get up and do it again the next day. When you get the opportunity to spend a month, two months, four months in one place, that kind of energy, constantly, is very strong so the impression you leave is very deep – and so was the impression the people left on me."

From Lisbon, a city to which she pays tribute on the new album, Gardot went to Brazil. The influence of that country's music emerged on her last record (and in my first interview with her, in 2008, when she said she was "tripping out" on the classic Frank Sinatra-Antonio Carlos Jobim recordings) – but here it's very obvious, not least in the involvement of the acclaimed Brazilian guitarist Heitor Pereira, who served as producer and collaborator.

As in Lisbon, Gardot made herself at home with the people she met in the favelas of Rio – so much so that she has committed to creating a music education programme for the children there. "Brazil is one of the most inspiring places, and that was why I refused to go there and just take," she explains. "How could I take from a place that already gave so much to me?"

Pushed as to how long she spent in Brazil, she replies: "I don't know. The whole thing took a year and a half. I spent the longest time by far in Portugal but then was journeying back and forth, like a dance. In some places it wasn't very long at all but it's a matter of time, which is irrelevant anyway. The time felt equal because I left at the moment I felt I was done. After Brazil, I realised I'd written what I needed to write and we travelled a bit more and then we were done."

You might assume the "we" refers to a boyfriend – but Gardot is talking about her guitar. "My guitar's in my bed at the end of the night," she says. "I didn't want anyone else with me. This was my own journey. I was getting calls from friends asking if they could come along but I'd put them off. I wasn't doing a touristic thing. I was staying somewhere, playing music and writing for seven or eight hours a day. That was my life. And if I woke up in the morning and wanted to move on to another place, that's what I did."

What seems to have struck Gardot most from the experience of writing and recording The Absence is the power of music as a means of communicating, and the way in which "the spirit of music is similar the world over". Certainly, all the disparate inspirations and styles seem to fuse together and be channelled through Gardot, who makes them all very accessible.

"This record's not me trying to be a tango singer, or a fado singer, or a samba singer, or trying to be Astrud Gilberto," she insists. "I'm myself, but the songs I've written are really influenced by those things."

Her journey continues, first with promotional duties across Europe, and later this year with what she describes as her favourite part of the process – touring. She bursts into laughter as she vividly recalls her Scottish date on the last tour – when a rather large and very drunk audience member heckled her so much that both he and the seat he was sitting on were removed, straight out of the auditorium, as she watched bemused from the stage.

It's something that could have happened anywhere. If there's one lesson that Gardot learned during her musical adventures, "from being in cultures and living among them, it's that we're all citizens of the world. There's no difference between us".

The Absence is released on Decca Records on Monday; the first single, Amalia, is out now.