Move over, Beethoven. A modern composer is winning classical music.

On the eve of his U.S. concert tour, Ludovico Einaudi enters the Watergate hotel with a mild-mannered stroll. An evening networking event has transformed the lobby into a chicken coop. Young professionals strut in close proximity, squawking with laughter and pecking at their drinks. They pay little attention to the bespectacled composer trying to pick a path through them to meet his interviewer. 

Your correspondent shakes Mr. Einaudi’s hand, gestures to the baby grand piano in the lobby, and half-jokingly asks if he’d like to play it. Mr. Einaudi smiles and shakes his head. A cocktail party is hardly a conducive atmosphere for hushed compositions such as his latest project, “Seven Days Walking.”

“With my music, I like that it is more like an inner experience,” the Italian musician explains later.

The lively networkers have unwittingly missed out on a free performance by a man who’s just about to play venues such as the nearby Kennedy Center and New York City’s Carnegie Hall. But the lobby revelers may already have heard Mr. Einaudi’s music anyway: He’s the most streamed classical artist in the world. His work, which has cumulatively racked up 2 billion streams, spans piano-based chamber music, orchestral pieces laced with electronic textures, and ambitious compositions that connect indigenous musical traditions from across the globe. What’s driving the demand? Perhaps it’s the mindful quality of his music, an organic escape from the hubbub of overscheduled, digital lives.

“Working with Ludovico on ‘The Taranta Project,’ I saw his qualities as leader of a large and diverse group of musicians – from West African griots to Japanese Taiko drummers, electronica artists, and Southern Italian traditional players,” says Justin Adams, a solo artist and longtime guitarist in Robert Plant’s band, in an email. “He led with calm grace and good humour, with humility and a beautiful limpid touch on the piano. He manages to make music that is direct and clear and straight to the heart, uncluttered by pretension or technical over-complication.”

As someone who appreciates quiet, Mr. Einaudi seeks refuge from the lobby in a nearby room with tulip-shaped, midcentury modern chairs. Comfortably seated, the maestro explains how “Seven Days Walking” was inspired by a daily hike along the same trail in the Swiss Alps. The project consists of seven albums – he’s releasing a new one each month through September – that explore variations of a theme. If the concept sounds as heady as the altitude at which it was conceived, the music is grounded in accessible, piano-based melodies in the minimalist tradition of the influential 19th-to-20th-century French composer Erik Satie. Each of the seven albums has a different mood that reflects different approaches to the recurring motifs.

“My vision of this piece of music was similar to my walk, because most of the time I was doing the same route with some variations,” he reflects, sometimes pausing to search for words in English. “I wanted to create something that was like a continuum of music, not just in terms of instrumentation, but also in terms of how the music is built and connected. Similar to how, for example, if you take a suite of Bach, you play the minuet and then you go to the gigue and then to the saraband. It’s like you end one and you enter into the other one with different movements, but they are all connected as part of one idea.”

Questing for inspiration

The most difficult part of the writing process, he admits, is staving off boredom by searching for inspirational fuel that sets his inner pilot light ablaze. He’s constantly searching for fresh musical approaches. To hear Mr. Einaudi tell it, his surprise success is the unintended result of that questing nature. At first, his musical career followed a seemingly ordained path. Born to a pair of pianists, Mr. Einaudi graduated from the prestigious Milan Conservatory in 1982. But he quickly tired of adhering to the conventions of his training.

“I felt that the academic world was in a way controlling my freedom. And the reasons why I started to make music were connected to the freedom that I wanted to express,” he explains. “So at a certain point I felt that I had to be completely sincere with myself and follow my vision and my credo.”

If anything, he shuns an intellectual approach to music, opting for instinctively embracing uncomplicated beauty – an approach that has resonated with his many listeners. From the time he was a young composer, he has yearned to experiment with different textures and also occasionally draw from his love of rock and pop. (He cites Radiohead, Portishead, Massive Attack, and alt-J as current examples.) Mr. Einaudi initially found liberation by writing for dance companies. Later, he was commissioned to pen scores for Italian arthouse movies and soundtracks for British TV shows, such as “Doctor Zhivago.” His popularity has grown alongside his substantial body of work, which has garnered radio play and been excerpted for TV spots. The academic world now views him as a black sheep, he says.

Grounded by natural spaces

More recently, Mr. Einaudi received attention for partnering with a very different high-profile collaborator: Greenpeace. In 2016, the environmental group filmed the pianist performing a solo piece, “Elegy for the Arctic,” while floating on a barge in the Arctic Ocean. The acoustics are enhanced by nearby glaciers.

“There was a moment where I was playing that there was a coincidence between what I was doing with the piano and the wall of ice falling down,” he recalls. “My body was completely covered with different layers and, of course, my hands couldn’t have gloves. I was stopping every five minutes to warm them up.”

Indeed, Mr. Einaudi’s work often takes its cues from nature, whether it’s the musical connections to geometry behind his 2015 album “Elements,” or the nocturnal play of shadows and light that informs his 2009 record “Nightbook.” On “Seven Days Walking,” compositions have self-explanatory titles such as “Fox Tracks,” “Low Mist,” and “Golden Butterflies.” Mr. Einaudi recalls feverishly scribbling those musical ideas with a pencil.

“I love to look at those manuscripts because I can see that there’s a lot of energy in the paper,” says the musician.

Asked where he thinks the music comes from, Mr. Einaudi pauses to think.

“There’s something that is, of course, part of your background, part of your interest in what you have done in your life. Part of this is also something unknown,” he muses. “I don’t know if there is a spiritual force. ... I mean, I don’t say yes or no – I don’t think too much about it – but I can accept the idea.”

The following night at the Kennedy Center, Mr. Einaudi is accompanied by the other two musicians on “Seven Days Walking”: Redi Hasa on cello and Federico Mecozzi on violin and viola. Half-shadowed by lighting that changes like phases of the moon, the trio are keenly attuned to each other’s delicate touch. Perched over the keyboard, often as still as a praying mantis, Mr. Einaudi leaves notes suspended in the air. The music’s spaciousness and tranquility are transportive.

“People say, ‘I was so relaxed at your concert,’” Mr. Einaudi noted during the previous day’s interview. “People get lost in their thoughts. Inside themselves, they start to have like a sort of internal voyage into their life. And this is more interesting because I think it’s a form of meditation that happens. I quite like that the concert generates a sort of inner experience in the deep.”