CONDOLEEZZA RICE trained to be a concert pianist. Alan Greenspan, former chairman of the Federal Reserve, was a professional clarinet and saxophone player. The hedge fund billionaire Bruce Kovner is a pianist who took classes at Juilliard.

Multiple studies link music study to academic achievement. But what is it about serious music training that seems to correlate with outsize success in other fields?

The connection isn’t a coincidence. I know because I asked. I put the question to top-flight professionals in industries from tech to finance to media, all of whom had serious (if often little-known) past lives as musicians. Almost all made a connection between their music training and their professional achievements.

The phenomenon extends beyond the math-music association. Strikingly, many high achievers told me music opened up the pathways to creative thinking. And their experiences suggest that music training sharpens other qualities: Collaboration. The ability to listen. A way of thinking that weaves together disparate ideas. The power to focus on the present and the future simultaneously.

Will your school music program turn your kid into a Paul Allen, the billionaire co-founder of Microsoft (guitar)? Or a Woody Allen (clarinet)? Probably not. These are singular achievers. But the way these and other visionaries I spoke to process music is intriguing. As is the way many of them apply music’s lessons of focus and discipline into new ways of thinking and communicating — even problem solving.

Look carefully and you’ll find musicians at the top of almost any industry. Woody Allen performs weekly with a jazz band. The television broadcaster Paula Zahn (cello) and the NBC chief White House correspondent Chuck Todd (French horn) attended college on music scholarships; NBC’s Andrea Mitchell trained to become a professional violinist. Both Microsoft’s Mr. Allen and the venture capitalist Roger McNamee have rock bands. Larry Page, a co-founder of Google, played saxophone in high school. Steven Spielberg is a clarinetist and son of a pianist. The former World Bank president James D. Wolfensohn has played cello at Carnegie Hall.

“It’s not a coincidence,” says Mr. Greenspan, who gave up jazz clarinet but still dabbles at the baby grand in his living room. “I can tell you as a statistician, the probability that that is mere chance is extremely small.” The cautious former Fed chief adds, “That’s all that you can judge about the facts. The crucial question is: why does that connection exist?”

Paul Allen offers an answer. He says music “reinforces your confidence in the ability to create.” Mr. Allen began playing the violin at age 7 and switched to the guitar as a teenager. Even in the early days of Microsoft, he would pick up his guitar at the end of marathon days of programming. The music was the emotional analog to his day job, with each channeling a different type of creative impulse. In both, he says, “something is pushing you to look beyond what currently exists and express yourself in a new way.”

Mr. Todd says there is a connection between years of practice and competition and what he calls the “drive for perfection.” The veteran advertising executive Steve Hayden credits his background as a cellist for his most famous work, the Apple “1984” commercial depicting rebellion against a dictator. “I was thinking of Stravinsky when I came up with that idea,” he says. He adds that his cello performance background helps him work collaboratively: “Ensemble playing trains you, quite literally, to play well with others, to know when to solo and when to follow.”

For many of the high achievers I spoke with, music functions as a “hidden language,” as Mr. Wolfensohn calls it, one that enhances the ability to connect disparate or even contradictory ideas. When he ran the World Bank, Mr. Wolfensohn traveled to more than 100 countries, often taking in local performances (and occasionally joining in on a borrowed cello), which helped him understand “the culture of people, as distinct from their balance sheet.”

It’s in that context that the much-discussed connection between math and music resonates most. Both are at heart modes of expression. Bruce Kovner, the founder of the hedge fund Caxton Associates and chairman of the board of Juilliard, says he sees similarities between his piano playing and investing strategy; as he says, both “relate to pattern recognition, and some people extend these paradigms across different senses.”

Mr. Kovner and the concert pianist Robert Taub both describe a sort of synesthesia — they perceive patterns in a three-dimensional way. Mr. Taub, who gained fame for his Beethoven recordings and has since founded a music software company, MuseAmi, says that when he performs, he can “visualize all of the notes and their interrelationships,” a skill that translates intellectually into making “multiple connections in multiple spheres.”

For others I spoke to, their passion for music is more notable than their talent. Woody Allen told me bluntly, “I’m not an accomplished musician. I get total traction from the fact that I’m in movies.”

Mr. Allen sees music as a diversion, unconnected to his day job. He likens himself to “a weekend tennis player who comes in once a week to play. I don’t have a particularly good ear at all or a particularly good sense of timing. In comedy, I’ve got a good instinct for rhythm. In music, I don’t, really.”

Still, he practices the clarinet at least half an hour every day, because wind players will lose their embouchure (mouth position) if they don’t: “If you want to play at all you have to practice. I have to practice every single day to be as bad as I am.” He performs regularly, even touring internationally with his New Orleans jazz band. “I never thought I would be playing in concert halls of the world to 5,000, 6,000 people,” he says. “I will say, quite unexpectedly, it enriched my life tremendously.”

Music provides balance, explains Mr. Wolfensohn, who began cello lessons as an adult. “You aren’t trying to win any races or be the leader of this or the leader of that. You’re enjoying it because of the satisfaction and joy you get out of music, which is totally unrelated to your professional status.”

For Roger McNamee, whose Elevation Partners is perhaps best known for its early investment in Facebook, “music and technology have converged,” he says. He became expert on Facebook by using it to promote his band, Moonalice, and now is focusing on video by live-streaming its concerts. He says musicians and top professionals share “the almost desperate need to dive deep.” This capacity to obsess seems to unite top performers in music and other fields.

Ms. Zahn remembers spending up to four hours a day “holed up in cramped practice rooms trying to master a phrase” on her cello. Mr. Todd, now 41, recounted in detail the solo audition at age 17 when he got the second-highest mark rather than the highest mark — though he still was principal horn in Florida’s All-State Orchestra.

“I’ve always believed the reason I’ve gotten ahead is by outworking other people,” he says. It’s a skill learned by “playing that solo one more time, working on that one little section one more time,” and it translates into “working on something over and over again, or double-checking or triple-checking.” He adds, “There’s nothing like music to teach you that eventually if you work hard enough, it does get better. You see the results.”

That’s an observation worth remembering at a time when music as a serious pursuit — and music education — is in decline in this country.

Consider the qualities these high achievers say music has sharpened: collaboration, creativity, discipline and the capacity to reconcile conflicting ideas. All are qualities notably absent from public life. Music may not make you a genius, or rich, or even a better person. But it helps train you to think differently, to process different points of view — and most important, to take pleasure in listening.