RED WING, MINN. — The most intimate relationship a musician may have is with a precious instrument. And when that relationship breaks down, an elite group of students here can fix it.

At Minnesota State College Southeast, about 85 students are learning to repair musical instruments. Most of them choose from among three specialties: band instruments, violins and guitars (whose students also learn to build guitars).

It’s a rare chance to learn these special skills. Only three schools in the country offer band instrument repair, according to school spokeswoman Katryn Conlin, and no other college offers violin repair. The rarity of the programs here attracts students to Red Wing from across the United States and Canada.

At age 18, Sarah Jensen of Clearfield, Utah, has already been working for several years in the instrument repair shop of her dad, who graduated from Red Wing in the 1990s. As she refurbished a tray of saxophone keys and pads, Jensen said she loves seeing the joy on people’s faces when they get their instruments back.

“I’m autistic,” she added, “and I think in certain ways. I like puzzles. For me, the saxophone is a 3-D jigsaw puzzle, and I love it.”

Michaela Alderink of Fairfax, Minn., had been working “a lot of not-fun jobs.” At age 33, she decided to enroll in the program after she opened her clarinet case from high school one day.

When she got a whiff of the wood and leather and metal inside, Alderink said, “I realized that I could be surrounded by this smell the rest of my life.”

Many of the students are musicians; some have advanced degrees in performance and have played professionally. But musicians often have to cobble together a living. Learning repair skills can be a welcome addition to income from playing and teaching.

John Maddox, a trombonist and instructor in band instrument repair, graduated from Red Wing in 2012 and began teaching here two years ago. Repairing an instrument, he said, is almost a sacred trust.

“You take a musician who has a 30-year relationship with their instrument,” Maddox said. “They may have spent more time with that instrument than they have with their children.

“So it’s not like repairing someone’s car. This is their voice. This is how they express themselves to the world.”

The repair shops are a sensory delight, filled with shiny brass and lustrous wood, with students tapping, pounding and scraping. The soundtrack is the scratch of emery paper, the soft hiss of a knife on a whetstone, the quick “whuff” of a lighted blowtorch.

Most students stay in the program for a year and receive a diploma in repair. Some stay for two years and earn an associate degree in applied science. Either way, few of them are likely to have any trouble finding work.

“If they want a job, they can definitely get one,” said Steve Rossow, who teaches violin repair.

Alex Kauffman of Detroit Lakes was working as a FedEx driver in Fargo before enrolling here. He’s already spent two years learning to build and repair guitars and is now studying violin repair.

“I’m not much of a musician,” said Kauffman, 30, as he reamed out holes for violin pegs. “I come to this not from the music side but from the craft side. I love working with wood.”

It’s an endlessly fascinating pursuit, said John Huth, a trumpeter and band instrument repair instructor.

“Each of us could work anywhere and probably make more dough,” he said. “But it’s the students. I just love teaching.

“And it’s a subject where you can never learn enough.”