Sometimes, the most important musicians are the ones farthest away from the spotlight.

Laurie Frink was a great trumpet player. Great enough to tour with jazz big bands led by Benny Goodman, Gerry Mulligan (where she played lead) and Maria Schneider; to be one of the first female trumpet players on the Broadway pit orchestra circuit in New York. As a freelancer, she was known for her ability to execute just about anything, no matter the level of difficulty.

Jazz trumpeter John McNeil first met Frink decades ago in a rock club. A week later, she showed up to a big band rehearsal he was attending.

"What she did, just for entertainment: She proceeded to play some of the warhorses of classical trumpet literature, like the Hummel Concerto and some of these others that everybody knows," McNeil says. "But she played them at light speed. It was the funniest thing I ever heard in my life — it sounded like a wind-up toy, or something played like a 33 [RPM vinyl] disc played on 78 [RPM], you know? It was hilarious — it sounded like a chipmunk playing trumpet. ... But I started thinking to myself as she's doing that, 'Yeah, that's pretty funny, but Jesus Christ, she's actually able to do that.'"

Though rarely an enthusiastic bandleader, Frink made a lot of bands sound good. But she was better known as someone who made a lot of other brass players sound better.

For the last 25-odd years, Laurie Frink was the go-to brass instructor in New York City, especially for improvising musicians. In addition to her private studio and online video-chat lessons, she was on faculty at three New York City universities — NYU, the New School, Manhattan School of Music — and the New England Conservatory. She attracted students from around the world.

Her method came from Carmine Caruso, a famedbrass guru and one of her own teachers. Caruso was a saxophonist by trade, but his particular method of technique exercises, paired with personable coaching, made him a revered instructor. After Caruso, she started teaching more heavily, based on his method.

This meant she worked personally with students on how to practice, often designing custom exercises with her students based on their goals. She would go so far as to regularly attend her students' gigs in order to better understand specifically what they wanted to work on. Those students included many of the top jazz musicians in New York — players like Dave Douglas.

"Technique, people think of as being something really cold," Douglas says. "And there was something very warm about the way Laurie understood how to talk to people. Some people refer to her as their 'trumpet mother,' because a session with her was part psychotherapy, part cheering section and part, 'Let's figure out the trumpet.'"

On the morning he was recording his second album with the Tiny Bell Trio, Douglas was having issues with his "chops" — his ability to execute. He was in Zurich, Switzerland, and placed a desperate call to Frink in New York.

"It must have been 6 in the morning in New York," Douglas says. "I left a message on her machine. I just said, 'This is crazy, but I'm in Zurich, and here's what's happening, and I'm really freaking out. Here's the hotel number, and if you happen to get the chance to call me, I'll be here for another hour or so.' This is before cell phones.

"Sure enough, the phone rings in 15 minutes. And I'm like, 'Oh, thank you so much for calling!' She goes, 'Shut up, put the phone down, and play this for me.' So I play it, and I pick up the phone, and she goes, "OK, now play this.' I play it, pick the phone back up, and she says, "OK, I've got three exercises for you. You got a pencil and paper?' So I wrote down the exercises, did 'em and you can listen to the record. ... She saved me."

With fellow Caruso student John McNeil, Frink wrote Flexus, a book of "trumpet calisthenics" designed to improve physical facility specifically for improvisers. This came about after she helped McNeil completely relearn how to play the instrument — twice — when a degenerative disease left him with limited muscle control.

"If it weren't for her teaching me how to be as efficient as possible, I wouldn't be playing today," McNeil says. "Absolutely not — I just wouldn't be able to."

Thousands of musicians sing her praises. "R.I.P MS Laurie Frink - changed my life !!" posted trumpeter Ambrose Akinmusire on Twitter. In a heartfelt essay, another trumpeter, Nadje Noordhuis, reflected on Frink's friendship and inspiration.

One time, I wrote that I was having a bad day. Within half an hour, she had emailed me a picture of herself in a hilarious costume. It was so unbelievably funny that I laughed uncontrollably for about half an hour. I'm laughing through my tears right now just thinking of it.

Though Frink dedicated her career to serving others without expectation of recognition, the Festival of New Trumpet Music, a nonprofit group which puts on trumpet-led concerts, feted her with a lifetime achievement award last year. Her student Jon Crowley wrote about the experience.

She sat in the back, uncomfortable with being the center of attention. ... There was a great photo montage of her giving the middle finger to the camera in various places, her sense of humor was another reason we all loved her. She got up at the very end when she was finally forced to talk and just said "This has been great, it's like being able to attend your own funeral and hear all the nice things people say about you!" It was a good night for close friends to thank Laurie for what she's given to us and for her friendship. I know it meant a lot to her.

Crowley never got to see her again. Laurie Frink died July 13 from lingering complications of bile duct cancer, according to her longtime partner Lois Martin. She was 62.

But for Crowley and other brass players, she remains with them in spirit. Long after her lessons, many of her students still do the exercises she designed specifically for them every day.

SeparatorLaurie Frink on NPR Music: