When tenor saxophonist Joshua Redman made his initial national splash in the late 1980s, winning the Thelonious Monk Saxophone Competition, he was a thoughtful, articulate and humble 22-year-old eager to learn everything he could as a novice in the big leagues. The product of a network of active, committed music-education programs in Berkeley, Redman subsequently developed into a blue-chip soloist and bandleader. It’s notoriously difficult to make a living playing jazz, but Redman’s single-mindedness kept him from becoming a jazz casualty.

Trumpeter Ambrose Akinmusire has a similarly impressive skill set, his fierce determination tempered with humility. He also attended the same high school as Redman — which has led jazz enthusiasts to wonder just what’s in that Berkeley water.

Angelenos will get a taste on Friday night, when the Ambrose Akinmusire Quartet makes an infrequent SoCal appearance at the New Roads School’s Moss Theatre, part of the Jazz Bakery’s peripatetic Movable Feast series.

Los Angeles occupies a special place in the 35-year-old trumpeter’s development. In 2007 Akinmusire took the honors at the Monk Institute’s trumpet competition, held at UCLA’s Schoenberg Hall. As part of his recital, Akinmusire played a lament for his recently departed grandmother that, while not blues per se, channeled the feeling and essence of blues through his instrument’s emotional expression. It was an impressive display from a young player.

Akinmusire’s preparation for that competition revealed a formidable mental toughness: He worked incessantly on the horn, hit the gym, meditated, read The Art of War and familiarized himself with the available recordings of members of the competition’s house band, led by pianist Geoff Keezer.

When it came time to hit, Akinimusire took the advice of New York trumpeter Avishai Cohen: Treat it like a performance and just make music. The trumpeter didn’t use his time in the spotlight to work out like an Olympic acrobat but instead concentrated on blending with the rhythm section — a rare occurrence in the contrived setting of a musical tournament.

Instead of looking for a record deal after his win, Akinmusire followed the path of apprenticeship. He played in the bands of saxophonists Joe Henderson and Steve Coleman, pianist Vijay Iyer and drum master Billy Higgins.

Now we can hear the result of that distillation process. Akinmusire’s own quartet recently released a live double album, A Rift in Decorum (Blue Note), that’s full of surprises. The forms meander and elongate, or sometimes lock in and repeat with changes in dynamics and tempo. The quartet works as an ensemble, rather than a rhythm section that supports a soloist. And its members are not afraid to let a piece end elliptically, rather than with a resounding conclusion.

From Armstrong and Gillespie to Hubbard and beyond, jazz has a tradition of trumpeters as fast guns. But as Walter Brennan’s character in Rio Bravo might have said about Akinmusire: “He ain’t like the usual kid with a gun.” His trumpet tramples bar lines and phrases in unusual ways. He prefers middle dynamics so that when he hits a note or chord hard, it’s almost a jolt. Akinmusire often improvises conversationally, and the intrigue lies in where those soliloquies go. His array of sounds — from smears to blurts to squirrelly asides — recalls individualists like Booker Little and Bobby Bradford.

From his home in San Francisco, the soft-spoken and thoughtful Akinmusire sums up his musical mission: “It’s to keep going forward and avoid getting stagnant — and never give up. My personal mission is to heal people, to make them comfortable to present all sides of themselves, and to bring about honest reactions.”Lest you think he’s an overly precious player, listen to the trumpet-and-drums dialogue on the crackling “Trumpet Sketch (milky pete).” Justin Brown busily erects a drum labyrinth, insistent and full of sharp edges. Akinmusire engages him mano a mano, firing back, taking his lumps and even offering a long, held accompanying tone. The level of ensemble engagement in this outfit is striking.

Let the healing begin at the Moss on Friday.

The Ambrose Akinmusire Quartet performs at the New Roads School’s Moss Theatre on Friday, June 16.