Where modern jazz in the Parker mold, better known as bebop, tended to be passionate and virtuosic, Mr. Konitz’s improvisations were measured and understated, more thoughtful than heated.

“I knew and loved Charlie Parker and copied his bebop solos like everyone else,” Mr. Konitz told The Wall Street Journal in 2013. “But I didn’t want to sound like him. So I used almost no vibrato and played mostly in the higher register. That’s the heart of my sound.”

Although some musicians and critics dismissed Mr. Konitz’s style as overly cerebral and lacking in emotion, it proved influential in the development of the so-called cool school. But while cool jazz, essentially a less heated variation on bebop, was popular for several years — and some of its exponents, notably the baritone saxophonist Gerry Mulligan and the trumpeter and singer Chet Baker, both of whom he sometimes worked with, became stars — Mr. Konitz for most of his career was a musician’s musician, admired by his peers and jazz aficionados but little known to the general public.

This was in part because of his personality: An introvert by nature, he was never entirely comfortable in the spotlight. And it was in part because of his musical philosophy, which valued spontaneity above all else and often led him to pursue daring improvisational tangents that could leave his less adventurous listeners feeling a little lost. (His way of preparing for a performance, he once said, was “to not be prepared.”)

“My playing was about making a personal statement — getting audiences to pay attention to what I was saying musically rather than giving them what they wanted to hear, which is entertainment,” he said in the 2013 interview, referring to his early struggles to find an audience. “I wanted to play original music.”