A reserved, professorial figure, Jimmy Giuffre (pronounced “Joo-free”) was a restless musician whose unorthodox career encompassed the big band era, lyrical folk-jazz, the avant-garde and — late in life — the more tasteful end of the jazz-rock spectrum. Although he enjoyed little commercial success after the 1950s, he commanded the unwavering respect of musicians and critics.

James Peter Giuffre’s first instrument was the clarinet, which he began playing in a YMCA band at the age of 9. As a teenager, Giuffre took up the tenor saxophone and later earned a bachelors degree in music from North Texas State Teachers College. After military service he began playing professionally and made his first recording at the relatively advanced age of 26.

During a brief stint with the Jimmy Dorsey band, he found time to sit in with an unorthodox eight-piece group that featured fellow saxophonists Stan Getz, Zoot Sims and Herbie Steward. The four men were soon signed up by Woody Herman — Giuffre purely as an arranger at first — and the result was Giuffre’s supple, reeds-based jazz standard, Four Brothers, a staple of the big band repertoire.

He later worked with Buddy Rich before becoming a regular participant in the jam sessions at the Lighthouse Café on Hermosa Beach, Los Angeles, crucible of the so-called West Coast school. Like many of the circle that formed around the trumpeter, Shorty Rogers, Giuffre sought to broaden the scope of jazz with the use of classical forms. He was particularly drawn to contrapuntal techniques, and in 1956 — partly inspired by the sonorities of a Debussy sonata for flute, viola and harp — he formed the first of a series of drummer-less and piano-less trios, with personnel including the guitarist, Jim Hall, and the trombonist, Bob Brookmeyer.

As he had declared earlier, his aim was to create “jazz with a non-pulsating beat”. He explained: “I’ve come to feel increasingly inhibited and frustrated by the insistent pounding of the rhythm section. With it, it’s impossible for the listener to hear the horn’s true sound, I’ve come to believe, or fully concentrate on the solo line. The essence of jazz is in the phrasing and notes, and these needn’t change when the beat is silent.”

He concentrated increasingly on the clarinet in this period, developing a smouldering, dulcet tone as he explored the depths of the chalumeau register (the chalumeau is an ancestor of the clarinet). On hearing that Giuffre would be teaching a summer school at Lenox, Massachusetts, the renowned French critic André Hodeir is said to have joked: “Who will be teaching the upper register?” At times Giuffre’s work — like so much West Coast jazz — could be self-conscious and bloodless. At its best, however, it was wholly original and beyond categorisation.

The 1956 Atlantic album The Jimmy Giuffre Clarinet gave full rein to his arranging skills and his taste for unorthodox instrumentation (some of the pieces featured the bassoon, oboe, bass flute and the celeste). But the most striking piece, perhaps, was the simplest: Giuffre playing a leisurely, blues-drenched clarinet solo, accompanied only by the tapping of his foot, as if he were sitting on a moonlit porch.

Another Atlantic album, The Jimmy Giuffre 3, contained what was to remain his most striking composition The Train and the River — a sprightly tune written after he had befriended the folk singer Cisco Houston. Giuffre’s performance of the piece at the 1958 Newport Jazz Festival remains one of the highlights of Bert Stern’s classic documentary film, Jazz on a Summer’s Day.

Giuffre composed a number of large-scale orchestral works that were recorded by the conductor and composer Gunther Schuller. Another change of direction — inspired in part by the tempestuous music of Ornette Coleman — led to the formation of a trio with Paul Bley on piano and Steve Swallow on double bass. Leaning increasingly towards atonalism, the austere improvisations on the Verve albums Thesis and Fusion won some admirers in avant-garde circles, but alienated the bulk of Giuffre’s mainstream audience. As he plunged ever deeper into the arcane realm of free jazz he virtually disappeared from view. Another trio album Free Fall did equally badly. From this point Giuffre concentrated on teaching at institutions such as the New School for Jazz and Contemporary Music, New York, while playing occasional club dates.

In 1978 he took up a post at the New England Conservatory. During the next decade he re-emerged with a highly accessible electric quartet that produced superbly textured soundscapes, with none of the high-volume bombast that is usually a byproduct of the fusion genre. The group made several accomplished albums on the Soul Note label, among them Quasar, Liquid Dancers and Dragonfly.

Seemingly reborn and playing a multitude of reed instruments, Giuffre toured Britain on a number of occasions (although even at this late stage,many concert promoters still did not know how to spell his name on posters). In 1992 he returned on tour after being reunited with Swallow and Bley, in order to promote a reissue of Thesis and Fusion. Their subsequent recordings, Fly Away Little Bird and Conversations with a Goose won enthusiastic reviews.

Giuffre, who had been suffering from Parkinson’s disease, retired from teaching in 1996. He leaves a widow, Juanita.

Jimmy Giuffre, jazz clarinettist, saxophonist and composer, was born on April 26, 1921. He died on April 24, 2008, aged 86