Nat Adderley may have spent a significant part of his career in the shadow of his better known older brother, the alto saxophonist Julian 'Cannonball' Adderley, but he was always a major contributor to their shared projects, and achieved a great deal in his own right after his brother's death in 1975.

He was born Nathaniel Adderley, and took up trumpet as a teenager in 1946. He began playing in local bands in Florida, and made what became a career long switch to the smaller cornet in 1950. He did so against the prevailing tide. Cornet had been the horn of choice for New Orleans trumpet players in the early days of jazz, but had fallen out of fashion in favour of trumpet by the bop era.

Adderley evolved a distinctive signature on the instrument, blending a rich tone and earthy warmth with the horn's inherent touch of astringency to great effect. He played in an army band for a time during his military service from 1951-3, then joined the band led by vibraphonist Lionel Hampton in 1954, his first association with an established jazz figure. He remained with Hampton until 1955, and cut his earliest recordings for the Savoy and EmArcy labels that same year.

Cannonball Adderley had made an early mark in New York when he sat in with bassist Oscar Pettiford at the Cafe Bohemia in Greenwich Village in 1955, but that did not translate into immediate success when the brothers joined forces in Cannonball's Quintet the following year. He broke up the group in 1957, and Nat worked with trombonist J. J. Johnson and bandleader Woody Herman before reuniting with his brother in 1959.

The earlier lack of success quickly evaporated. The band's funky, gospel-tinged jazz became one of the most successful sounds on the hard bop and soul jazz circuit, and they even scored an unexpected chart hit with 'Mercy, Mercy, Mercy' in 1966. Cannonball had featured alongside John Coltrane in Miles Davis's classic Sextet which made the legendary Kind of Blue album in 1959, and that association provided the boost he needed to take off as a star in his own right, with the cornetist very much his right hand man.

Nat had continued to record under his own leadership, and made his most famous record for the Riverside label in January, 1960, with a band which featured guitarist Wes Montgomery. The resulting album, Work Song , included the tune which remains his best known composition, 'The Work Song'. Its bluesy call-and-response chorus was an emblematic example of the hard bop style of the period, and is still widely played.

It became a mainstay of the Adderley's as well as the hard bop repertoire, but was not the only composition by the cornetist to do so. His significant contributions as a composer also include widely performed tunes like 'Jive Samba', 'Hummin'', 'Sermonette', and 'The Old Country'.

His role as a soloist was no less significant, and he was equally adept at uptempo hard bop excursions and richly delineated ballads. Miles Davis had been an early influence on his style, but he developed a highly individual and very expressive voice of his own, which included a sparing but effective use of the very low registers of the horn.

Nat remained a central part of his brother's various projects until the saxophonist's unexpected and premature death from a stroke in 1975. Their collaboration included an ambitious but very uneven "folk musical" based on the tale of the mythical black hero figure, John Henry, with lyrics by Diane Lampert and Peter Farrow. It was released on record as Big Man (Fantasy) in 1975, with the late Joe Williams singing the title role, and soul diva Randy Crawford making her recording debut as Big John's woman, Carolina.

A concert performance was given at Carnegie Hall the following year as a tribute to the saxophonist, and a full theatrical production under the title Shout Up A Morning was eventually staged at the Kennedy Centre for the Performing Arts in Washington and the La Jolla Playhouse in California in 1986.

The cornetist had formed his own band shortly before his brother's death, and he continued to lead it until 1997, when his right leg was amputated following complications from diabetes, which would eventually lead to his death.

Bassist Walter Booker was a virtual ever-present in the band, but Adderley was equally open to the younger generation of players, and featured the likes of pianist Rob Bargad and alto saxophonist Vincent Herring for extended periods. He was appointed artist in residence to the faculty of Florida Southern College in 1996, and was inducted into the Jazz Hall of Fame in Kansas City in 1997.

If he made his classic contributions to the music in the early 60s, he remained a highly resourceful and always musical performer throughout his long career, and left a rich recorded legacy in his many albums with his brother, under his own leadership, and as a sideman.

His son, Nat Adderley, Jr, is also a musician. He is also survived by his wife, Ann; his daughter, Alison; and five grandchildren.