‘It was always a good day when you ran into Don,” the trumpeter Steven Bernstein said as he began his set at the Jazz Standard on Saturday.

Amen to that. Don Cherry, who left us much too young at the age of 59 in 1995, was the most approachable of jazz icons. When he wasn’t off playing in the plains of Africa or the mountains of Tibet, Cherry could usually be found on the steps of a brownstone in the East Village, hanging with local characters and imparting lessons of music and life to young players. This year, which would have marked his 70th birthday, Cherry is the central figure in the Fourth Annual Festival of New Trumpet Music (FONT), which continues throughout October in a variety of venues across the city.

The young Cherry was best known as Ornette Coleman’s most important co-conspirator in the first wave of the free jazz revolution, and he also served as Mr. Coleman’s deputy in key recordings by John Coltrane and Sonny Rollins. Later, Cherry pursued an interest in world music, but from the beginning he was also keenly interested in channeling the energy of the new music into extended compositions like “Complete Communion” (1965), “Symphony for Improvisers” (of 1966, which was played a week earlier by Dave Douglas at Merkin Hall), and “Relativity Suite” (1973).

Last weekend, FONT presented two onenight programs of Cherry’s music as played by three different trumpeters in two very different ensembles. On Saturday, Mr. Bernstein and his nine-piece Millennial Territory Orchestra played the “Relativity Suite”; on Sunday, Dave Douglas and Graham Haynes assembled a set of Cherry compositions for smaller ensembles from a more than 30-year period. Interestingly, the three trumpeters played several variations on the horn — Mr. Bernstein played both the slide and the standard valve instrument, while both Messrs. Douglas and Haynes played cornets — but no one thought to play the diminutive pocket trumpet, the horn most associated with Cherry.

On Sunday, Messrs. Douglas and Haynes were accompanied by the younger tenor J.D. Allen and two veteran rhythm players who both worked with Cherry: the bassist Henry Grimes and the drummer Andrew Cyrille. They began with “Awake Nu” from “Where Is Brooklyn?,” a 1966 album featuring Mr. Grimes. Playing arco, the bassist was the principal soloist in the second piece, “Living Streams,” an original by Mr. Douglas inspired by Cherry, with a dirge like melody that felt like a kaddish, or prayer for the dead.

“Cherryco” was a memorable melody written by Cherry for his 1960 meeting with Coltrane; in those early days of free jazz they still played tempered notes in countable meter. The 1988 “Art Deco” found Cherry looking back, not only to the beginnings of free jazz but to his youth in the 1930s, and was played in something like a swing style by Mr. Haynes using a tight harmon mute. Catchier still was “Mopti,” a slice of Africana written for the band “Old and New Dreams” (on which Cherry originally played piano), which ended with the quintet humming the theme in a Ladysmith Black Mambazo fashion. The show concluded with an excerpt from “Elephantasy,” the second half of “Complete Communion.”

The original cover of “Relativity Suite” — one of the more important jazz LPs not yet reissued on CD — shows a quilt depicting various cultural and religious symbols, which probably indicates that the music therein is a patchwork of different styles and approaches, from European marches to Asian interludes. The suite was commissioned by the Jazz Composer’s Orchestra in 1970 and recorded with an all-star edition of that band three years later. Normally, the Millennial Territory Orchestra performs gonzo versions of old jazz standards, but this time Mr. Bernstein reversed his approach, presenting a more coherent, better-organized version of what was originally a sprawling epic.

Like later postmodern suites, “Relativity Suite” begins with a melodic idea gradually coming into focus, realizing itself in a tenor solo originally played by the late Frank Lowe and here by Tony Malaby. The central tune first takes the shape of something like a ballad but eventually develops into a funk riff. Mr. Bernstein assumed Cherry’s role in a blues section, in which he led the rest of the band in a call and response episode playing slide trumpet. Mr. Bernstein made several instrumental substitutions, giving a prominent role to the clarinetist Doug Wiselman and the baritone saxist Erik Lawrence (more or less assuming alto saxist Carlos Ward’s role on the record), and, cleverly, having the guitarist Matt Munisteri replicate on banjo the Japanese instruments employed by Cherry.

“Relativity” — whose title apparently means that all these musics are related — ends with a percussion feature. The drum solo (played by Ed Blackwell in 1973 and Ben Perowsky here) is framed by a vaguely Scottish-sounding drone; perhaps the Anglo reference suggested the fiction of J. R. R. Tolkien to the composer, who titled this ending section “The March of the Hobbits.” Like “Lord of the Rings,” this ambitious work seemingly takes forever to get going and then to stop, but the middle is glorious.