In “Ganjam” trumpeter-orchestrator-bandleader Randy Sandke has come up with the ultimate blindfold test item. First you hear exotic percussion of the kind that jazz orchestrators have traditionally used to depict the mysterious East. Then comes a polyphonic vamp underscored by a baritone saxophone that calls to mind Duke Ellington’s “Koko.” The alto saxophone passage that follows could only have been conceived in the modern or postmodern era. The way the solo horns chase each other around, first with clean breaks, then slightly overlapping, suggests the classically influenced Third Stream movement of the 1950s and ’60s.

Hearing it, an educated listener would come up with a variety of guesses. Ellington, in his later, more modern phase – perhaps a leftover track from “The Far East Suite”? Charles Mingus, in a vaguely Asian mode? Maybe a Hollywood hot-shot arranger like Andre Previn, trying to freak everyone out? Or some wiseguy Juilliard student attempting to stump the band with a concoction of neoclassical jazz modes? “Ganjam” actually is the last thing anyone would guess: a hitherto unknown composition by New Orleans jazz pioneer Jelly Roll Morton, as reinterpreted by a musician normally associated with early jazz.

The song appears on “Outside In” (Evening Star ES-110), one of four newly released CDs featuring Mr. Sandke with completely different bands. The others are “Trumpet After Dark” (Evening Star ES-109), which is subtitled “Jazz in a Meditative Mood” and features a string quartet; “Now and Again” (Arbors Jazz 19310), a set of duets, mostly on standards, with pianist Dick Hyman; and “The Mystic Trumpeter” (Evening Star ES-108), recorded with the Metatonal Band. Mr. Sandke will make an appearance with that last group this weekend at the Jazz Standard as part of the third annual Festival of New Trumpet Music.

“Outside In” spotlights the collective Mr. Sandke calls the Inside Out Band, which debuted in 2000 with another genre-spanning effort titled “Inside Out.” This gang of virtuosos is primarily supported by traditional jazz and swing fans but is thoroughly versed in the more modern schools.

The distinctive clarinetist Ken Peplowski, like Mr. Sandke, played in Benny Goodman’s last band. A few summers ago the bassist Greg Cohen played within a few weeks with both Woody Allen’s ultra-conservative Dixieland band and with the trio of free jazz iconoclast Ornette Coleman. Alto saxophonist Marty Ehrlich and pianist Uri Caine, both members of the contemporary downtown scene, make more than an occasional nod to earlier forms. And the Lincoln Center faction is represented by trombonist Wycliffe Gordon, who is especially eloquent in New Orleans, gospel, and blues.

Mr. Sandke has written compositions that do justice to many eras of jazz history at once. It was unavoidable that some of the music should seem a bit self-conscious (especially on Mr. Sandke’s “Mobius Trip”), but for the most part it’s both swinging and thought-provoking. Apart from “Ganjam,” the only non-original tune on “Outside In” is Ellington and Billy Strayhorn’s “Tonk.”

Mr. Sandke’s notes explain that this piece was originally inspired by a card game, which led to the idea of two musicians playing on the same instrument against each other. The famous original version was the most notable two-piano duet ever recorded by the two composers, but Mr. Sandke has revised it substantially for two clarinetists, Mr. Peplowski and Mr. Ehrlich. Even though one appears regularly at the 92nd Street Y and the other at Tonic, their intertwined duet shows they are more alike than different.

The multi-instrumentalist virtuoso Scott Robinson, who could probably play “Potato Head Blues” on a real potato, is a prominent voice throughout. He plays “optical theremin” (as opposed to a keyboard-operated theremin, I suppose) and something called “water pipe” on “Mobius Trip.” His baritone opens “Ganjam,” and on the second track he descends several octaves even deeper, on the leviathan-sized contrabass sax.

“Genesis 1,” like Ellington’s “In the Beginning, God,” offers a personal take on creation, using the lowest saxophone notes imaginable rather than the baritone male voice employed by Ellington. Mr. Sandke follows this with “Revelations 8:11,” a musical depiction of the apocalypse. Mr. Caine’s feature, “Raising Caine” has the pianist improvising a solo part against a prewritten background, and sounding halfway between Meade Lux Lewis trying to play free jazz and Cecil Taylor attempting to stride.

Finally, Mr. Ehrlich takes center stage on alto on “Two as One,” which makes another good blindfold test: Although Mr. Ehrlich’s supple tone is recognizably the same as on his own records, here he calls to mind the bubbly, boppish alto timbre of the late Oliver Nelson while also suggesting such sweet-toned swing players as Marshall Royal. He also holds forth on “Ornette Chop Suey,” an abstract collage of themes from the Hot Five. Think of this piece – and indeed this whole album – as a jazz answer to the Genesis/Revelations paradigm, contemplating the beginning and end of that particular evolution of the music that began with Louis Armstrong and ended with Ornette Coleman.