It’s been an Ornette Coleman kind of week. On Tuesday, the SF Jazz Collective, led by Joshua Redman, began a three-night run at Zankel Hall with a program pegged to Mr. Coleman’s music, which included an aggressive and thoughtful octet based on Coleman classics like “Peace” and “Una Muy Bonita.” On Wednesday at Birdland, the pianist Dado Maroni opened the second night of the Top Italian Jazz series with Mr. Coleman’s “When Will the Blues Leave?” imaginatively re-harmonized into something like a bebop blues.

But the big event of the week, Ornette-wise and otherwise, is a six-day celebration of guitarist James “Blood” Ulmer, a longtime Coleman collaborator. The South Carolina-born guitarist first played professionally in blues and funk bands, and came to the attention of the jazz world playing alongside the organist Big John Patton in 1969. Mr. Ulmer played with Mr. Coleman in Prime Time and other electric bands of the 1970s and ’80s, and Mr. Coleman paid him the rare honor of appearing as a sideman on Mr. Ulmer’s second album, 1978’s “Tales of Captain Black.”

Mr. Ulmer, 63, acknowledges the ongoing inspiration of Mr. Coleman and the so-called “harmolodic music system” the great saxophonist worked out in the ’70s. Everyone who attempts to define “harmolodics” comes up with a different answer; the best I’ve heard is that it’s a diatonic system involving whole tone rows and an absence of accidentals, which also allows different players to solo and improvise simultaneously, hitting the same notes in different keys. Put simply, it’s an extension of the style Mr. Coleman earlier referred to as free jazz.

On Wednesday night, Mr. Ulmer performed with Odyssey the Band, the trio he put together for the celebrated “Odyssey” album in 1983. Odyssey the Band is Mr. Ulmer on guitar and occasional vocals, Charles Burnham on electric violin, and Warren Benbow, drums. The group recently released a new album – only its second – titled “Back in Time” (Pi Recordings 18).

Odyssey the Band plays a kind of futuristic roots music that might be described as “free blues.” The threesome draws on the total palette of the blues and its descendants and antecedents: its roots in African rhythms and the pentatonic scales of traditional Spanish music and Celtic music; its migration up from the Mississippi Delta through the country and folk regions of the South and Midwest; the echoes of Appalachia, of the Louisiana swamps, and of the Texas plains that inspired Mr. Coleman; its adoption by electric Chicago players like Muddy Waters and Lightnin’ Hopkins; its absorption into mainstream pop; and its role in the psychedelic rock of Jimi Hendrix.

Mr. Ulmer absorbs these influences in a distinctly nonlinear fashion, spinning them back at us all at once. He even plays some longish, distorted solos that would please heavy-metal fans.

On a blindfold test, Odyssey the Band sounds like it includes two electric guitarists. Mr. Burnham reproduces the sound and sensibility of a guitar on his violin, which he processes with a wah-wah pedal to get an anguished, vocalized tone. Both string players use the distortions associated with electric instruments and turn them into an alternate universe of sound – kind of a science-fiction approach to the blues. The guitar and violin duo was one of the signature sounds of pre-war jazz, but Mr. Burnham has nothing in common with any jazz violinist you’ve ever heard.

Any description of this music risks making it sound cerebral and inaccessible, but it’s just the opposite. On the new album in particular, Odyssey’s music is driven by short tracks and direct, catchy melodies. Rhythmically, the band plays everything from slow, erotic, grinds to fast, peppy marches like “Water Tree,” a multi-culti square dance that fits Gary Giddins’s term, “harmolodic hoedown.”

The trio also specializes in tension and release and frequent exchanges between the two string players, in which they play both with each other and against each other. They vary between loud and soft and passages that are unspeakably dense and heavy with electronic profundity, and others in which Mr. Ulmer will play a few light riffs surrounded by long stretches of empty bars.

The last two pieces on Wednesday night gave a clear sense of the band’s direction. “Let’s Get Married,” on which Mr. Ulmer sings, is a fundamental blues that could have been played by Robert Johnson. Mr. Benbow’s composition “Free for Three” is a free-form piece that, like much Ornette-influenced music, seems to be going everyplace at once, and also to be there already.

Mr. Ulmer will perform with his Memphis Blood band March 31 & April 1, and he’ll play a solo show April 2 at the Jazz Standard (116 E. 27th Street, 212-576-2232).