Alessi has a sense of rhythm: His own

Dizzy Gillespie wanted to shake jazz up around 1945; Ralph Alessi wants to again. Gillespie delivered his message like a comic; Alessi does it like a scientist.

The austere mood at Disney Hall’s compact REDCAT auditorium Saturday night was far from St. Patrick’s Day revelry, as New York trumpeter Alessi renewed his association with CalArts (“the best school in the world” was one of his few utterances) in a quietly triumphant return to Los Angeles.

Alessi and two members of his This Against That quintet -- tenor saxist Ravi Coltrane and pianist Andy Milne -- are also graduates of saxist Steve Coleman’s groundbreaking ensembles, and that association reflects in their complex, intellectual schematics, which yet retain the slightest whiff of Gillespie’s bebop.

Dressed simply, attitudes serious as they read from music stands, the five laid out Alessi’s compositions with sensitivity and precision. The central tenet of Alessi’s method is the way he relocates the rhythms -- no walking patterns or tick-a-booms from bassist Ben Street or drummer Gerald Cleaver. Street established the strongest reference with off-center riff repetitions; Cleaver shooed the energy forward with omnidirectional flicks of his brushes.

The group pulse, often in unusual meters, coalesced from accents of all the musicians in quick succession, and they pulled off that trick with seeming ease despite the enormous concentration required. Alessi’s approach to harmony is unusual too: High forehead and sharp features emphasizing the severity of his concepts, he often blew lines that conflicted harshly with those of the sax or piano, then entered into perfect unison, finally settling on a long note held in shivering parallel to Coltrane’s, maybe a quarter-tone apart to illustrate the arbitrary nature of what we consider correct.

Still, beauty reigned -- in Alessi’s soft-featured tone and occasional romanticism; in Coltrane’s rounded attack and untethered imagination; in Milne’s touch, like finger painting on a balloon, and the way he sometimes reached inside the piano to shape the timbre of a note. In the prodding, yearning “Hands,” from This Against That’s current “Look” CD, Alessi even owns a lovely melody playable within the bastard realms of radio.

At second set’s end, the audience -- no common audience, to be sure -- rose applauding to its feet.