It was just about two weeks ago that the St. Lawrence String Quartet was here, stirring up excitement at Hill Auditorium in an “American Mavericks” concert with the San Francisco Symphony.

Thursday evening, the group returned again under University Musical Society auspices, this time to Rackham Auditorium. Though the concert program was identical to one the group was to have played here this fall and had to cancel, the proximity to the San Francisco gig—which featured John Adams’ new “Absolute Jest”—gave the core of Thursday’s concert a decidedly “American Mavericks, Part the Second” cast.

Only this time around, the mavericks were North American (Canadian R. Murray Shafer) and South American (Argentinian Osvaldo Golijov).

Even with two Haydn quartets bookending the concert, the evening had the incredible energy, and sense of informality, of the San Francisco concerts, abetted by violinist Geoff Nuttall’s off-the-cuff commentary on each piece, much in the mode of conductor Michael Tilson Thomas. All Nuttall had to do was to suggest that folks might like to come up on stage at intermission to take a gander at the Schafer score—most definitely not your standard string quartet—for half the house to clump up on stage to peer at the notation.

But the excitement started with the opening Haydn, Op. 74, No. 1, in C Major. It’s a great quartet, but what made it extraordinary was the playing by Nuttall, in the first violin chair; Scott St. John, second violin; Lesley Robertson, viola; and Christopher Costanza, cello.

All the quartet’s delicious, bumptious rusticity came through in the group’s peasant-sturdy rhythms, the body English on the accents and syncopations and the rough-hewn, hearty tone. The clarity of the voices matched the clarity of the group’s intent, and if an audience member chimed in a bit early with final applause - in the manner of a singer mistakenly intoning the last “Hallelujah” on the big rest before the final push in the most famous chorus of Handel’s “Messiah,” it seemed only appropriate given the energy on stage. Nuttall made a point of endorsing it when he came onstage to introduce the Schafer piece, which was next up.

It was truly time for something completely different in Schafer’s String Quartet No. 3, from 1981. Nuttall clued the audience in, with comments about Schafer’s interest in the spatial qualities of the music; his interest in dissonance; and his commitment to adding a dose of levity to the dead-seriousness with which mid-20th-century composers approached their work.

All that is indeed there in the quartet, but there is also eerie beauty: in the repeated notes of the extended first cello solo, magnificently played by Costanza; in the way the viola responds to the last dying note of that solo; and in the slow entrances of the violins and viola—literal entrances, since they approach from the the hall from backstage (viola) and the back of the hall (the two violins) to join Costanza, who begins the piece literally alone.

The first movement is a sort of mating dance: Costanza’s solo seems to summon his musical partners to the stage for an entwining tryst. The second movement is wild, a sort of war chant, filled with whoops and hollers from the players that seem causative of the sounds issuing from their instruments. Or maybe it’s the other way ‘round. In any case, it’s hilarious and exhilarating, a series of battles that bristle and wane, ebbing at one point into a sort of punch-drunk, woozy waltz. The final movement, like the first, is slow, a retrograde of the first, in a way. Nuttall leaves the stage playing a four-note figure that diminishes at first to a three-note figure before settling into ever-quieter reiterations as he gets more distant from the three players left on stage. As for them, it’s silence that overtakes them.

After intermission, it was time for something really new, though. In fact, the Golijov, long delayed, is still not really finished. Or maybe it is: no one, Nuttall said, really knows whether Golijov will write the third movement, the one that would embody the ideas that led him to title the work “Kohelet,” or Ecclesiastes.

Of the two movements extant (since late 2011), it’s the first that is the grabber, with St. John, in the first violin chair, intoning a high, long-limbed melody over a thrumming accompaniment by the rest of the quartet. It’s like clouds moving across the sky as seen from the ground. The second movement was harder to stick with; there’s something very static about it, even as it alternates between misty passages and flurries of excitement. I found myself drifting—like the clouds that seemed so compelling in the first movement.

But the final Haydn quartet, Op. 76, No. 2 in d minor (“Quinten”) was riveting enough. Here again, the players found the right sound for this particular Haydn: cheerful, light-filled, buoyant. And as in the opening Haydn, there was never any doubt about where the peak of the phrase was, where the music was heading or where the joke or slyness lay.

As an encore, there was more Haydn, the 2nd of the adagios from the “Seven Last Words of Christ on the Cross,” arranged for string quartet. It’s a meditation on “Verily, I say unto you, today shalt thou be with me in paradise.” That’s where the music, and indeed, the whole concert led Thursday evening.