The Yo La Tengo concert on Sept. 13 at the State Theatre felt like two concerts in one. The three-hour show had no opening act and was divided into two very distinct sections. The first was a quiet and gentle acoustic set; the next, a loud, electric-rock set. It was hard to believe the two sets were performed by the same indie-rock trio, but they both showcased the members’ vocal harmonies and excellent playing.

The band, formed in Hoboken, N.J., in 1984, consists of guitarist Ira Kaplan, drummer Georgia Hubley and bassist James McNew. This concert showcased the band’s astonishing versatility, ranging from soft, hazy dream-pop to noise rock.

Yo La Tengo began the show with an acoustic version of “Ohm,” the first track on its latest album, “Fade.” The band was deeply focused, and the chemistry between the musicians was immediately apparent. Between the longevity of their career together and an excellent meshing of styles, the bandmates seemed like they were meant to play together. Two members always formed the rhythmic foundation that allowed the third to add embellishment.

Generally, Kaplan led the beat of the song, with Hubley and McNew acting as the rhythm but occasionally taking the lead as well. The three musicians played side by side at the front of the stage, with orange and red lights overhead casting a warm glow upon them. After a few more songs in the slow, atmospheric style, the players took some time to address the audience.

“We’re gonna play quietly for a little bit,” Kaplan said. “And then we’re going to come back and play loud.”

After half an hour of soft music, it was hard to believe this band was capable of playing loudly.

Kaplan showcased his acoustic guitar skills during a cover of Neil Young’s “For the Turnstiles,” with a brief solo showing off his melodic fingerpicking style. The next song, “Tom Courtenay,” from the EP “Camp Yo La Tengo,” featured Hubley on lead vocals. She has a wide vocal range and can seamlessly make the switch between contralto and piping soprano within one song. The trio played three more songs from “Fade,” all of which maintained the same basic style as the rest of the set while sounding slightly faster. The best of these three was “I’ll Be Around,” an acoustic guitar–driven piece with lovely, introspective lyrics such as “When I stare into space/ I’m looking for you.” The first set finished with its 2006 song “Black Flowers,” in which McNew’s bass is the foundation while Kaplan’s guitar and Hubley’s keyboard intersect nicely with each other.

When the band returned after a 30-minute intermission, it made good on Kaplan’s promise that it would play loud. The gentle, soothing Yo La Tengo from half an hour before was completely replaced by a new, ear-splitting version. Kaplan, who was impressive with the beauty of his acoustic playing, now showed that he could jam with the best of them. Their performance of the 1997 song “We’re an American Band” was the climactic point of the concert. While the studio version is six and a half minutes long, the song became an extended jam breakdown in concert. Hubley’s frantic drums and Kaplan’s chords began to resemble Rage Against the Machine — guitarist Tom Morello’s trademark feedback-heavy style.

Kaplan was in his element throughout “We’re an American Band.” At times, he played doubled over with his fingers flying and his entire body shaking with every note, and at other points he began waving the guitar in every direction to achieve high screeching feedback. The band continued in this vein throughout the rest of the set, each song more face-meltingly noisy than the last. It ended the set with “I Heard You Looking,” which was a perfect closer, with all three band members rising to a crescendo together.

For the encore, the band played the keyboard-driven “Autumn Sweater,” which contained one of the best lyrical lines of the show: “So I looked for your eyes and the waves looked like they’d pour right out of them.”

The show ended with a cover of George McCrae’s “You Can Have It All.” Hubley sang lead while Kaplan and McNew’s backing vocals made it sound like a doo-wop group. This song was slow and quiet enough to sound similar to the first set, bringing the whole show full circle. Yo La Tengo is an excellent choice for fans of soft acoustic indie-pop as well as fans of noise music. All three are virtuosic players, while Kaplan’s guitar alone is worth the price of the admission.