Tens of thousands of notes hurtled by during the Mars Volta’s nearly nonstop two-and-a-half-hour set at Terminal 5 on Monday night. Compared to virtually any other band that’s equally popular, the Mars Volta is a progressive-rock whirlwind, constructing maniacally complex music and performing it with a mixture of rigorous virtuosity, psychedelic euphoria and punk intensity.

Omar Rodriguez-Lopez, the band’s guitarist and composer, raced through parts that leaped all over the guitar or played wailing, pealing guitar-hero leads. Cedric Bixler-Zavala, the band’s singer and lyricist, belted verse after polysyllabic verse of hallucinatory imagery in his high voice. The two of them — both skinny guys with big hair — twitched and jittered all over the stage. Thomas Pridgen, the band’s latest drummer, buffeted his kit as if every song were supporting a flamboyant drum solo, even as he meticulously subdivided each beat. Jams spun off into gusts of saxophone, vertiginous synthesizer swoops, busy Latin percussion, spiraling guitar excursions and between-song stretches of looping, echoing noise.

So it might seem odd to say that the Mars Volta, which is still rock’s finest avatar of excess, is aiming for a degree of concision on its fourth full-length album, “The Bedlam in Goliath” (Strummer/Universal), which is scheduled for release Jan. 29, and which provided half the songs for Monday’s set.

The Mars Volta’s new concision isn’t necessarily in the length of the songs or the number of distinct episodes that are packed into each one. Both are ample. But the components of the songs are all a little more terse, as if the Mars Volta — having gleaned all the ideas it wanted from the likes of Yes, Rush, King Crimson and Led Zeppelin — has now turned to less abstruse sources, from blues-rock to the Police. The guitar riffs are earthier and the vocal lines are shorter, though for some reason Mr. Bixler-Zavala reaches up to his highest, most piercing falsetto for many of the new songs.

No one is likely to mistake the latest Mars Volta songs for pop ditties; the band’s new strategy is hardly a sellout. The story line of “The Bedlam in Goliath” has something to do with a haunted Ouija board and a demonic force demanding to be reincarnated, and the music would still trip up anyone trying to clap along. But the Mars Volta has stopped trying to trump the complexity of its previous efforts. It has untangled its music ever so slightly, and it’s already braced for a reaction. Taking a rare breather between songs, Mr. Bixler-Zavala dedicated “Drunkship of Lanterns,” from the band’s first album, to “all the people who don’t want us to keep writing the first two albums all over and over again.” But that song’s barrage of long lines and convoluted ideas, each knocking the last one newly askew, was a glorious excess.