The first two full-length music features from the Mars Volta (2003’s De-Loused in the Comatorium and 2005’s Frances the Mute) were amazing and strange rock operas. Both concept albums sounded like surreal sci-fi soundtracks — Fellini’s version of Flash Gordon — written and scored by the Latin Queen, aka Cedric Bixler-Zavala and Omar Rodriguez-Lopez. The records probed a heady new form of hardcore punk rock, akin to At the Drive-In (of which the two were former members), recast into neo-prog-rock sagas that feast on free-flowing jazz structures, bizarre true-life gothic tales, and Bixler-Zavala’s piercing vocals (sung in both Spanish and English).

Equally absurd and beautiful art-rock overtures can be found throughout Amputechture. “Tetragrammaton” is signature Mars Volta, a cerebral 17-minute opus based on the real murder of a Romanian nun, who was killed because she was supposedly possessed by the devil. It’s broken into symphonic movements interspersed with indulgent guitar solos, otherworldly studio effects, and Bixler-Zavala’s creepy screams.

“Viscera Eyes,” the most accessible single, may begin with catchy rapid-fire guitar (played by the Red Hot Chili Peppers’ John Frusciante), but it devolves into a nine-minute Yes edifice that ends in white noise and wah-wah pedals. The other songs are just as exhausting and extraordinary, requiring the patience and endurance of an audiophile who enjoys the hedonism of such art noise.