Talking about Sigur Rós’ music is difficult at best. Most have either a love or hate relationship with the Icelandic quartet: Those who are fond of the music enjoy the band’s crescendo-prone dynamic and the warm chill that sets in with their four-to-twelve minute tomes, while those who deride it sense it as repetitive, long-winded and boring.

Still, there are those in the middle, those who refer to the string-and-bell gossamer of the band’s quietest moments as “nice,” but often pine that the climaxes–hard, long, multiple–are heavy-handed.

Case in point: “There’s much of ( ) that’s immediately gorgeous in a way that defies description,” Peter Marsh writes in a bubbling review for BBC Online of the band’s enigmatic 2003 opus, ( ). One British reader, however, summed up the dissent well, albeit inaccurately: “Oh come on, it sounds like the Smurfs. Singing Chinese. On drugs.”

Granted that the band can be a bit self-indulgent, Sigur Rós is one of the few post-rock acts in the world taking the genre’s arched anthems to new heights. It’s an approach they’ve been synthesizing in modulus for nearly a decade, and now, with Takk… , their fourth full-length due Sept. 13 on Fat Cat, they’ve hit their weighty mark.

With their 1997 debut Von, which finally saw its American issue late last year on One Little Indian, Sigur Ros cracked the code of tones and moods, stowing customarily electronic coldness into an envelope of warmth, a place where it was possible to turn a chill into a long shadow cast by a flickering flame. That was the beginning.

Then, with 1999’s Ág tis Byrjun (thankfully introduced to many Americans by Cameron Crowe’s placement of Vanilla Sky), they took those tones, bundled them together and effectively aimed it all, propelling this not-rock music–chirping, multi-tracked, idiosyncratic vocals sung in Icelandic, guitars slicing in and out of echoes and folds, crescendo-friendly drums, organs, pianos and strings–into new rock territory that would eventually settle just barely under the mainstream’s radar, much like Radiohead would do the next year with Kid A (whose opening track rolled during the opening sequence of Vanilla Sky).

The synthesis continued with the band’s third full-length, ( ). The individual tones were still in place, and–as they did with Ágœtis Byrjun–the weight was still directed toward something bigger than the sum of the parts: long roads to exploding, cathartic, bursting-at-the-seams apexes, falling somehow, without gravity, often straightaway into the next track. It all connected into one atmospheric, thematic piece, employing the art music concept of repetitious leitmotifs across eight unnamed tracks. The 71-minute LP came split onto two sides, one building on another, each saying something about the other’s existence, despair and hope. It wasn’t the perfect album, but–musica mundana, described by Anicius Boethius in the sixth century–had at last been committed to tape.

Now, with Takk… , it seems that Sigur Rós has simultaneously regressed and progressed. The album marks the band’s return to Icelandic, following the use of their own, open-tablet syntax–called “Hopelandic”–for ( ). The fire behind Ágœtis Byrjun is as hot as it ever was, and, if anyone ever doubted the existence of Sigur Ros as a rock band, this is the album–with its wail of “Mílanó,” skating rhythms of “Gong” and the transcendent reverie of “Meo Blóonasir”–that will silence those doubts. Where ( ) was developed live before its studio takes were conceived, many of the tracks on Takk… make their debut with the tour leading up to and following the album’s release. As such, the distended, extended improvisational approach of ( ) has been discarded on Takk… . Only one track here breaks the 10-minute mark, though a quartet of those on ( ) did so. The short track lengths mean more frequent explosions: Seven minutes into it, an isolated, frequency-scrabbled cymbal thrashes around in confused isolation, a wrecking ball let loose. Leitmotifs do not evolve into and devolve from piece to piece. Like Ágœtis Byrjun, themes come and go, never again to reappear. Of all things, a fanfare even blossoms for the cadenza of “Sé Lest,” recalling Sousa, not Debussy.

Sigur Rós offers a blank (not quite) canvas for the mind’s eye. Through Jon Thor Birgisson’s voice and the emotional domain that the band is able to navigate, this canvas isn’t as blank as much as it is pre-treated, more conducive to some colors, emotions and contexts than to others. Where some post-rock bands just lay it out for completely personal interpretation, Sigur Rós succeeds when it offers shape and form to its suggestion. Painting, really, has never been quite so charging.

Sigur Rós plays Durham’s Carolina Theatre on Wednesday, Sept. 7. Amina will open, then join the band. The show is sold out.