Layers of chilly keyboards, echoing guitars, mournful strings and the occasional odd sonic effect blow through dreamy musical landscapes at once unearthly and unsettling yet comfortably familiar. Guiding the music's slow, somber and very deliberate journey, a warm, ethereal voice alternately soars and whispers in an often indecipherable language, making the landscape seem strangely less isolated.

Mainstream it's not. Heck, even the long critically adored but still niche-selling music of fellow Icelandic export Bjork comes off sounding J.Lo commercial by comparison.

But if the world's music tastemakers embrace Sigur Rós once again this year as expected, chances are good you'll be hearing about the band far beyond its first-ever Honolulu concert Tuesday at the Hawai'i Theatre.

Sigur Rós' fourth full-length CD, "Takk" — set for worldwide release Sept. 12 — is one of the year's most critically anticipated new recordings. But that's hardly a surprise, considering Sigur Rós' second and third discs — 1999's "'g3⁄4tis Byrjun" and 2002's "( )" — secured well-deserved spots on many year-end music critic top-10 lists (including this writer's).

Bons mots used by music writers to describe the band's music include "music for afterlife listeners" and "space-agey stoner rock." British music magazine Melody Maker went so far as to compare Sigur Rós' music to the sound of "God weeping tears of gold in heaven, like a glacier sweeping through the harsh Icelandic landscape (and) the whale song beamed to earth from a distant planet."

Bet that took some deep thought.

Naysayers keep things simpler, calling the band's music "somnambulant," "self-indulgent," "pretentious" or, well, "space-agey stoner rock."

Soft-spoken Sigur Rós bassist and founding member Georg Holm couldn't manage his own personal description of the band's music. But he knew what he didn't like.

"I really don't like the categorization 'prog-rock,' " said Holm, simply. "I really dislike that one."

Its penchant for crafting elegantly arranged, if funereal-paced, mini symphonies dusted with odd instrumentation and sung largely in Icelandic — or in the case of "( )," a language made up by the band — has won Sigur Rós a wildly devoted and growing international fan base. Radiohead even name-checked "'g3⁄4tis Byrjun" as an influence on its post-"OK Computer" studio experimentation.

Many dates on Sigur Rós' current European and American tour — its largest, and first in more than three years — are sold out or close to it. (Here at home, there are still lots of tickets.)

And the four very unassuming, interview-disdaining, group-photo-averse members of Sigur Rós? They'd just like you to enjoy their music and leave them, for the most part, alone to make it, thanks.

"Fame is nothing that we're looking for," said Holm, on the phone from a Tokyo tour stop last week. "We really feel strongly about the music that we make. ... We want to sell as many records as humanly possible, because we want everybody to hear it.

"But fame? No, thank you."

Holm relayed this information in a humble, extremely polite voice, blending trace elements of shyness and discomfort. Then again, he was also working off a mean cold.

Sigur Rós (pronounced "sih-ur rose," it is Icelandic for "victory rose") formed in 1994 when Reykjavik teenagers Holm, guitarist/vocalist Jónsi Birgisson and now-departed drummer 'g<thorn>st ¨var Gunnarsson grew bored with the bands they were in.

"Bands in Iceland become friends. Everybody knows each other. You'll have, like, 10 bands ... and five people who are in all 10 of those bands," said Holm, chuckling. "People mix up a lot, and play with each other."

Sigur Rós was not one of those bands.

"We've actually always been quite private in that sense. Since this band was formed, there was nothing else."

That first trio, whose formation Holm called "an almost nice accident," didn't even have similar tastes in music at first, save a collective fondness for atmospheric alt-rockers Smashing Pumpkins' "Siamese Dream" CD and English rock experimentalists Spiritualized.

Honing its live chops in Iceland community halls and pubs, Sigur Rós developed its sound through lengthy instrumental jam sessions in a municipal-swimming-pool-turned-studio in Reykjavik where it still records its CDs. Sigur Rós' music — since 1999 created by Holm, Birgisson, keyboardist Kjartan Sveinsson and drummer Orri P2/3ll Dyrason — continues to flow somewhat effortlessly from such sessions.

"When we make the music, it's almost like a natural process. The music writes itself, in a way," said Holm. "It's not very hard for us ... writing. It sort of just wants to be the way it is ... the music. And we don't really try to change it in any way.

"Everything about our music is very unintentional. When it comes to mixing and finishing what we have, we really focus on it ... and that's when it becomes intentional. ... It's unintentional intentional music."

Don't worry if you didn't get that last statement. Holm seemed a bit tentative about the explanation himself.

Talk moved to the buzz surrounding "Takk" — Sigur Rós' followup to "( )," which has sold 227,000 units in the United States. "Takk" is Icelandic for "thanks," but Holm didn't want to read too much into the title other than "thanking people for listening to our music" and the desire that humans "try and be more thankful, in general."

"It's definitely a lot happier than anything we've done before," said Holm, laughing. "One of the songs is probably the poppiest thing we've ever done."

Don't expect Sigur Rós to compete with Coldplay or even Gwen Stefani for a summer radio hit just yet. But the band's blogosphere is awash with rumors suggesting that "Takk" actually rocks.

"When we say there's more rock, it would be in context of our previous music. It would be more rock in that sense," warned Holm, still chuckling. "I think this album is more 'full on' than what we've done before."

Full on?

"There's more power. There are not many relaxed moments."

The growing collection of electronic gadgets, odd instruments and musical bric-a-brac taking up space in the band's studio post-"Takk" might be testament enough to that fact.

"There's lots of vintage gear and lots of crappy instruments," said Holm. "It's full of all kinds of stuff from eBay."