TV on the Radio finally lives up to its long-smoldering ambition with its third album, “Dear Science” (DGC/Interscope), which is out today. This 11-track effort features all of the Brooklyn quintet’s so-called experimental hallmarks — Dave Sitek’s choppy, layered production; Tunde Adebimpe and Kyp Malone’s pyrotechnic harmonies; an insouciant stylistic hybrid that freely borrows from funk and avant jazz, 1950s pop, and 1970s progressive rock; and the band’s sober but hopeful worldview — more maturely and skillfully managed, orchestrated, and executed. And the results are downright stunning. “Dear Science” is just as risky and heady as the band’s 2006 major-label debut, “Return to Cookie Mountain,” only where that album wrapped its quasi-critical politics inside an aggressive, abrasive, and self-consciously arty affront, “Dear Science” slyly conveys the same desperation and optimism inside instantly catchy hooks and seductive grooves.

Many have waited a long time for the band to reach this stylistic balance. Founded in 2001 as a trio consisting of Messrs. Adebimpe, Malone, and Sitek, TV on the Radio’s kitchen-sink experiments sounded better on paper than they did on record or onstage. Worse, the shadow of influences seeped through its early, brittle, and claustrophobic productions. The group’s 2003 EP “Young Liars” and 2004 LP “Desperate Youth, Bloodthirsty Babes,” despite rabid critical enthusiasm, sounded like the obvious progeny of Talking Heads eclecticism, mid-to-late 1970s David Bowie, and 1980s new wave and house music.

Those albatrosses started to fly away on “Return to Cookie Mountain,” on which Mr. Sitek started to let an organic groove enter the band’s supple instrumentation — aided in large part by the addition of workhorse multi-instrumentalists Jaleel Bunton and Gerard Smith. That attitude spawned an album that nearly suffocated under the weight of its own gargantuan aspiration. But with “Dear Science,” the band finally feels at ease with this looseness, and it makes a radical difference. TV on the Radio songs still have about 20 different ideas and genres floating around inside them, but they are used more sparingly, tastefully, and effectively to accent and sculpt the overall emotional and rhythmic tenor of the music and lyrics.

The effect is palpable from the very first song. “Halfway Home” begins with a rumble of percussion and synthesizer drone, over which Mr. Adebimpe chants an onomatopoeic “ba-ba-ba-ba-bomp.” After he sings the first line — “The lazy way they turn your head / into a rest stop for the dead” — reverberative hand-claps add another rhythmic ripple to the tense backing beat. Then other elements creep in: a soft loop of Mr. Adebimpe’s “ba-bas,” another buzzing texture, a slicing electronic snip, a crunching mechanical pulse. Over all this, Mr. Adebimpe sings about fighting through the cynical indifference of cultural alienation. The song itself rewards this effort about four minutes later when a punch of guitars and drums barrels in and lifts the song into an outright rocker. It’s an arresting and effective orchestration, and a taste of the smart, dramatic, and creative arrangements to come.

“Dear Science” overflows with such deft production collisions. A funky guitar and Cure-like keyboard line punctuates “Crying;” a spacey, funereal electronic tapestry rustles in the background of “Stork and Owl”: a 1970s bass funk dances against a 2000s belching dance-floor bass in the swirling “Golden Age”; and a sweeping string section powers the absolutely gorgeous “Family Tree.”

Best of all, a full horn section lays a triumphant brassiness behind the Afrobeat-jittery, scathingly funky “Red Dress,” one of TV on the Radio’s most effective marriages of dance grooves and politics. The upbeat barn burner is an indictment of everyday apathy, and the insistent tempo gives Mr. Adebimpe’s lyrics a more poignant and probing frame.

TV on the Radio may still be a bit too odd for mainstream pop, but everything on “Dear Science” shows the band learning from its previous efforts and growing into an act capable of making arena-sized music brimming with modern ideas. Whether or not it cracks the Billboard Top 10, “Dear Science” is TV on the Radio’s first genuine success.

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The Scottish quartet Mogwai, on the other hand, hasn’t learned enough from its past mistakes. Arguably the most impudent band to come out of Glasgow in the late 1990s, Mogwai turned abrupt instrumental shifts — from stately, ornate guitar lines to excessive sheets of bowel-rumbling volume — into a gesture as blithely lewd and casually liberating as raising a middle finger during a class photo.

The band wisely turned this fleeting joy into its entire ideal on early singles and choice cuts, from the skull-splitting “Like Herod” to the epic “My Father My King.” Since 2001’s “Rock Action,” though, the band has erred on the side of pleasantries and melodies rather than restless dynamics. Mogwai now foregrounds its intricate guitars — very much like the soporific Explosions in the Sky — rather than its muscular bursts. Quite simply, these days the band is too much action and not enough rock.

Its sixth album, “The Hawk Is Howling,” out today on Matador Records, doesn’t divert from that course. A perfectly pretty 10-song album of interlocking guitar lines knitted together at a leisurely pace, “The Hawk” is yet another Mogwai album that delivers a healthy dose of what the band does well — velvety layered webs of guitars — without following through on what it can do better than anybody else, namely spit on that prettiness with a teeth-rattling thunderbolt of speaker-busting nerve.

There’s plenty to enjoy here if you’re looking for a sound track for the morning paper. The song titles may retain the band’s insolent attitude — “The Sun Smells Too Loud,” “I Love You, I’m Going to Blow Up Your School,” “I’m Jim Morrison, I’m Dead” — but only two tracks deliver the Mogwai goods. “Batcat” wastes no time getting to the distorted swing, as the entire band finds an ornery groove early and stays there for the next five minutes. And album-closer “The Precipice” is both a blessing and a curse. As a slow-building, nearly seven-minute mini-symphony, it’s a crisp reminder that Mogwai can still make some of the best instrumental rock in music. But having to sit through 50 minutes of mediocre music to get there isn’t worth the reward.