Since Franz Ferdinand’s emergence out of some vague early-2000s Glasgow dance-indie “scene” of which I can’t seem to recall another member, their music has been most often associated with the vocabulary of geometry. While similar linguistic trends are often the result of lazy music reviewer groupthink, with FF, this was decidedly not the case — send me an e-mail if you can think of a better adjective than “angular” to describe those opening guitar lines on “Take Me Out.” Paul Thomson’s drumming? Symmetrical. Bob Hardy’s bass guitar? In perfect parallel with the percussion. The appeal of their first two albums — with the exception of some delightful, airy acoustic experiments — centered around a precision, a regularity, a reliance on some sublime formula that always spit out tight, toe-tapping dance rock.

It seems that that formula has been torn up and tossed out of the proverbial window to litter the Glaswegian cobblestones. If Franz Ferdinand’s third album, “Tonight,” is purely an exercise in shaking off the band’s associations with Euclid and Archimedes, then it’s a success. But by any other measure, it’s a shambling mess, occasionally redeemed by hints at past mathematical elegance or future genre-bending.

The opener, “Ulysses,” begins with lead singer Alex Kapranos testing out a George-Michael-circa-“Faith” power-whisper, later complemented by a transition to a weak attempt at glammy falsetto (“I’ve found a new way!”). Indeed, much of this album’s fleeting appeal derives from its here-and-there tributes to the less-defensible pleasures of ’80s pop — be it the Journey-esque first wave of guitar on “Twilight Omens” or the initial percussive swell of “Lucid Dreams” (think “Welcome to the Jungle” turned down from 11). But these occasional details are too often presented among a loosely arranged mess of muddled vocals and dull melodies.

If the band can be held to former evaluative standards, precisely three of the 12 songs pass the most rudimentary of dance-rock exams: whether they make this reviewer, alone in his room, wearing T-shirt, boxers and socks and nursing a bloody nose due to the too-dry central heating, tap his feet in abstract joy. “Turn It On” is a successful elaboration on the old FF formula — the new element being a casual call-and-response setup. “Can’t Stop Feeling” has a pleasantly dizzying circularity. And “Live Alone” is a parti-colored delight of Devo-ish keyboard, frenzied guitar work and vocals offered with hypnotic regularity (“I’ll be here, I’ll be here, wishing I could be there”).

But the remaining tracks are only remarkable in their sheer inability to make any sort of impression. You hear one, and then it’s gone. While the band makes a concerted move away from the hurry-up-and-get-to-the-chorus arrangements of previous hits, the teasing, the tempo shifts, the unexpected bridges feel like last-ditch attempts to lend artistry and texture to indistinct material. I found myself wishing for at least a catchy hook or clever turn of phrase to take away with me.

At least until the closer, “Katherine Kiss Me,” which recalls the elegant down-tempo exercises of “You Could Have It So Much Better.” It’s the odd track out in the best sense: Kapranos actually sings a melody, slipping out of his loungy default, and light acoustic guitar floats over it all. It isn’t precise — there isn’t much to it — but the sum of those simple components amounts to more than all else “Tonight” has to offer.