Try telling some 15-year-old Fall Out Boy fan that what he's listening to isn't real emo, and he'll rightfully LOL in your face. Because that's just not how words work in the real world—especially slang, and especially genre tags. No label is formal enough to approve or bar membership—if I say I'm punk, I'm punk, and all you can do is disagree (or, if things get bad enough, renounce your own membership). Once a word takes on a popular meaning, no matter how much it conflicts with its original meaning—well, you can't put the genre back in the bottle. If a handful of old music critics and hardcore nostalgists disagree with 1,000,000 MySpace profiles about what constitutes emo, who's more right? Probably the kids with the eyeliner.

Still, for those who grew up in the '80s and '90s, what passes for emo in the malls of America these days must seem like a bad joke. Without getting too much into the history (for that, see the excellent history of the Washington, D.C., punk scene Dance of Days, specifically the chapters "Spring" and "Drink Deep"), a brief origin story: blues —> rock —> punk —> hardcore —> emo. But sometime in the '90s, the second wave of emo bands—Cap'n Jazz, Braid, and their Midwestern progeny—started incorporating increasing amounts of pop influence, and by the '00s, we'd pretty much lost the plot. What the word now describes looks a hell of a lot more like glam or '80s hair metal than it does Rites of Spring.

Old story: Capitalism happily commodifies earnest youth movement into aesthetics and fashion, which can be marketed, bought, and sold. But good old-fashioned Marxist dialectics demand an antithesis arise whenever things get too bad (and common wisdom says that 10- or 20-year cycles of pop-music trends demand about the same thing).

Enter Bow + Arrow, a Seattle band who balk at the emo tag (as bands have since the term was coined), but who nevertheless exist squarely within its tradition. Now a trio, the band began two years ago as the duo of Lucas Thilman on vocals and guitar and Benjamin Rouse on drums and vocals. Jonny Carr joined the band on bass nine months later, and for a few months they had a second guitarist, who's since left the band.

"I would say that we're emo in the same way that Unwound was an emo band," says Rouse. "If you want to split hairs about musical genres, which is kind of a waste of time.

"We all listen to a lot of Unwound and Cap'n Jazz and stuff from the '90s," he continues, "as well as D.C. stuff—Hoover and Fugazi and whatever. But a lot of the stuff that's coming out now, as far as what a lot of the kids are into, is frankly kind of boring."

The band's new self-released debut album, Mathematics Is the Study of History, perfectly recalls those and other emo antecedents, offering a humble corrective to the genre's current malaise. The album is full of typically vague, melodramatic emotions, values, and calls to action backed by rollicking, frequently derailing rhythms and drum rolls, and Thilman's clean guitar playing, which alternates between straight-ahead charges and deftly feinting melodies with only the occasional hint of distortion. Their songs are populated with cowards, courage, dreams, loss, entreaties to not surrender, refusals to conspire, and, bizarrely, the word "pulchritude." There are gang vocals.

"Harbor Stories," the first song the band wrote together, is a visceral bike-rider's anthem, full of wind, cold, and cracks in the pavement. "This Is Why We Can't Have Nice Things" contains an almost laughably cliché hardcore breakdown: Over palm-muted, distorted eighth-note down-strokes and some ambling, clean guitar melody, a voice shouts, in a cadence that suggests a deep intake of breath every few syllables for maximum annunciation, "And I always thought/that you'd be around/but just like always/you had to prove me wrong." It's the sort of line a certain type of smartass kid might think up to make fun of precisely this kind of music some 10 years ago. The fact that it's deployed here with apparent sincerity can only make the smartest of asses feel genuinely nostalgic.

Lyrically, the band say they take inspiration from "bicycles, basement shows, quality friendships, and the DIY ethos."

"At least at one point, we decided that we weren't going to do love songs or songs about breakups," says Thilman. Between songs at their record-release show at the all-ages Vera Project (where the album was also recorded), Rouse says there are more important things to sing about, like sharing feelings with your friends. It's quintessentially emo—an exultation of fraternal friendship that nearly borders on contempt for romantic entanglements.

There are three instrumental passages on Mathematics: a brief, looping electronic intro; an epic, winding outro; and, most notably, an interlude that samples the closing monologue from cult documentary Paris Is Burning—an '80s NYC drag queen's tragically sad riff on coming to grips with disappointment and failed ambitions.

"That sample almost brings tears to my eyes every time I hear it," says Thilman. "The entire feel of that movie is just people struggling to do what they want to do, to be who they are and not having to fight anybody for it. That quote is insanely powerful."

"It also informs how we fit into the DIY community and what that means," adds Rouse, who cooperates on seattlediy.com (both he and Thilman have volunteered or worked at local teen centers and all-ages venues). "In Paris Is Burning, they were doing all that stuff to create a community whether they became famous or not, and that's kind of the idea behind a lot of what we do."

At the record-release show, Bow + Arrow play on the lobby floor rather than the main stage, mics facing the drums in a tight huddle, creating a kind of ersatz basement-show feel. A small, friendly crowd dances and sings along to their songs. It's no Paris Is Burning, but it's clear the band have carved out a space for themselves, their friends and fellow artists, and for a musical style too often overshadowed by its lesser descendants. Just don't call it emo.

Bow + Arrow's "Nick Water"