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Modern heavyweights Coheed and Cambria — who play Showbox SoDo Tuesday — have, since 2002, wowed headbangers, guitar geeks, comic-book readers and growing mainstream audiences with their metallic fusion of progressive rock and science fiction.

The New York foursome’s ambitious scope — and frontman Claudio Sanchez’s impossibly high voice — draws frequent comparisons to Geddy Lee and Rush, while its hair-raising execution often recalls post-hardcore gurus the Mars Volta.

Dead serious about concept albums, Coheed’s first five releases, taken together, may be the longest one ever made. Each soundtrack is a different installment in an original literary saga called “The Amory Wars.”

Sanchez began writing the series as a teenager, naming the band for its two lead characters. Now 34, he finally ended it in 2010 with “Year of the Black Rainbow,” a 53-minute set accompanied by a 352-page novel. A Mark Wahlberg-produced big-screen adaptation is in the works.

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Via telephone en route to rehearsals, Sanchez talked about the group’s new double-disc “Afterman: Ascension/Descension.”

“The last five records were the tale of Coheed and Cambria taking you through their creation and death,” he explained. “The new one is about the mythology’s namesake, Sirius Amory, the astronomer who discovers the value of this energy source that binds all the planets together.”

Though still a tall order for those not into prog rock or sci-fi, “Afterman” is a varied, inviting effort.

By dialing down the volume, guitarist Travis Stever breaks his own mold. Delayed U2 prettiness guides “The Afterman.” “Goodnight, Fair Lady” attempts dueling Thin Lizzy riffs. “Subtraction” is an intimate unplugged lullaby.

Sanchez experiments, too. Atonal yet accessible, “Holly Wood the Cracked” marries a guttural growl to a stadium-sized chorus, while “Evagria the Faithful” delivers anthemic hooks with Michael Jackson elasticity, breathy “oh’s” trailing each line.

Regarding his Sting-inspired vocal on the funked-up, Latin-tinged “Number City,” Sanchez calls the singer’s ’80s smash “Englishman in New York” a favorite “since age 9” and notes Police drummer Stewart Copeland’s creative influence on Coheed’s Josh Eppard, whose return from a six-year leave adds to “Afterman’s” intrigue.

Eppard has “gone down the proper channels to sobriety,” says Sanchez. “He’s in a great head space … his enthusiasm has certainly spilled into our consciousness.”

Reflecting on his concept-rock ensemble’s gradual rise and possible peak — “Ascension” debuted at number five nationally — Sanchez says it’s “as interesting, fun and challenging as ever.

“There’s the music, sure, but also the other side of getting it to live on in other mediums … books, comics, [and now] movies. Finding new ways to present the conceptual dimension of what we do will always be exciting.”

Charlie Zaillian:

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