True Faith is a terrific, somnolent and exhilarating exhibition, focusing both on the truncated but still influential career of Joy Division and its much longer afterlife, without Ian Curtis, as New Order. Joy Division’s dark, painful music, its sonic gloom and echoing aural spaces dominate the first half of the show. Darkness gives way to light in the second half, with New Order’s brighter, danceable synthpop and clever lyrics.

But things are not so simple. This is an exhibition about more than the vicissitudes of a group of musicians and the artists, designers and film-makers who accrued around them. It is about the convergence of art and pop (if Joy Division were ever really “pop”), about growing up, and about the way culture gets made, how it changes and how it changes us. That’s what I’m telling myself, anyway.

The absent presence of Curtis is everywhere. At the end of the show, framed, are his handwritten lyrics to Love Will Tear Us Apart. Earlier, we see him in bootleg videos (one, recorded in colour but shown in black and white, was shot at Joy Division’s concert at the Manchester’s Apollo theatre in October 1979); and in several paintings – by Julian Schnabel, Glenn Brown and Dexter Dalwood, whose dedicatory titles name-check the late singer.

Echoes of Ian Curtis … Glenn Brown’s Dark Angel (2002). Photograph: Courtesy the artist

Unearthly and ghostly, Curtis coalesces in a blizzard of static. The videotape fizzes with degraded information; it is a magnetic ruin. Whatever Curtis was experiencing, with his frantic, jerky movements (sometimes, he would experience epileptic fits on stage, and have to be carried off, mid-song), finds an eerie equivalence in the electronic noise. Except, in this video from Slater B Bradley’s 2001-04 Doppelganger Series, it is not Ian Curtis on stage at all, but a double (Bradley’s other Doppelganger video portraits portray Kurt Cobain and Michael Jackson). The harder you look, the more difficult it is to grasp the image. The singer is only a trace: pinwheeling arms, a jerky back-and-forth shuffle, a looming face that comes and goes, that sonorous baritone voice, a thing more solid and permanent than this fleeting figure. He’s anchored by the song. This, maybe, is to see too much and read too much into Bradley’s work, an unavoidable consequence of what we know became of the singer.

The first space at Manchester Art Gallery is illuminated by the spiky, strip-light branches of brutalist trees that stand between the artworks. The frames of metal benches that have lost their seats, and angular metal rubbish bins that disobey the laws of perspective are dotted about. We are plunged into a liminal wasteland, a fictional, feral urban space. Martin Boyce’s 2002 trees, benches and bins are titled Our Love is Like the Flowers, the Rain, the Sea and the Hours, a line from The Village, a track on New Order’s 1983 album. Boyce’s work is more than just a setting.

Liminal wasteland … Martin Boyce’s Our Love is Like the Flowers, the Rain, the Sea and the Hours (2002). Photograph: Courtesy the artist

Power, Corruption and Lies has as its cover a close-up detail of Ignace Henri Theodore Fantin-Latour’s 1890 Basket of Roses. This lovely painting, on loan from the National Gallery, hangs on the wall. A postcard of the painting hangs nearby. The postcard provided the initial inspiration for Peter Saville’s album cover. Something of Fantin-Latour’s opaque, crusty brushwork is echoed in the blundering Schnabel that hangs around the corner.

So bad it is almost good, Schnabel’s 1980 painting Ornamental Despair (Painting for Ian Curtis) glowers portentiously from the wall. All scuffed white paint on black velvet, Schnabel’s work is derived from Peter Saville’s cover for Joy Division’s second album Closer, from the same year. Saville’s cover reproduced a photograph of a 19th-century, neo-classical sculptural tableau of a tomb in Genoa, the image lifted from Zoom magazine. In the Schnabel, a single draped figure is prostrated against emptiness on one side of the diptych. The curlicues of an empty picture frame decorate the other blank half of the painting.

Closer was released not long after Curtis hanged himself (his third suicide attempt).. Schnabel’s painting is one of many works in True Faith that are either inspired by Joy Division and its reincarnation as New Order, or which provided the inspiration for Saville’s brilliant album covers and graphics for the two bands.

So bad it’s almost good … Julian Schnabel’s Ornamental Despair (1980). Photograph: Courtesy the artist

More than exercises in style, Saville’s album covers, posters and other graphic work have an enigmatic, serious and implacable sophistication, as though secrets were contained in their imagery and typefaces. They appear to belong to some other time – a parallel, alternative culture, a future that has bypassed the foibles of the immediate present. Signals from a distant pulsar, like the seismic graphs of heartbeats, a 19th-century still life, typography that might belong to the Bauhaus or to the binding of some arcane manifesto from some ultra-serious art movement, augmented with colour codes and other graphic interventions. They look like something from the Warburg Institute misfiled in the racks of the local record store. It is as if Saville were insinuating an art history lesson and an injection of high taste into the heads of kids who have never set foot in a gallery. Early modernism, the 19th century avant-garde and modern graphic colour keys and codes collide, marked as much by rigour as a postmodern free-for-all.

New York artist Robert Longo – who went on to direct the hectic, energised video for New Order’s single Bizarre Love Triangle in 1986 – said of Joy Division’s Unknown Pleasures, which he picked up from a music store’s album bin: “I will always associate this music and album cover with the beginning of my professional life as a practising artist. I would listen to it late at night, and I would always keep the cover in view.” The music and the design are weirdly inextricable.

Flower power … Ignace-Henri-Théodore Fantin-Latour: A Basket of Roses (1890), which inspired Peter Saville’s cover for Power Corruption and Lies.

Mannequins hang around the twilit gallery, empty faces turned towards the things on the wall, or inwards to their thoughts and the distant music. Their parkas and jerkins are emblazoned with Saville’s graphics for the bands. These figures, and their garments, were created by Belgian fashion designer Raf Simons (working in conjunction with Saville) in 2003. Rather than a retro fashion-statement, they invoke a feeling of stalled time, the persistence of a certain malaise that goes beyond fickle fashion, a belligerent lassitude.

I am looking into a past that is not mine. Faint as a receding memory, a 1996 drawing by James Pyman depicts the view across the lid of a desk in a school classroom. The desk is carved with a heart, surrounding the names Ian, Bernard, Peter, Steve, the members of Joy Division. The drawing is titled 1979, the year the band released their first abum, Unknown Pleasures. A wan little thing, the carved heart signals boredom and hope, frustration and infatuation, yearning and a dream of some sort of escape.

Beats leak from another room, the soundtrack of Mark Leckey’s Dream English Kid, 1964-1999 AD. Leckey is speaking, I think, of more than himself. Born in 1964, he saw Joy Division play a Liverpool club in 1979. Leckey found bootleg footage of the gig online, and trawled the internet to reconstruct the Liverpool of his youth. What a tough, dismal place this country and that city were. As much as it is a reconstruction of the past, Dream English Kid presages a future no less grim.

‘A wan little thing’ … James Pyman’s 1979 (1996). Photograph: © James Pyman, courtesy Maureen Paley, London

Nearby, in the half-light of Boyce’s trees, stands a blocky, windowless architectural model, a new work by Liam Gillick. Printed phrases decorate the exterior. TNT, they say, ATROCITY EXHIBITION, UNKNOWN PLEASURES. The phrases lead us in different directions. It’s titled Scale Model of a Social Centre for Teenagers for Milan 1993 (yet another time-slip in an exhibition that evades nostalgia and speaks of the present as much as the past) and I don’t know what – or perhaps even how – to think about it. Gillick has also been involved in the staging of New Order’s series of concerts at this year’s Manchester international festival.

Joy Division were both timely and untimely. They still sound like the future, and more current and urgent than anything by New Order, no matter how good they are. And Saville’s contribution is just as vital as the later posters for New Order made by artists John Baldessari, Barbara Kruger and Lawrence Weiner, or the pop videos directed by Jonathan Demme (who made the great Talking Heads concert film, Stop Making Sense), Kathryn Bigelow, Robert Frank and others. The showreel screening of their videos is exhilarating. But Joy Division and Saville are the real heart of this exhibition. They made things that still feel new. The rest is art.