Two albums stood out in 1967, that turbulent year half a century ago. One came from the British side of the Atlantic – the Beatles’ Sgt Pepper’s Lonely Hearts Club Band – and the other from its American shore – The Velvet Underground & Nico. Between them, they changed the sound of sound.

This week, the Velvets’ album comes home, to where it was conceived and recorded, to where the seed was planted: New York. John Cale, who co-wrote the music and played viola and bass guitar, will perform songs from the album – and a few other Velvet treasures – at the Brooklyn Academy of Music, on Thursday and Friday, as anchor with his current band and a cast of guests.

The Velvet Underground & Nico sleeve artwork by Andy Warhol. Photograph: Getty Images

The album had a sonority and mood unlike any before or since: a painful beauty, a languid ennui, a timbre, oddly perhaps, both warm and metallic. To listen to it was – and still is – like having an exposed nerve stroked, sometimes softly, sometimes a little too roughly.

The album was recorded in a rehearsal space in Ludlow Street on the Lower East Side; only Lou Reed on vocals had headphones. It was produced by Andy Warhol – whose artwork also graced the album sleeve – though apparently he barely spoke. “He was there,” says Cale. “He’d say a few things, but they’d be effective.” Not much was said, either, between the musicians. “We weren’t there to fuck around,” Cale told Rolling Stone.

The quartet and German singer Nico struck an alchemical balance: the meeting of ice and flame in Nico’s voice, and that droll, sagacious detachment in Reed’s. But what really marked the album was its sound texture, infused with Cale’s inimitable drone: a cross-pollination between rock music and classical training in his native Wales, work with John Cage at the Tanglewood music academy in Massachusetts, and experiments with the composers La Monte Young and Terry Riley.

The album was a slow burner, selling only 30,000 copies in five years, though as Brian Eno famously said, “everyone who bought one of those 30,000 copies started a band”. And this is its endurance: as a soundscape, the album’s influence is immeasurably deep and wide, not only on the sensibility and feelings of its public but also on music and musicians. That entwinement of rock and drone – that unique tonality and timbre – flowed into almost all that followed: punk, electronic-wall-of-sound, even avant-garde jazz and contemporary “classical”.

In a year that saw the death of Che Guevara, uprising in Mexico and a military coup in Greece – in a world on the eve of the eruptions of 1968 – the album was studiedly apolitical.

“It’s all subliminal”, Cale says, “it’s all implication.” Emotions in The Velvet Undergound & Nico are raw and honest, sometimes scalpel-edged, but in an age of idealism, these songs are as far removed from the “summer of love” as you can get.

And perhaps, 50 years on, the record is vindicated as such, as we find ourselves not so much in the aura of an “age of Aquarius” as in what Percy Bysshe Shelley described two centuries ago as “an age of despair”. Some people found the album cynical at the time, but the diagonal glance of Cale and Reed saw more accurately into their future – our present – than the lambent gaze of Joan Baez or Grace Slick.

Most of the Velvet Underground are now literally so: Warhol, Reed, Sterling Morrison and Nico herself are all dead. Drummer Moe Tucker lives, more privately than Cale, who returns to New York this week as a musician of restless innovation; each of his albums since that 50 years ago different from the last.

If his album Paris 1919 advanced The Velvet Undergound & Nico’s mood to reflect desolate Europe at the end of the first world war, a full orchestration of the same material performed in Cardiff and London during 2010 reached Mahlerian proportions. Recent experiments with a string orchestra and choir have entwined electro-symphonic scale with chromatics you would expect to hear in Janáček. And on Saturday in New York, the tributes done, there is a third concert of solo music, with choir and orchestra.

But it all started there in 1967, with the music this week’s concerts will bequeath to another, present, generation. The Velvet Underground & Nico has hitherto been performed twice on this anniversary loop: in May this year at Clarence Dock in Liverpool, where Nadine Shah gave a luxuriously velvetine version of Femme Fatale, and Cale’s drone injected Venus in Furs with feverish pulse.

Before Merseyside, in spring 2016, at the Philharmonie in Paris, Cale and guests were in concert. The acoustics were crystalline-clear enough to hear every mysterious nuance of Mark Lanegan’s All Tomorrow’s Parties, and to know that you don’t need Pete Doherty crashing his way through White Light/White Heat, but highlighting the wonderfully articulate but understated touches on guitar – in the spirit of the original – by Dustin Boyer, now Cale’s longest-standing musical partner.

John Cale on a US TV show in 1963

By way of anticipation for this week, Cale and “slam poet” Saul Williams did something extraordinary for the Paris rendering of Heroin: instead of Reed’s introspective reflection on the opiate itself, Williams sang, with epic rage, a song not so much about a narcotic as a cry against whatever it is in society that would drive someone to want to “nullify my life”. Goes to show what 50 years and a generation can do to a song.

So these are the surprises that will make this week’s New York homecoming much more than an excursion down memory lane – the album speaking to present and future. Even though the unforgettable detail in Paris was a calling of the ghosts, when Cale took it upon himself to sing Sunday Morning, sung by Reed on the record.

Cale swallowed one line, out of sheer emotion, and said next day: “I’d never sung that song. Did you catch the choking? The thing about music is that you never know when your subconscious is going to jump up and bite you in the back of the neck. I was back there, in that loft on the Lower East Side – Sunday morning indeed, at the harmonium, playing that song.”