"The term 'supergroup' didn't exist until we formed," says David Crosby of the time in 1968 when the ex-Byrds singer and guitarist joined forces with former Buffalo Springfield guitarist and singer Stephen Stills, and Hollies vocalist and guitarist Graham Nash. "We were the first second-generation band to form. We had all been in successful bands before, but something like us had never happened. We set the precedent. And for us to become even bigger than our previous bands, that was even more unique."

Crosby was already well acquainted with his soon-to-be bandmates, but it took an informal jam at the house of Mamas And The Papas' singer Cass Elliot's to indicate that lightning could be captured in a bottle by a blend of their three voices.

"In a sense, we knew what we were after," Crosby says. "I had heard Stephen's songs, and they were great. He was the up-and-coming young writer in LA. He was the guy with the best songs. So I started singing with him. [Sings] 'In the morning when you rise…'

Nash, hanging out nearby, came over and asked the two to sing the song (what was to become You Don't Have To Cry) again. "Stephen and I looked at each other and said, 'OK, sure,' and we sang it again," Crosby says. "When we were done, Nash said, 'Can you do that one more time? Just one more time.' The third time we sang it, Nash joined in and added a top harmony line. It was amazing! It really was."

Nash, already disillusioned with the creative direction of The Hollies and their lackluster reaction to the new songs he was writing, quickly turned in his walking papers to the British pop group and set about recording an album with his new mates. The resulting record, an inventive mixture of folk and light rock highlighted by the three's supreme vocal harmonies, ran counter to the musical flavor of the time.

"It was the year of the guitar player – Clapton and Hendrix," says Crosby. "Everybody wanted to go in that direction, and we had this completely different thing, even though Stephen was a really fine guitar player. We wanted to do this thing with our voices, because it worked. And we had songs – really good songs. We knew we had our own sound."

Released on 29 May 1969, the album Crosby, Stills & Nash was an immediate smash, spawning two radio hits (Marrakesh Express and Suite: Judy Blue Eyes) and creating a massive shift in popular music, one which would place an emphasis on harmony-laden songs. Although the trio of Crosby, Stills & Nash would occasionally include a floating member, Neil Young, for the lineup of Crosby, Stills, Nash & Young, the supergroup that formed in Cass Elliot's living room has survived and thrived through countless personal dramas and musical changes over the years.

Next month, to celebrate the conclusion of their 80-date 2012 world tour, Crosby, Stills & Nash will close out their five-night stand at New York City's Beacon Theatre by performing their debut album in its entirety. " It's not a concept we invented, but I think it's a wonderful thing to do," Crosby says.

"Only recently we were able to play the Suite [Suite: Judy Blue Eyes] after 20 years. Stephen got into a good place and started being able to do it. We tried it by ourselves, then we played it live, and people went batshit. They were literally going out of their gourds. So we thought, Hey, that's pretty cool. If we could do that, we could certainly do all the other stuff. The Suite's the hard one."

On the following pages, David Crosby offers his track-by-track reflections on the writing and recording of the album, Crosby, Stills & Nash.