Leonard Cohen died in Los Angeles last week but, by the time his death was announced, his body had been flown back to his home town, Montreal, and buried next to his parents in the cemetery of the shul where his family worshipped.

"I have a deep tribal instinct," he told David Remnick, editor of the New Yorker magazine, in his last interview a couple of months ago, "I grew up in a synagogue that my ancestors built. I sat in the third row. My family was decent. They were good people. They were handshake people."

Throughout his extraordinary life that took him to many places, many loves, many moods, many drugs, many worldly triumphs, and a long immersion in Zen (30 years including six living in a Buddhist monastery as a monk), Judaism and family and home never lost their centrality.

Cohen's Montreal milieu was not the scrabbling, hustling St Urbain Street of Mordecai Richler; it was refined, moneyed Westmount. His shul is the largest and oldest Ashkenazi community in Canada, Shaar Hashamayim - the gate of heaven.

This summer, when it became certain that his cancer would soon take him to these burial grounds and to the gated celestial destination for which they are named, he did things that made for a characteristically gracious exit.

On being told that Marianne Ihlen, his lover and muse from the 1960s, subject of one of his most loved songs, was very close to death in Norway, he immediately wrote her a letter, a final beautiful "so long": "I think I will follow you very soon. Know that I am so close behind you that if you stretch out your hand, I think you can reach mine".

Despite being in constant pain, he agreed to do the long talk with Remnick that produced a suitably memorable and enlightening article and, most of all, he made a final wonderful album of songs foreshadowing his death. The man who wrote Hey, That's No Way to Say Goodbye knew precisely how to say it.

A poet since adolescence, a novelist in his twenties, by the time he made his first album - a painful and laborious business but with indelibly marvellous results - he was already in his thirties.

Fed up with the slim pickings of a modicum of praise and cultural respectability that came with an excess of penury and large-scale obscurity, he turned to music as "the economic solution to being a writer". Nobody ever suggested he wasn't a poet, they just didn't pay him for it.

Naysayers question whether his old friend Bob Dylan, a mere songwriter, can possibly be entitled to the Nobel prize for literature. Cohen has said of himself: "There's no difference between a poem and a song. All my writing has guitars behind it. Even the novels."

For half-a-century, he has been loved by many but misunderstood and rejected by many, many more. His skilfully wrought, profound, soulful ballads sung in his far-from-golden voice had him identified as "the godfather of gloom", making "music to slash your wrists by." This was never true.

Lawrence Breavman, Cohen's alter ego in his 1963 autobiographical novel The Favourite Game, is described as "hoaxing the world with disciplined melancholy". So it was to some extent with Cohen. Those with the ears to hear, and especially those who have seen him perform live, know him also as witty and playful , a mesmerising presence. A Leonard Cohen concert of whatever vintage was an event you emerged from elated by his brilliance and charm. He didn't look for sympathy, he had the gift of empathy.

In the early days, he had a terror of going on stage and he continued to have some bad moments. In Jerusalem in 1972, unhappy with how things were going, he slunk off in mid-song. The whole audience reassured him by singing Hevenu Shalom Aleichem.

"How sweet can an audience be," reflected Cohen, "they turned into one Jew saying 'what else can you show me kid?'" After a break, he returned in triumph (having imbibed some LSD, which may have helped).

In 2009, after years immersed in Buddhist contemplation and with his music career behind him, financial catastrophe forced him back on tour, something he had never expected to do. His manager had taken all his money. It was a victory march. Hallelujah, a song he wrote in 1984, on an album his label rejected, had become the hit everyone wanted to sing. Cohen, his charisma now marinated by age, took the world by storm. In 2008, he played Glastonbury. Michael Eavis, the festival's founder, said it was the best set they'd ever had.

In 1993, when he was already nearly 60, Cohen took part in a long conversation about religion which was printed in an American Jewish publication.

"I never rebelled against my parents, even when I was taking acid and living in the Chelsea Hotel in New York [not a suitable place for a nice Jewish boy]," he said, " I always thought my family practice was great, and I've tried to keep it up in my half-ass way. I'm a member of my synagogue, I light the candles Friday night. I feel very close to the whole trip.

"I think there is the prophetic element in Judaism, that world vision articulated, let's say, by Isaiah. I think that's not taken seriously. Our faith is full of atheists and agnostics. I think that there are lots of nominal Jews around. But there are people who really believe, who have really had an experience, who have really been embraced, who have felt themselves dissolve in the midst of a prayer."

For Cohen, Zen immersion did not exclude his Judaism, it enabled it.

Dylan once told him: "Your songs are like prayers." Some of them actually are prayers: Who by Fire, a checklist of how sinners might be punished, is straight from the Yom Kippur service.

His new song about his impending death, You Want it Darker, has allusions to the Kaddish his shul choir and chazan sing, and there's repetition of Hineni ("here I am") - an ordinary Hebrew word but most famously spoken by Abraham to God and to his son Isaac at the Akedah, the story also told by Dylan in his 1965 song Highway 61 Revisited – "Oh God said to Abraham, 'Kill me a son'/Abe says, 'Man, you must be puttin' me on'"

Randy Newman starts his blindingly bleak God's Song "Cain slew Abel, Seth knew not why/for if the children of Israel were to multiply/why must any of the children die?"

These boys, these Jewish geniuses, know their Bereshit. These post-septuagenarians, along with Paul Simon, are songwriters beyond compare, a golden generation, counterparts of Roth, Bellow, Heller and Mailer in literature, products of the Jewish American mid-20th century. We shall not see their like again.

Leonard Cohen is gone but in death he has been celebrated as never before. His work is timeless. Hallelujah!