We weren't entirely unprepared. In August, as Cohen's former lover and one time muse Marianne Ihlen lay dying in Norway, he sent her a fond letter in which he wrote 'we are so old and our bodies are falling apart and I think I will follow you very soon.' Then, three weeks ago, Cohen appeared at an event at the Canadian consulate in Los Angeles, in which he commented 'I think I was exaggerating. I've always been into self-dramatization. I intend to live forever.'

With hindsight, this was Leonard Cohen showing his old-school good manners. He must have known he was ill, yet he preferred his fans and admirers to think he was fine, rather than let them fret about him. His courtesy was legendary: he gave the best interviews, responding to intelligent questions with thoughtful answers, and to superficial questions with laconic hilarity, although New Yorker editor David Remnick got a terrifying dressing-down from Cohen after inadvertently showing up late for an interview.

Cohen spent a lifetime wrestling with things: spirituality, sexuality, very expensive wine, but above all, language. Of all the singer-songwriters to have come of age in the 1960s he was the greatest wordsmith, having studied English at McGill under two of Canada's greatest poets, Irving Layton and Louis Dudek, and publishing three poetry collections and two novels before he decided to try being a musician. His first three albums define the early Cohen: raw, haunting and sparsely produced, they chart a progression from the suave melancholy of 1967's Songs of Leonard Cohen through the vulnerable Songs From A Room to 1971's bleak and disturbing Songs of Love and Hate, made while Cohen was about to enter a serious depression. But Cohen never flaunted his struggles; no matter how turbulent his music got, he was the still centre of it. This was, as he would have been the first person to admit, partly because of his own limitations as a singer. He told with great amusement of how, at the start of his music career, he was about to go onstage at a rock festival when he had an attack of nerves. He turned to his manager and said 'This is ridiculous. What am I doing? I can't sing.' His manager replied 'None of you guys can sing. When I want to hear singing I go to the opera.' The lesson, if there was one, is that the relative weakness of Cohen's voice was appealing, because it made him seem vulnerable. As he grew older and smoked more cigarettes, it sank lower and lower and became an ominous rumble, to the point that on his last tours he was forced to tune his guitar down from E to C, so that he could play the same songs in the positions he was used to.

Between 1967 and 2016 Cohen released only fourteen studio albums, but it wasn't for want of inspiration. He would work tirelessly at a song until he felt it was ready: his best-loved song 'Hallelujah' took years to write, and he liked to ruefully compare himself to his friend and rival Bob Dylan, who could and did write classic songs in the space of a taxi ride. Cohen carried himself with a grace and coolness that was maybe born of his own struggles with depression, or maybe he just had it in him all along: there is a story that during the troubled making of 1977's Death of a Ladies' Man, producer Phil Spector held a gun to the singer's neck and said 'Leonard, I love you,' whereupon Cohen slowly pushed the barrel away and replied 'I hope you do, Phil.'

His star slowly fell over the course of the 1980s. 1984's Various Positions, the album which features not only 'Hallelujah' but the equally enduring 'Dance Me To The End of Love', was actually rejected by Columbia for US release. But then in 1988, Cohen released I'm Your Man, and suddenly, Leonard Cohen was no longer just music to see you through a dark night. He had a new swagger, and the deadpan wit which had always lurked in his earlier stuff was on full display. In the mid-2000s it emerged that his manager had embezzled most of his money, so that he was forced to go on tour for the first time in 15 years, yet he was wonderfully unbowed by misfortune and became the hit of Glastonbury. Most famous elderly musicians keep touring because it's just what they do, but there was a poignant pleasure in going to see Cohen in the knowledge that he needed you too. His output increased, dramatically and gratifyingly. His final album, out last month, is one of his best.

Leonard Cohen was very proud of his Jewishness – his maternal grandfather was a prominent rabbi, and his paternal grandfather was the first president of the Canadian Jewish Congress – and his best songs come home to you like prayers, or at any rate like prayers are supposed to. However far they travelled into anguish and confusion, there's always a sense that he's got some sort of map or guidebook, even if he can't always decipher it. In these dark times, people will take from him what consolation or encouragement they can find, because he knew how it feels to lack hope; but for now, let's just be grateful for what he's left us. As he put it himself:

Now I bid you farewell, I don't know when I'll be back
They're moving us tomorrow to that tower down the track
But you'll be hearing from me baby, long after I'm gone
I'll be speaking to you sweetly
From a window in the Tower of Song.

Or, as he sang fourteen years earlier in 'Chelsea Hotel #2': we are ugly, but we have the music.