So how many Hallelujah choruses have you sung along to this Christmas? An amateur Messiah at your local church, a choir of thousands at the cathedral, a karaoke version in the village hall, and then whichever of the dozens of Leonard Cohen "Hallelujah"s currently jostling one another in the pop charts have grabbed your fancy. Probably all of them, given the Hallelujah hysteria gripping the nation, though for my money there's no surpassing Cohen singing it himself. Only he knows what his song is about; only he has a voice bruised enough to express its bittersweet lacerations.

As for the quivering Alexandra Burke, for whom, on her night of nights, the sight of the bouncing Beyoncé was as a profound religious experience, the least said the better. "Hallelujah" has too much wit and deviant sex in it to be sung by anyone the dumb side of 45, least of all the belt-it-out-while-holding-back-the-tears sort of diva the sight of whom is a profound religious experience to the judges of The X Factor.

When Moses saw God's retreating back on Mount Sinai he was so overawed that his face turned bright red, a colour which thereafter never left it. Would that The X Factor judges had the decency to blush similarly for the rest of their lives.

I take that back about Leonard Cohen knowing what his song is about. By his own account he doesn't, having added and then subtracted a further 80 verses in an attempt to complete it. Not what you expect from this column, I know – show-business gossip and a second column about Leonard Cohen in a month. And reader, it gets worse; I could even tell you the name of the New York hotel in which he wrote the song and how long he paced the corridors penning those 80 verses.

But there you are: after a life of high-principled cultural austerity I have succumbed, like everyone else, to the craze for Cohen. I am hoping it is just an end of year thing that will be gone by Twelfth Night, along with the holly and the mistletoe. Otherwise... Well, otherwise expect to see me auditioning next year for The X Factor myself. They have not yet, I think, had anyone singing "Ah, Sweet Mystery of Life" the way it should be sung.

The story of its vexed, unsatisfactory creation only adds, of course – talking of mystery – to the fascination of "Hallelujah". We love lost chords and songs that never finish and words we cannot ever get to the bottom of. We are all exegetes and hermeneutists at heart. Hence the enduring appeal of religion. We are suckers for the numinous. Something atheists and rationalists never seem able to grasp: that not everybody wants to understand the world completely. Remember the sardine tin in Alan Bennett's sermon in Beyond the Fringe? All of us looking for the key. And when we find it there is still that "bit in the corner you can't get at". Best joke of the 20th century. But it didn't put vicars out of business. People still congregate in churches, synagogues and mosques in order to search together for that bit in the corner of the sardine tin of life, and together not find it.

Where Alan Bennett played with the absurdities of Old Testament allusion – "My brother Esau is an hairy man, but I am a smooth man" – Leonard Cohen sounds its lyricism. Maybe you have to be Jewish. It is, anyway, that strange conjunction of Old Testament voluptuousness and foreboding that explains to me the peculiarly haunting quality of "Hallelujah". Don't forget that Hallelujah is a Hebrew word meaning "Praise the Lord, ye people", an injunction to devotion which takes on a melancholy tinge over time as the Lord in question becomes increasingly silent and remote. The meaning of a song isn't the only meaning that can elude us. And it isn't only women who go away.

Loss, reader. Ah, the enduring love affair we have with loss! And don't deny it. We're all singing it. "Love is not a victory march / It's a cold and it's a broken Hallelujah." Hallelujahing first happens in the Book of Psalms. Cohen knows his Old Testament. Many of the psalms were written by King David, poet and musician as well as soldier, the same King David with whom Cohen's poem opens. "Now I've heard there was a secret chord / That David played and it pleased the Lord." The difference between the poet-king and the poet-poet being that the former's music goes down well with the Lord, whereas Cohen appears to be singing to someone who doesn't "really care for music, do ya?". Great ironic rhyme: Hallelujah /Do ya.

As for who she is, this woman with a tin ear, we can only guess. One of Cohen's fictional gypsy wives, no doubt, out betraying him in the moonlight, as beautiful as Bathsheba, wife of Uriah the Hittite, whom the ageing King David, walking the rooftops, espies in the bath (Bathsheba that is, not Uriah the Hittite), and as dangerous as Delilah, the demon hairdresser from the Valley of Sorek who bound and emasculated Samson.

The passage from the Book of Judges which prompts the lines "She tied you / To a kitchen chair / She broke your throne and she cut your hair" goes as follows – "And she made him sleep upon her knees; and she called for a man, and she caused him to shave off the seven locks of his head; and she began to afflict him, and his strength went from him." Hot or what? And she began to afflict him. Oof! Gimme that old-time religion. If it's sex you're after, there's no beating the Old Testament. Now can you see where Leonard Cohen got his taste for the eroticism of exhaustion and betrayal?

I am not, of course, arguing that every one of these references and echoes is present to us when we sing "Hallelujah", or that the persistence of ancient erotic Jewish melodies in the contemporary music of sexual frustration explains why girls and their mothers are queuing to buy the record in the HMV store in Tunbridge Wells. But who's to say what meanings come to us in music and song?

Our emotional vocabularies, like our memories, are complex and dynamic. Which is where those educationalists who think children should read novels only about their own environments, like the atheists who say we should believe only in that which can be proved, are mistaken. We do not live simply where we are domiciled. We are not moved merely by that which we fully understand. Mystery thrives. Hallelujah.