This might seem a strange admission from a classically trained singer, but most of my favourite singers have voices that are an acquired taste by most people’s standards.

In Leonard Cohen’s wonderful Tower of Song, there is a joke at the beginning of the third verse, as he whispers: I was born like this, I had no choice / I was born with the gift of a golden voice …” Cohen knows as well as we do that he does not have the kind of voice that is traditionally referred to by this epithet, nor has he become rich as a result of it.

And yet Cohen undoubtedly possesses one of the most unforgettable voices in the music business, and over the past four decades that voice has become indistinguishable from the words it has crafted and sung.

Other favourites of this blog – Dylan, Tom Waits, Randy Newman, Nick Cave – have similarly received reluctant praise for their singing at times, yet each of them is a great singer.

This has everything to do with the way in which they move the listener. They do this by evoking and creating complex emotional realities out there and inside us. When Waits sings, “Anywhere, anywhere I lay my head / I call my home”, he sounds more wasted than any human being should ever sound, but there is something triumphant in his voice, and this is borne out by the change of tone at the end of the song, when a New Orleans-style marching band suggests the exuberance of funeral processions.

Nick Drake is another, very different example of this quality: his ethereal voice floats above the faultless guitar playing that grounds it in a way that suggests that he is both earthbound and somehow not of this world.

Then there is Mary Gauthier’s I Drink, in which the protagonist sums up the state of the world in the chorus with a resigned shrug: “Fish swim, birds fly / Mamas yell, daddies cry / Old men sit and think / I drink.” Gauthier’s voice, smoky and no doubt altered by years of hard living, can cut through the stoniest heart. It manages to summon an irretrievable loss at the centre of the song which gives the lie to that shrug and yet somehow contains it.

There is a huge gap at the centre of our experience – a gap between what we are and what we might be, what we would like to be but cannot reach. In the voices and songs of great singers it feels, for a moment, as if we can touch all these possibilities in ourselves at the same time. The pleasure they give us is like vertigo, but we cannot help looking down.

Maybe that is why we forgive them when they sometimes sing between the notes.